saqarTvelos teqnikuri universiteti

ლ.ფერაძე, მ.სორდია

maTematikuri sistema

M a t h c a d

damtkicebulia stu_s

saredaqcio-sagamomcemlo

sabWos mier

Tbilisi

2008

2

uak. 621 397

winamdebare saxelmZRvaneloSi pirvelad qarTulad sruli saxiT aRwerilia Mathcad maTematikuri sistema (Mathcad 11.0 versia), romlis meSveobiTac sruldeba

yvela saxis maTematikuri gamoTvlebi da miiReba amocanebis amoxsna rogorc

analizuri, aseve ricxviTi saxiT – saWiroebis SemTxvevaSi maTi grafikuli

warmodgeniT. wignSi ganxilulia Mathcad–is ZiriTadi cnebebi da gansazRvrebebi,

aRwerilia menius brZanebebi, instrumentTa panelebi, funqciebi da operatorebi,

daprogramebis SesaZleblobebi.

naSromi gankuTvnilia mkiTxvelTa farTo wrisaTvis: sxvadasxva specialobis

studentebisaTvis, doqtorantebisa da mecnier muSakebisaTvis. SesaZlebelia misi

rogorc TviTmaswavleblis gamoyeneba. avtorebi madlobas uxdian prof. T. kupataZes da asoc. prof. d. beriaSvils

Rirebuli rCevebisaTvis masalis momzadebis procesSi.

recenzentebi:

telekomunikaciis departamentis

sruli profesori, t.m.d. s. SavguliZe,

saqarTvelos maTematikosTa kavSiris prezidenti, f/m.m.d. j. SariqaZe.

3

s a r C e v i

თavi I sawyisi cnebebi 7

1.1 maTematikuri sistema Mathcad_is zogadi mimoxilva 7

1.2 Mathcad–is instalireba 9

1.3 Mathcad_is gaSveba 10

1.4 Mathcad–is dokumentis fanjris struqtura 10

1.5 ZiriTadi cnebebi da gansazRvrebebi 11

1.6 kursoris formebi 12

1.7 maTematikuri gamosaxulebebis Seqmna 13

1.8 monacemTa ZiriTadi tipebi 16

Tavi II menius punqti File (faili) 21

2.1 mTavari menius File punqtis Semadgenloba 21

2.2 Mathcad–is dokumentis Seqmna, Senaxva, gaxsna da daxurva 21

2.3 gverdebis parametrebis dayeneba, beWdviswina daTvalierebis 24

da beWdvis reJimebi

Tavi III dokumentis redaqtirebis meTodebi 27

3.1 redaqtirebis zogadi xerxebis mokle mimoxilva 27

3.2 maTematikuri gamosaxulebebis redaqtirebis magaliTebi 28

3.3 mTavari menius Edit (redaqtireba) punqtis Semadgenloba 32

3.4 redaqtirebis operaciis gauqmeba_aRdgena 33

3.5 dokumentis fragmentebTan muSaoba 33

3.6 teqstis an gamosaxulebis fragmentis Zebna da Secvla 35

3.7 dokumentis sasurvel gverdze gadasvla 36

Tavi IV menius punqti View (xedi) 37

4.1 mTavari menius View punqtis Semadgenloba 37

4.2 instrumentTa panelebi 37

4.3 saxazavi, mdgomareobis striqoni da areebi 38

4

4.4 masStabis Secvla da ganaxleba 38

4.5 gverdis kolontitulebis Seqmna da gaformeba 39

Tavi V menius punqti Insert (Casma) 41

5.1 mTavari menius Insert punqtis Semadgenloba 41

5.2 grafikis Casma 41

5.3 organzomilebiani X_Y grafikis ageba da redaqtireba 42

5.4 polaruli grafikis ageba da redaqtireba 46

5.5 3_ganzomilebiani zedapiris grafikis ageba da redaqtireba 48

5.6 konturuli grafikis Seqmna 52

5.7 wertilovani da svetovani grafikebis Seqmna 54

5.8 veqtoruli velis grafikis Seqmna 55

5.9 grafikebis Seqmna ostatis meSveobiT 55

5.10 matricis Casma dokumentSi 57

5.11 funqciebis Casma 58

5.12 sazomi erTeulis Casma 58

5.13 naxatis Casma 59

5.14 ubnis formireba da gverdis gawyveta 60

5.15 maTematikuri da teqsturi areebis Casma 60

5.16 komponentebis Casma 61

5.17 monacemebis Casma 63

5.18 mmarTveli komponentebis Casma 66

5.19 Mathcad_is dokumentSi sxva obieqtis Casma 67

5.20 miTiTebebis Casma 69

5.21 hipermimarTvis damyareba 70

Tavi VI simboluri operaciebi Mathcad_Si 72

6.1 Symbolics menius da Symbolic panelis Semadgenloba 72

6.2 maTematikuri gamosaxulebebis warmodgena analizuri saxiT 74

6.3 maTematikuri gamosaxulebebis gamartiveba (simplify) 76

6.4 maTematikuri gamosaxulebis gaSla (expand) 78

6.5 maTematikuri gamosaxulebebis da ricxvebis martiv mamravlebad 79

daSla (factor) 6.6 maTematikuri gamosaxulebis mwkrivad gaSla msgavsi 80

wevrebis SeerTebiT (collect) 6.7 polinomis koeficientebis gansazRvra miTiTebuli 81

cvladis mimarT (coeffs) 6.8 gantolebebis da utolobebis amoxsna miTiTebuli 82

cvladis mimarT (solve)

5

6.9 gamosaxulebis Casma miTiTebuli cvladis magivrad (substitute) 83 6.10 maTematikuri gamosaxulebebis diferencireba da integreba 85

6.11 maTematikuri gamosaxulebebis teiloris mwkrivad gaSla (series) 86

6.12 maTematikuri gamosaxulebebis warmodgena elementaruli 88

wiladebis jamis saxiT (parfrac) 6.13 matricebis transponireba, Sebruneba da determinantis gansazRvra 89

6.14 maTematikuri gamosaxulebebis gardaqmnebi 91

6.15 simboluri gamoTvlebis Sedegebis gamotanis stilis dayeneba 93

6.16 cvladebis mniSvnelobebis SezRudva da instrumentTa 93

paneli Modifier (modificikacia) 6.17 simboluri gamoTvlebis Sedegebis warmodgena kompleqsuri ricxvis 95

saxiT da mcocavi wertiliT (complex, float)

Tavi VII daformateba Mathcad_Si 97

7.1 Format menius da Formatting panelis Semadgenloba 97

7.2 maTematikuri gamosaxulebebis daformateba 98

7.3 ricxviTi Sedegebis daformateba 100

7.4 teqstisa da abzacis daformateba 104

7.5 tabulaciis poziciebis dayeneba 106

7.6 stilis daformateba 106

7.7 obieqtis Tvisebebis dayeneba 108

7.8 grafikebis daformateba 110

7.9 ferebis dayeneba 112

7.10 ubnebis daformateba 113

7.11 areebis gancalkeveba da sworeba. gverdebis xelmeore numeracia 114

Tavi VIII mTavari menius Tools (instrumentebi) punqti 115

8.1 mTavari menius Tools punqtis Semadgenloba 115

8.2 marTlweris Semowmeba da koreqtireba 115

8.3 animaciuri klipebis Seqmna da aRwarmoeba 116

8.4 samuSao furclis dacva 119

8.5 gamoTvlebis reJimebi 120

8.6 calkeuli maTematikuri aris gaangariSebis procesidan gamoricxva 121

8.7 gamoTvlebis optimizacia 121

8.8 Secdomis wyaros gamovlineba 122

8.9 samuSao furclis ofciebi 124

8.10 parametrebis momarTva 125

6

Tavi IX mTavari menius Window (fanjara) punqti 127

9.1 mTavari menius Window punqtis Semadgenloba 127

9.2 fanjrebis kaskaduri ganlageba (Cascade) 127 9.3 fanjrebis horizontaluri da vertikaluri ganlageba 128

(Tile Horizontal, Tile Vertical) 9.4 dokumentebis fanjrebis marTva 129

Tavi X sainformacio resursebi. mTavari menius Help punqti 131

10.1 mTavari menius Help (daxmareba) punqtis Semadgenloba 131

10.2 Mathcad_is sacnobaro sistema 131

10.3 sainformacio resursebis gamoyeneba (Resource Center) 133 10.4 daxmarebis sxva saSualebebi 136

Tavi XI funqciebi Mathcad_Si 137

11.1 momxmareblis mier funqciebis Seqmna 137

11.2 CaSenebuli funqciebis mimoxilva 137

11.3 momxmareblis mier operatoris Seqmna 147

Tavi XII daprogrameba Mathcad_Si 149

12.1 Programming instrumentTa panelis operatorebis aRwera 149

12.2 miniWebisa da striqonis Casmis operatorebi 150

12.3 pirobiTi gadasvlis iperatori 151

12.4 ciklis operatorebi 153

12.5 Break, Continue da Return operatorebi 155

12.6 operatori on error 155

gamoyenebuli literatura 157

7

თavi I sawyisi cnebebi

1.1 maTematikuri sistema Mathcad_is zogadi mimoxilva

maTematikuri gamoTvlebis avtomatizirebis aucileblobam ganapiroba

kompiuteris Seqmna. eleqtronul milakebze agebulma pirveli Taobis

kompiuterebma farTo gamoyeneba ver hpova sxvadasxva mizezebis gamo.

mikroeleqtronikis ganviTarebasTan erTad gamoCnda specializirebuli,

maTematikuri gamoTvlebisTvis gankuTvnili miniaturuli kompiuteri –

programirebuli kalkulatori, romelic amJamadac gamoiyeneba. bolo wlebSi

masiuri gavrceleba hpova ufro mZlavrma, swrafma da universalurma

personalurma kompiuterma, romelsac gaaCnia grafikebis agebis, logikuri da

analizuri gamoTvlebis SesaZleblobanic.

Tavdapirvelad kompiuterze maTematikuri gamoTvlebis SesrulebisaTvis

aucilebeli iyo romelime daprogramebis enis, rogoricaa: fortrani, beisiki,

paskali da sxva, Seswavla. es aucilebloba Tavidan acilebuli iqna bolo dros

farTo masebSi gavrcelebul iseT maTematikur sistemebSi rogoricaa: Mathcad, Mercury, Matlab, Mathematica, Maple da sxv. maTematikuri sistema Mathcad–i warmoadgens amerikuli firmis MathSoft–is produqcias. igi muSaobs grafikuli garsis mqone operaciuli sistema Windows–is marTvis qveS, rac ganapirobebs am ukanasknelis tipiuri da farTo

SesaZleblobebis Mathcad–Si gamoyenebas: dokumentis redaqtireba, yvela tipis

printeris, yvelaze metad gavrcelebuli simboloebis gamoyenebis SesaZlebloba,

Sriftebis mravalferovneba, mausis moxerxebuli manipulireba, amomwuravi

eleqtronuli cnobari, OLE meqanizmis gamoyeneba da sxv. Mathcad–s, teqsturi redaqtoris msgavsad, gaaCnia WYSIWYG (What you see is what

you get – rasac xedav, imas iReb) interfeisi, rac iTvaliswinebs dokumentis

dabeWdvas imave saxiT, rogori saxec mas displeis ekranze aqvs. Mathcad–Si SesaZlebelia rogorc urTulesi maTematikuri gamoTvlebis, aseve martivi

simboluri gardaqmnebis Catareba. mas gaaCnia maTematikur simboloebze

orientirebuli interfeisi da grafikebis agebis saSualebani, aseTive saxe aqvs

gamoTvlebis Sedegebsac, rac sruliad amarTlebs misi saxelis abreviaturas

(cad _ Computer Aided Design – kompiuteris meSveobiT proeqtireba).

iseve, rogorc eleqtronul cxril Excel–Si, Mathcad–is dokumentSic

cvlilebebis Setana moaxdens arsebuli dokumentis formulebis Sesabamis

gadaangariSebas, aseve avtomaturad cvlilebebs ganicdis agebuli grafikebic.

eleqtronul wignSi Tavmoyrilia gamoyenebiTi formulebi da grafikebi, romlis

kopireba da Casma momxmareblis dokumentSi martivad sruldeba. aseve

8

SesaZlebelia gamoviyenoT ukve gamzadebuli, konkretuli amoxsnili magaliTebi,

romlebic moTavsebulia e.w. standartul biblioTekebSi (Quick Sheets). Mathcad–Si dokumentis Seqmnis procesSi daSvebuli Secdomebis aRmofxvra

advilad xdeba, radgan masSi sruldeba sintaqsuri da semantikuri Semowmeba.

daSvebuli Secdomebi gamoiyofa wiTeli simboloebiT. masze amomwurav pasuxs

gvaZlevs eleqtronuli cnobari, romlis gamoZaxebac xdeba klaviaturidan F1 Rilakis gamoyenebiT.

Mathcad–Si formulis Cawera advilad xorcieldeba grafikuli

maTematikuri simboloebiT. formulebi Caiwereba analizuri saxiT da ar

moiTxoveba sayovelTaod miRebul maTematikur simboloebTan (mag.,, ! , , )

dakavSirebuli gamoTvlebis proceduris dawvrilebiTi aRwera. aseTi midgoma

aadvilebs maTematikur moqmedebaTa arsis aRqmas da momxmarebels acilebs

daprogramebis enis (mag: fortrani, beisiki, paskali da a.S.) gamoyenebis

aucileblobas.

ra Tqma unda, es ar niSnavs imas, rom sistemas ar gaaCnia misi daprogramebis

ena. sinamdvileSi igi arsebobs – algoriTmuli, maRali donis daprogramebis ena,

romelic maTematikur simboloebze orientirebulia da gvexmareba sistemasTan

dialogis damyarebaSi. am daprogramebis enis meSveobiT SesaZlebelia dasmuli

amocanis amoxsna da Sedegis miReba sasurveli formiT.

imis mixedviT Tu romel obieqts (teqsti, formula an grafiki) qmnis

momxmarebeli Mathcad–Si, sistema Tavad aformirebs programas daprogramebis enis

meSveobiT, romelic inaxeba operatiul mexsierebaSi manam, sanam ar iqneba

Senaxuli diskze failis saxiT, romlis tipia .mcd. momxmareblisaTvis Mathcad–is gamosayeneblad sakmarisia masSi obieqtze orientireba. yvela operators gaaCnia

maTematikuri simboloebis saxe, romlis arCevac advilad SesaZlebelia mausis

meSveobiT, xolo maTematikuri funqciebi (mag: sin, cos da a.S.) SegviZlia

klaviaturidan avkriboT ise, rogorc gviweria, an avirCioT instrumentTa

panelidan, specialuri siidan, rac funqciis Seyvanisas SecdomaTa albaTobas

amcirebs.

Mathcad 11.0 Pro versiaSi wina versiebidan gansxvavebiT damatebulia axali

SesaZleblobani rogoricaa: dokumentis feradi gaformeba, animaciuri (moZravi)

grafikebis ageba da xmovani gaformeba, teqsturi, formulebis da grafikuli

redaqtorebis gaerTianeba. aseve SesaZloa sxva simbolur maTematikur mZlavr

sistemebTan gaerTianeba urTulesi gamoTvlebisaTvis. aqedan gamomdinareobs aseTi

sistemebis saxelic _ integrirebuli sistemebi.

bolo dros mniSvnelovan interess iwvevs kompiuteruli algebris

sistemebis unari Seasrulos ara mxolod cifruli, aramed analoguri

gamoTvlebic.

IBM PC–Tvis SemuSavda simboluri maTematikuri (kompiuteruli algebra)

sistemebi, iseTebi rogoricaa: Mathcad, Matlab, Derive [10], Maple V da Mathematica2 da 3. maTi gamoyeneba aadvilebs yvelaze rTul maTematikur, statistikur da

9

finansur–ekonomikur gamoTvlebs, romlis CatarebisaTvis manamde saWiro iyo

maRali donis maTematikos_analitikosebis Careva.

aRsaniSnavia, rom liderebad kompiuteruli algebris sistemebSi iTvlebian

kompania Waterloo Maple Software–is produqcia Maple V da firma Wolfram–is

Mathematica3. am sistemebs gaaCniaT simboluri maTematikis amomwuravi

SesaZleblobani, rac mosaxerxebelia maTematikosebisaTvis, magram ara farTo

masebisaTvis. am ukanasknelTaTvis ufro moxerxebul maTematikur sistemad rCeba

Mathcad–i, romelSic SesaZlebelia rTuli maTematikuri ricxviTi gamoTvlebis da

agreTve simboluri operaciebis Catareba. amisaTvis firma Maple–is licenziiT

Mathcad–Si gamoyenebulia ramodenime ZiriTadi simboluri operacia Maple–dan. maTi

raodenoba SezRudulia im minimumamde, romelic saWiroa masiuri

momxmareblisaTvis. amis dasadastureblad sakmarisia moviyvanoT statistikuri

Sedareba. Maple VR4 Seicavs 2800 (!) funqcias, rodesac Mathcad-11.0 Pro–Si maTi

ricxvi 300 umniSvnelod aRemateba da aqedan simboluri maTematikis funqciebi

sul raRac or aTeuls utoldeba.

amrigad, Mathcad–is ZiriTadi ganmasxvavebeli Tvisebebia:

Mathcad–i maTematikuri amocanebis amoxsnis universaluri sistemaa, farTo

momxmarebelze orientirebuli;

maTematikuri amocanebis Cawera Mathcad–Si sxva sistemebTan SedarebiT

miaxloebulia Cveulebriv Caweras, rac aadvilebs mis gamoyenebas;

Mathcad–i ramdenjerme iafia Tavis analogebTan SedarebiT.

1.2 Mathcad–is instalireba

Mathcad 11.0–is instalirebisaTvis aucilebelia garkveuli aparaturuli da

programuli uzrunvelyofa.

aparaturul uzrunvelyofaSi vgulisxmobT IBM firmis personalur

kompiuters.

kompaqt_diskze (CD_ROM) arsebuli maTematikuri sistema MathCAD–is

pirdapiri kopireba vinCesterze yovlad dauSvebelia. misi instalirebisaTvis

aucilibelia:

1. movaTavsoT diski kompakt–diskis diskur mowyobilobaSi;

2. avirCioT ZiriTadi menius punqti Start Run... ; 3. mivuTiToT kompakt–diskis saxeli (mag. D:\setup.exe).

instalirebis procesi umtkivneulod mimdinareobs, magram Tu warmoiqmneba

raime problema, SegviZlia misi gadaWra, Tu gavecnobiT detalur instruqcias

instalirebis Sesaxeb readme failSi.

10

1.3 Mathcad–is gaSveba

Mathcad–is CatvirTva SesaZlebelia yvela im wesiT, romelic miRebulia

operaciuli sistemaMAWindows –is garemoSi: samuSao magidaze Mathcad–is niSnakze Tagvis marcxena RilakiT orjeradi

dawkapunebiT;

sastarto menius Start → Programs → MathSoft Apps → Mathcad brZanebiT;

Sesabamisi katalogis sarCevSi Mathcad.exe failze orjeradi dawkapunebiT;

Start → Search dialogur fanjaraSi .mcd gafarToebis mqone failebis

moZebniT da ormagi wkapuniT erT-erT aseT failze (am dros programa

avtomaturad CaitvirTeba Sesabamisi dokumentis fanjarasTan erTad);

saqaRaldis sarCevSi Mathcad–is dokumentze orjer dawkapunebiT (am dros

programa avtomaturad gaiSveba da gaixsneba Sesabamisi dokumentis fanjara);

Start → Run… brZanebis dialogSi Mathcad.exe failze mimarTvis gzis

miTiTebiT an Mathcad–is dokumentis failis saxelis miTiTebiT;

Tu Mathcad–is piqtograma gadatanilia swrafi gaSvebis (Quick Launch) panelze, am piqtogramaze dawkapunebiT.

1.4 Mathcad–is dokumentis fanjris struqtura

Mathcad–is gaSvebis Semdeg ekranze gaixsneba misi fanjara (nax.1.1).

nax.1.1. Mathcad–is fanjara

11

Mathcad–is fanjris stრuqturaa: Mathcad–is fanjris pirveli striqonia saTauris striqoni – marcxniv

miTiTebulia dokumentis saTauri, xolo marjvniv ganlagebulia sami

Rilaki: dakecvis, mTel ekranze gaSlisa (Tu fanjara gaSlilia, am adgilas

gvaqvs aRdgenis Rilaki, romelic aRadgens fanjris zomas, romelic mas

hqonda mTel ekranze gaSlamde) da daxurvis.

meore striqonia menius striqoni, sadac Tavmoyrilia menius punqtebi:

File (faili) – failebTan muSaoba;

Edit (redaqtireba) – dokumentis redaqtireba; View (xedi) – fanjris struqturis dayeneba;

Insert (Casma) – obieqtebis Casma; Format (formati) – obieqtebis daformateba; Tools (instrumentebi) – programis zogi parametris da reJimis dayeneba; Symbolics (simbolika) – simboluri operaciebi;

Windows (fanjrebi) – sistemis fanjrebs Soris marTva;

Help (daxmareba) – damxmare eleqtronuli cnobari.

menius striqonis Semdeg gvaqvs instrumentTa panelebis striqonebi.

mizanSewonilia ekranze Candes Standard, Formatting, Math panelebi, romelTa

moxsna_dayeneba menius View → Toolbars brZanebis CamonaTvalidan xdeba.

danarCeni panelebi rogorebicaa Boolean, Symbolics, Calculus da sxv. SegviZlia

ganvalagoT samuSao areSi moTxovnilebis Sesabamisad View → Toolbars brZanebis CamonaTvalidan an Math panelze Sesabamis Rilakze dawkapunebiT.

fanjris ZiriTadi nawili ukavia samuSao ares (WorkSheet), sadac xdeba

maTematikuri amocanebis amoxsna.

fanjris qveda nawili ukavia mdgomareobis striqons (Status Bar), romlis

moxsna_dayeneba xdeba menius View → Status Bar brZanebiT.

fanjris standartuli saxe iTvaliswinebs agreTve vertikaluri da

horizontaluri gadafurcvlis zolebs – dokumentis im ubnebis

dasaTvaliereblad, romlebic ekranze ar Cans.

1.5 ZiriTadi cnebebi da gansazRvrebebi

Mathcad_is dokumenti Sedgeba sxvadasxva tipis (formulebi, teqstebi,

grafikebi, cxrilebi da a.S.) calkeuli blokebisagan. TiToeul bloks uWiravs

marTkuTxedis formis garkveuli are.

blokebis ganlagebas dokumentSi (teqsturi blokis garda) principialuri

mniSvneloba aqvs. isini sruldeba marcxnidan marjvniv da zemodan qveviT, amitom

blokebma ar unda gadafaron erTmaneTi, Tumca umniSvnelo gadafarvas

mniSvneloba ara aqvs.

12

blokebis konstruirebisaTvis Mathcad–Si CaSenebulia sami redaqtori:

teqsturi, formuluri da grafikuli (Sesabamisad teqsturi komentarebis,

maTematikuri gamosaxulebebis da grafikebis Seqmnis saSualebebi).

maTematikuri are – es aris are maTematikuri gamosaxulebiT an grafikiT.

masSi Setanili nebismieri cvlileba aisaxeba mis qvemoT da marjvniv ganlagebul

yvela danarCen maTematikur areSi.

teqsturi are – es aris marTkuTxedis formis teqstis gansaTavseblad

gankuTvnili are. teqstur ares xmaroben komentarebisaTvis. teqsturi aris

Sesaqmnelad arsebobs ramdenime xerxi:

menius striqonidan Insert → Text Region brZanebiT; klaviaturidan “ simbolos gamoyenebiT;

sityvis an Tundac erTi simbolos Setanis Semdeg klaviaturidan “hari”

klaviSis akrebiT.

zemoTCamoTvlili SesaZlo variantebis gamoyenebisas gamoCndeba

marTkuTxedi, sadac standartuli wesiT Seitaneba teqsti, amasTan SesaZloa

sasurveli Sriftis, misi zomisa da maxasiaTeblebis dayeneba. teqstur areSi Enter klaviSze dawkapunebiT gadavalT axali abzacis pirvel striqonze, xolo Enter + Shift–iT mimdinare abzacis Semdeg striqonze. teqsturi aris marTkuTxeds aqvs

markerebi, romelTa meSveobiT SeiZleba teqsturi aris gadideba–dapataraveba.

1.6 kursoris formebi

kursorma SeiZleba miiRos Semdegi formebi:

+ jvaredini wiTeli feris kursori _ viziri _ miuTiTebs samuSao areSi

pozicias, sadac SeiZleba formulis, teqstisa da grafikis blokebis ageba;

misi gadaadgileba SesaZlebelia klaviaturidan kursoris gadaadgilebis

klaviSebis gamoyenebiT an mausiT – sasurvel poziciaze dawkapunebiT;

kursoris wiTeli vertikaluri xazi miuTiTebs teqstur blokebSi

simboloTa Casmis an waSlis adgils;

kursoris lurji kuTxis forma miuTiTebs maTematikur blokSi morigi

simbolos Casmis pozicias da agreTve gamoyofil calkeul nawils an mTli-

an gamoyofil ares. misi saxe damokidebulia simboloebis Setanis

mimarTulebaze. klaviaturidan am mimarTulebis Secvla SesaZlebelia Insert Rilakis gamoyenebiT. maTematikur areSi saxelis an ricxvis redaqtirebisas

kursori Seicvleba da miiRebs Semdeg formas: .

13

1.7 maTematikuri gamosaxulebebis Seqmna

maTematikuri gamosaxulebebis Sesaqmnelad ZiriTadad viyenebT Math

instrumentTa panelze arsebul maTematikur palitras. misi yoveli RilakiT Tavis

mxriv gamoiZaxeba maTematikur simboloTa da moqmedebaTa esa Tu is paneli. Math instrumentTa panelis Rilakebia:

– Calculator panelis gamoZaxeba. am panelze ganlagebulia ariTmetikuli

operaciebis niSnebi da xSirad gamoyenebadi funqciebi;

– Graph panelis gamoZaxeba, romelzec moTavsebulia or an samganzomi-

lebiani grafikebis Sablonebi;

– Matrix panelis gamoZaxeba, romelzec moTavsebulia matricebis da

veqtorebis operatorebi;

– Evaluation panelis gamoZaxeba. am panelze ganlagebulia miniWebis,

tolobis, simboluri gardaqmnebis da momxmareblis mier operatoris

ganmsazRvreli niSnebi;

– Calculus (maTanalizis) panelis gamoZaxeba, romelSic ganlagebulia

diferencialebis, integralebis, zRvrebis, jamis da namravlis Sablonebi;

– Boolean panelis gamoZaxeba, romelSic ganlagebulia Sedarebis niSnebi da

logikuri algebris operatorebi;

– Programming panelis gamoZaxeba. am panelze ganlagebulia operatorebi,

romlebic gvaZleven daprogramebis saSualebas;

– Greek panelis gamoZaxeba, romelzec ganlagebulia berZnuli anbanis

asoebi;

– Symbolic panelis gamoZaxeba. am panelze ganlagebulia simboluri

gamoTvlebis operatorebi.

vTqvaT, gvinda gamovTvaloT Semdegi gamosaxulebis mniSvneloba:

2

32 2

1

xyx.

amisaTvis:

1) Calculator panelze avirCioT (Tagvis marcxena Rilakze dawkapunebiT)

niSnuli n (an davaWiroT Ctrl + \ ). gamoCndeba fesvis Setanis

Sabloni. Savi marTkuTxedebiT naCvenebia, Tu sad unda aucileblad

moTavsdes garkveuli maTematikuri informacia;

14

3 1

x2 2x y

2) klaviaturis klaviSis meSveobiT an Shift + Tab–is daWeriT

gadavalT poziciaSi, sadac iwereba fesvis xarisxi (gamosaxulebis

nebismier adgilze kursoris dayeneba xdeba agreTve am adgilze

TagviT dawkapunebiT);

3) SevitanoT klaviaturidan an Calculator panelidan cifri 3. ekranze

gveqneba 3

;

4) klaviSis meSveobiT an Tab–is daWeriT gadavalT poziciaSi,

sadac unda SevitanoT fesvisqveSa gamosaxuleba;

5) Calculator panelze avirCioT ( ), ekranze gamoCndeba 3 ( ) ;

6) imave panelze avirCioT /, gveqneba

3

;

7) mricxvelSi avkriboT 1;

8) Tab klaviSis gamoyenebiT aRmovCndebiT mniSvnelSi;

9) Calculator panelidan gamoviZaxoT kvadratuli fesvis Sabloni (an

davaWiroT klaviaturaze \ ), gveqneba ;

10) Calculator panelze avirCioT 2x . gamoCndeba kvadratSi ayvanis Sabloni

3 1

2

. markeris adgilas SevitanoT x ;

11) klaviSis gamoyeneba dagvayenebs sasurvel poziciaSi, sadac

gavagrZeloT mniSvnelis Setana – klaviaturidan Tanmimdevrulad

avkriboT simboloebi +2x*y (2–isa da x–is Soris gamravlebis niSnis

Setana ar aris aucilebeli; sistema TviTon mixvdeba, rom 2

warmoadgens koeficients). miviRebT ;

12) mimarTulebis klaviSis orjer gamoyenebis Semdeg avkriboT

klaviaturaze ^2 .

gamosaxulebis Seqmnis procesi damTavrebulia. maTematikuri aridan

gamosasvlelad davawkapunoT aris gareT an davaWiroT Enter klaviSs.

gamosaxulebis gamosaTvlelad movniSnoT is anu lurji kuTxis kursoriT

movicvaT is mTlianad da SevitanoT tolobis niSani (klaviaturidan, Evaluation an Calculator panelebidan). Tu x–isa da y–is mniSvnelobebi winaswar ar iyo

gansazRvruli, ekranze wavikiTxavT informacias amis Sesaxeb da Sesabamisi

cvladi iqneba gaferadebuli wiTlad. Tu Setanili formulis zeviT an marcxniv

3 1

15

x–s da y–s mivaniWebT mniSvnelobebs, Cvens mier Seqmnil maTematikur gamosaxulebas

miewereba Mathcad–is mier gamoTvlili pasuxi.

aRvniSnoT, rom maTematikuri gamosaxulebis Seqmnisas da

klaviSebis meSveobiT xdeba gadaadgileba erTi poziciiT marjvniv an marcxniv,

xolo Tab–isa da Shift + Tab klaviSebiT Sablonis erTi marTkuTxedidan meoreze –

Sesabamisad win da ukan. gamosaxulebis nebismier adgilze kursoris dayeneba

SesaZlebelia agreTve am adgilze Tagvis dawkapunebiT.

axarisxebis, fesvis amoRebis da gayofis operatorebs aqvT Semdegi Tviseba:

yvelaferi, rac Seitaneba am operatorebis Semdeg, aRiqveba Sesabamisad xarisxis

maCveneblad, fesqveSa gamosaxulebad da mniSvnelad. imisaTvis, rom es SevwyvitoT,

davaWiroT an Space (hari) an klaviSs.

nax.1.2–ze moyvanilia sxvadasxva maTematikuri gamosaxulebebi.

nax.1.2. maTematikuri gamosaxulebebis magaliTebi

miniWebis operatoris niSania : = , xolo = niSani gamoiyeneba maTematikuri

gamosaxulebis ricxviTi mniSvnelobis gamosatanad. Evaluation (an Symbolic) panelis

→ (simboluri tolobis niSani) punqtiT miviRebT gamosaxulebis mniSvnelobas

analizuri saxiT.

16

miniWebis operaciebis pirveladi Setanis dros SesaZlebelia gamoviyenoT =

niSani. sistema TviTon gardaqmnis mas miniWebis niSnad (: =), magram Tu SemdgomSi

viyenebT igive cvlads gansxvavebuli mniSvnelobiT, aucilebelia miniWebis niSnis

gamoyeneba rogorc klaviaturidan : simbolos akrebis meSveobiT, aseve Calculator an Evaluation panelebis : = punqtze dawkapunebiT.

1.8 monacemTa ZiriTadi tipebi

Mathcad–Si monacemTa ZiriTadi tipebi aris mudmivebi (konstantebi),

cvladebi, masivebi da failebi.

konstanta es aris saxelis mqone obieqti, romlis mniSvneloba ar icvleba.

konstantebi SeiZleba iyos sxvadasxva tipis.

ricxviTi konstantebis magaliTebia: –682, 86.4, 5.281x10+2. ricxviTi

konstantebis modulebis mniSvnelobebis diapazoni MathcadD–Si aris 10307–dan 10-307–mde (manqanuri usasruloba da manqanuri nuli).

Mathcad_is konstantebi SeiZleba iyos agreTve mocemuli orobiT, rvaobiT

da teqvsmetobiT sistemebSi. orobiTi ricxvebis bolos miewereba laTinuri aso b (binary niSnavs orobiTs), rvaobiTi ricxvebis bolos – laTinuri aso O (Octal niSnavs rvaobiTs), xolo TeqvsmetobiTi ricxvebis bolos – aso h an HH (hexagonal niSnavs TeqvsmetobiTs). mag., 11110001b warmoadgens aTobiTi sistemis 241. orobiTi,

rvaobiTi da TeqvsmetobiTi sistemiT warmodgenili ricxvi unda iyos 231_ze

naklebi.

Mathcad–s SeuZlia muSaoba rogorc namdvil, ise kompleqsur ricxvebTan.

kompleqsuri ricxviTi konstantebis magaliTebia: 2+i x 3 an 3–j x 10 , sadac i da j simboloebiT aRniSnulia warmosaxviTi erTiani. kompleqsur ricxvebTan muSaobis

win rekomendirebulia mivaniWoT i–s an j–s 1 mniSvneloba an SevamowmoT, am ori

simboloTagan romels xmarobs sistema warmosaxviTi erTianis aRsaniSnavad.

Mathcad–i muSaobs agreTve iseT konstantebTan, romlebsac ricxviTi

mniSvnelobebis garda gaaCniaT miTiTeba fizikur sidideze (droze, sigrZeze,

masaze, muxtze da a.S.). amisTana konstantebis Cawerisas iyeneben gamravlebis

niSans ricxviTi mniSvnelobis da sididis aRmniSvnel simboloebs Soris.

ricxviTi konstantebis garda, Mathcad–i agreTve muSaobs striqonuli tipis

monacemebTan, romlebic warmoadgenen striqons brWyalebSi, mag., "Insert Matrix", "The rezult is valid". striqonuli tipis konstanta SeiZleba Sedgebodes erTi an

ramdenime simbolosagan an sityvisagan.

arsebobs agreTve sistemuri konstantebi (, e, ∞), romelTa mniSvnelobebi

winaswar gansazRvrulia.

cvladi – es aris saxelis mqone obieqti, romelsac gaaCnia mniSvneloba da

es mniSvneloba SeiZleba Seicvalos programis Sesrulebis msvlelobisas.

17

cvladis tipi ganisazRvreba misi mniSvnelobiT. igi SeiZleba iyos ricxviTi

tipis, striqonuli da a.S.

identifikatori warmoadgens mudmivis, cvladis an sxva obieqtis saxels.

identifikatoris sigrZe praqtikulad ar aris SezRuduli. is warmoadgens

laTinuri an berZnuli asoebis, cifrebis da zogi specialuri simbolos

mimdevrobas, romelic asoTi iwyeba. mag: a, x1, alfa,YY_coordinate. identifikatoris

CanawerSi dauSvebelia haris gamoyeneba. zogi specialuri simbolo, (mag.,@_ ) daSvebulia identifikatorebSi, zogi (mag., ariTmetikuli moqmedebis niSnebi)

akrZalulia. sistema ganasxvavebs nusxur asoebs da asomTavrulebs. aRvniSnoT

agreTve, rom identifikatori unda iyos unikaluri anu ar SeiZleba, magaliTad,

identifikatorad vixmaroT sin, radgan es aris CaSenebuli funqciis saxeli.

Mathcad–Si agreTve gvaqvs e.w. sistemuri cvladebi, romelTa mniSvnelobebs

gansazRvravs sistema. mag., Tol cvladis mniSvneloba (es cvladi gansazRvravs

ricxviTi meTodebis cdomilebas) winaswari SeTanxmebiT udris 0.001 . saWiroebis

SemTxvevaSi sistemuri cvladis mniSvneloba SeiZleba SevcvaloT da mivaniWoT mas

sxva mniSvneloba.

rogorc ukve vTqviT, cvladisaTvis mniSvnelobis misaniWeblad iyeneben

niSans : = . : = niSniT gansazRvrul miniWebas hqvia lokaluri miniWeba. pirvel

miniWebamde cvladi ar aris gansazRvruli da sistema, cxadia, ver Seasrulebs

gamoTvlebs am cvladis monawileobiT. miniWebisaTvis iyeneben aseve niSans. am miniWebas hqvia globaluri miniWeba. is SeiZleba Caiweros dokumentis nebismier

adgilas. magaliTad, Tu Cven CavwereT globaluri miniWeba dokumentis bolos,

Sesabamisi cvladis mniSvneloba iqneba igive dokumentis dasawyisSic. ra Tqma

unda, globaluri miniWebis Semdeg dasaSvebia cvladis mniSvnelobis Secvla

lokaluri miniWebiT.

Mathcad–i orjer kiTxulobs dokuments, orivejer marcxnidan marjvniv da

zevidan qveviT. pirveli wakiTxvis dros sruldeba globaluri miniWebis

operatoriT nakarnaxevi yvela SesaZlo moqmedeba. meore wakiTxvisas Sesruldeba

lokaluri miniWebis operatorTan dakavSirebuli moqmedebebi.

Mathcad–s aqvs bevri CaSenebuli funqcia. Ffunqciis saxelis Semdeg

frCxilebSi Caiwereba argumentebis sia. Mathcad–Si SesaZlebelia momxmareblis

funqciebis Seqmna.

maTematikuri gamosaxulebis calkeuli elementebi erTmaneTTan

operatorebiT dakavSirebulia. operatorebis saxeobebia: ariTmetikuli

operatorebi ( + , – , / , ! , n , da sxv.), logikuri operatorebi ( < , > , ≤ , ≥

, = da sxv.), maTanalizis operatorebi ( , b

a

, X ,

n

miX ,

n

miX da sxv.),

gamoTvlebis operatorebi ( = , : = , da sxv. ), daprogramebis operatorebi ( if, otherwise, for, while, break, continue, return ), veqtorebis da matricebis operatorebi,

simboluri gamoTvlebis operatorebi. Mathcad–Si momxmarebels SeuZlia Seqmnas axali operatorebic.

18

diskretuli (ranJirebuli) cvladi es aris cvladi, romelsac gaaCnia

ramdenime fiqsirebuli mniSvneloba. diskretuli cvladis mniSvnelobebi icvleba

fiqsirebuli bijiT sawyisi mniSvnelobidan bolo mniSvnelobamde. nax.1.3–ze

moyvanilia diskretuli cvladebis magaliTebi. ranJirebuli cvladis Sesatanad

virCevT Matrix panelze m..n Sablons an viyenebT klaviaturis ; niSans.

masivi aris ricxviTi an simboluri elementebis sasruli simravlis

mowesrigebuli erToblioba. Mathcad–Si xmaroben erTganzomilebian masivebs

(veqtorebs) da organzomilebian masivebs (matricebs). veqtorisa an matricis

elementebis indeqsebi axasiaTeben elementis adgilmdebareobas. qveda indeqsi

SeiZleba iyos 0–is an 1–is toli. misi mniSvneloba mocemulia sistemuri cvladiT

ORIGIN da winaswari SeTanxmebiT udris 0–s. Tu gvsurs, SeiZleba SevcvaloT

ORIGIN cvladis mniSvneloba da gavxadoT is 1–is toli.

veqtori da diskretuli cvladi arsebiTad ar gansxvavdeba erTimeorisagan.

nax.1.3. diskretuli (ranJirebuli) cvladebis magaliTebi

veqtorebis da matricebis Sesatanad Mathcad–Si gaTvaliswinebulia

ramdenime xerxi:

Insert → Matrix... brZanebiT;

swrafmoqmedebis klaviSebiT Ctrl + M;

19

Matrix panelze matricis Sablonze dawkapunebiT. yvela aRniSnul SemTxvevaSi gamoCndeba dialoguri fanjara Insert Matrix

(matricis Casma), sadac unda mivuTiToT matricis striqonebisa (Rows) da svetebis (Columns) raodenoba. veqtorebis SemTxvevaSi erT-erTi am parametrebisgan 1–is

tolia. Tu svetebis raodenoba udris 1, saqme gvaqvs veqtor–svetTan, xolo Tu

striqonebis raodenoba udris 1, veqtor–striqonTan.

Insert Matrix dialogur fanjaraSi striqonebisa da svetebis raodenobis

miTiTebis Semdeg ekranze gamoCndeba matricis Sabloni markerebiT. pirveli

elementis Setanis Semdeg davaWiroT an Tab klaviSebs, gadavalT Semdeg

markerze da a.S. nebismier markerze gadasvla SesaZlebelia agreTve masze

dawkapunebiT an kursoris gadaadgilebis klaviSebiT.

matricis elementi warmoadgens indeqsirebul cvlads. indeqsi SeiZleba

iyos mxolod mTeli ricxvi.

ganvixiloT magaliTis saxiT zogierTi moqmedeba matricaze. vTqvaT, gvaqvs

Semdegi A matrica:

A

1

5.6

9.1

2

6.88

10

3

7.1

11

4

8

12.45

.

matricis elementi Mathcad–Si Caiwereba Semdegnairad: A1,3 – me_2 striqonisa da me_4 svetis gadakveTaze myofi elementi (radgan winaswari SeTanxmebiT

elementebis indeqsebis Tvla iwyeba 0_dan). misi mniSvnelobis gamosatanad:

1) A simbolos akrebis Semdeg qveda indeqsis poziciaSi gadasasvlelad

avirCioT [ simbolo (igives mivaRwevT Matrix panelidan Xn Sablonis

gamoZaxebiT);

2) avkriboT 1,3;

3) gamoviyenoT klaviSi;

4) avkroboT = .

ekranze vnaxavT A1,3=-–8. Tu ORIGIN cvladis mniSvneloba gvqonda Secvlili 1–iT, ekranze

vnaxavT A1,3=-–3 . matricis nebismieri svetis amosaRebad viqceviT Semdegnairad:

1) avkriboT A; 2) davaWiroT Ctrl + 6 klaviSebs an Matrix panelze avirCioT M< > punqti;

3) gamoCndeba A

, Savi markeris adgilas SevitanoT svetis nomeri;

4) gamovyoT kursoriT akrebili gamosaxuleba mTlianad da avkriboT = .

Tu ORIGIN iyo 0–is toli, miviRebT:

A 1 2

6.88

10

.

20

sxva SemTxvevaSi (rodesac ORIGIN udris 1–s) :

A 1 1

5.6

9.1

.

imisaTvis rom miviRoT A matricis romelime striqoni, saWiroa A–s Setanis

Semdeg jer Ctrl + 1 klaviSebis meSveobiT movaxdinoT matricis transponireba, mere

Ctrl + 6 klaviSebiT miviRoT kuTxis PfrCxilebi da Savi markeris adgilas

mivuTiToT striqonis nomeri. igives mivaRwevT Matrix panelze M< > da MT punqtebis

Tanmimdevruli SerCeviT da miRebuli Sablonis SevsebiT (ix. nax.1.4).

nax.1.4_ze naCvenebia matricebi da operaciebi matricebze.

nax.1.4. matricebi da operaciebi matricebze

monacemTa faili Mathcad–Si arsebiTad warmoadgens igive veqtorebs da

matricebs, romelTa elementebi Cawerilia failebSi maT bunebriv formatSi –

mimdevrobiTi teqsturi failebis saxiT. es aris failebis tipi, romelic

miRebulia sxva programebSic, rac gvaZlevs monacemTa gacvlis saSualebas

Mathcad–sa da sxva programebs Soris.

21

Tavi II menius punqti File (faili)

2.1 mTavari menius File punqtis Semadgenloba

menius punqti File (faili) emsaxureba dokumentis failebTan muSaobas.

faili – es aris monacemTa mowesrigebuli erToblioba, romelsac gaaCnia

saxeli da gafarToeba. Mathcad–is dokumentis failebs aqvs gafarToeba .mcd , romelic iwereba uSualod failis saxelis Semdeg.

avirCioT menius punqti File (an davaWiroT klaviSebis kombinacias Alt + F). is Sedgeba Semdegi qvepunqtebisagan:

New... (axali) Ctrl + N – axali dokumentis gaxsna;

Open... (gaxsna) Ctrl + O – arsebuli failis gaxsna;

Close (daxurva) – aqtiuri dokumentis daxurva;

Save (Senaxva) Ctrl + S – dokumentis Senaxva;

Save As... (Senaxva rogorc) – failis saxelis an adgilmdebareobis Secvla;

Save as Web Page... – Senaxva Web gverdis saxiT;

Page Setup… – gverdebis parametrebis dayeneba;

Print Preview – beWdviswina daTvalierebis reJimi;

Print… (beWdva) Ctrl + P – beWdvis parametrebis dayeneba;

Send… (gagzavna) – aqtiuri failis gagzavna eleqtronuli fostis meSveobiT;

gagzavnisas saWiroa gvqondes romelime damxmare programa, iseTi rogoricaa

Microsoft Exchange, Microsoft Mail an Eudora;

Exit – programidan gamosvla.

2.2 Mathcad–is dokumentis Seqmna, Senaxva, gaxsna da daxurva

File → New… brZanebis an Standard instrumentTa panelis New Rilakis arCevisas gamoCndeba dialoguri fanjara New.

nax.2.1. dialoguri fanjara New

22

movniSnoT Blank Worsheet (sufTa samuSao furceli) punqti da davawkapunoT

Rilak OK–ze. gamoCndeba axali samuSao furceli, romelsac jer saxeli ar

gaaCnia Untitled: 1. menius punqt File–s gaaCnia Senaxvis ori qvepunqti: Save da Save As... . dokumentis pirveladi Senaxvis dros SesaZlebelia nebismieri maTganis

arCeva, ris Sedegad gamova Save As dialoguri fanjara (nax.2.2).

nax.2.2. dialoguri Ffanjara Save As Save in: siisebur velSi mivuTiToT adgili, sadac gvsurs Cveni dokumentis

ganTavseba da File name: kombinirebul velSi mivaniWoT mas saxeli.

winaswari SeTanxmebiT (by Default) Mathcad–i Seinaxavs fails .mcd gafarToebiT

anu Mathcad–is formatSi, magram Tu saWiroa, SeiZleba avirCioT sxva gafarToeba

Save as type: velSi miTiTebuli siidan. imisaTvis, rom movaxdinoT dokumentis

Senaxva Web gverdis saxiT anu HTML formatSi, avirCioT File menius Save as Web Page... brZaneba. dokumentSi Semdgomi cvlilebebis Sesanaxad viyenebT File →Save brZanebas (an

klaviaturis F6 klaviSs an Standard instrumentTa panelis Save Rilaks ).

ukve arsebuli failis saxelis an mdebareobis Sesacvlelad (an orivesi

erTdroulad) viyenebT brZanebas Save As... . gamova failis Senaxvis dialoguri

fanjara, sadac SevitanT sasurvel cvlilebebs. Cancel RilakiT xdeba Setanili

cvlilebebis gauqmeba da dialoguri fanjris daxurva, xolo OK RilakiT

fanjara daixureba da daiwyeba brZanebis Sesruleba.

23

arsebuli dokumentis gaxsnisaTvis:

1) avirCioT menius File → Open... brZaneba an davaWiroT Standard instrumentTa

panelis Open Rilaks , SesaZlebelia agreTve klaviaturis F5 funqcionaluri

Rilakis an Ctrl + O klaviSebis gamoyeneba.OgamoCndeba dialoguri fanjara Open ,

nax.2.3. dialoguri fanjara Open

romlis zeda Look in: velSi miTiTebulia im diskos an saqaRaldis saxeli, sadac

Sesruldeba failis moZebna. CamonaTvalSi vnaxavT qvesaqaRaldeebis da .mcd gafarToebis mqone failebis saxelebs. Tu Look in: velSi miTiTebuli disko an

saqaRalde ar gvawyobs, gavxsnaT siiseburi velis diskoTa da katalogTa xe da

avirCioT sasurveli.

2) dialoguri fanjris CamonaTvalSi movniSnioT failis saxeli an avkriboT

is File name: velSi;

3) davaWiroT Open Rilaks. gaixsneba dokumentis fanjara.

dokumentis fanjris gaxsna SesaZlebelia agreTve mis saxelze mausiT

orjeradi dawkapunebiT.

dokumentis swrafad gaxsna SesaZlebelia menius File punqtis qvemeniudan,

sadac Exit punqtis zemoT moTavsebulia bolos gaxsnili dokumentebis

CamonaTvali, an sastarto menius Start → Documents kaskadSi moTavsebuli

dokumentebis siidan.

24

File → Close brZaneba daxuravs aqtiur (mimdinare) fanjaras da sistema daiwyebs

muSaobas wina dokumentTan. amasTan Tu mimdinare dokumenti iyo muSaobis seansis

msvlelobisas modificirebuli, gamova dialoguri fanjara kiTxviT gvsurs Tu

ara modificirebuli dokumentis Senaxva.

nax.2.4. SekiTxvis dialoguri fanjara

Tu dokumenti ar iyo modificirebuli, Sesabamisi fanjara daixureba

SekiTxvis gareSe.

Tu Cven vmuSaobT erTdroulad ramdenime fanjarasTan da gvsurs yvela

fanjris daxurva, mosaxerxebelia Close punqtis nacvlad visargebloT Exit brZanebiT. am dros yvela aramodificirebuli fanjara daixureba avtomaturad,

xolo modificirebuli – dokumentebis Senaxvis Sesaxeb kiTxvis Semdeg.

aRvniSnoT, rom Save As da Open dialogur fanjrebSi gvaqvs instrumentTa

paneli Semdegi RilakebiT:

Go To Last Folder Visited – gadasvla im saqaRaldeSi, romelSic bolos

vimyofebodiT;

Up One Level – erTi doniT zeviT gadaadgileba;

Create New Folder – axali saqaRaldis Seqmna; View Menu – CamonaTvalSi miTiTebuli failebis warmodgena sxvadasxva

saxiT.

2.3 gverdebis parametrebis dayeneba,

beWdviswina daTvalierebis da beWdvis reJimebi

gverdebis parametrebis dasayeneblad viyenebT File → Page Setup… brZanebas. gamoCndeba dialoguri fanjara (nax.2.5), sadac Size: velSi SeirCeva furclis

zomebi, Source: (wyaro) velSi qaRaldis miwodebis xerxi, Orientation areSi SeirCeva furcelze teqstis ganlagebis wesi: grZivi (Portrait) an ganivi (Landscape), Margins (mindvrebi) areSi misaTiTebelia marcxena (Left:), marjvena (Right:), zeda (Top:) da qveda (Bottom:) mindvrebis mniSvnelobebi. SesaZlebelia davayenoT alami Print single page width – erTi gverdis siganis dokumentis dabeWdva.

25

nax.2.5. dialoguri fanjara Page Setup

File → Print Preview brZanebis SerCeviT an Standard instrumentTa panelze

Rilakis daWeriT SevdivarT dokumentis beWdviswina daTvalierebis reJimSi,

romlis fanjaraSi (nax.2.6) naCvenebi iqneba dokumentis mimdinare gverdi. am

nax.2.6. dialoguri fanjara Print Preview

26

dialoguri fanjris zeda nawilSi ganlagebulia Semdegi Rilakebi: Print… –

beWdvis reJimSi gadasvla, Next Page – Semdegi gverdis daTvaliereba, Prev Page – wina gverdis daTvaliereba, Two Pages – ori gverdis erTdrouli daTvaliereba, Zoom In – gamosaxulebis gadideba, Zoom Out – gamosaxulebis dapataraveba, Close – dialoguri fanjris daxurva da beWdviswina daTvalierebis reJimidan gamosvla.

File → Print... brZanebiT an Standard instrumentTa panelze Print Rilakze dawkapunebiT gamoiZaxeba Print dialoguri fanjara (nax.2.7),

nax.2.7. dialoguri fanjara Print

romelSic SeirCeva printeri da beWdvis parametrebi. Print range (beWdvis diapazoni) areSi All gadamrTvelis CarTva gamoiwvevs mTeli dokumentis dabeWdvas, Selection gadamrTveli gamoiyeneba winaswar gamoyofili fragmentis dasabeWdad, Current Page – aqtiuri furclis dasabeWdad, xolo Pages gadamrTveli gamoiyeneba

dasabeWdi gverdebis konkretuli diapazonis misaTiTeblad. am SemTxvevaSi from: velSi Seitaneba diapazonis pirveli gverdis nomeri, xolo to: velSi – bolo

gverdis nomeri. Copies areSi Number of copies: velSi misaTiTebelia dasabeWdi

egzemplarebis raodenoba. erTze meti egzemplaris dabeWdvisas Collate almis

dayeneba–moxsniT ganisazRvreba maTi miRebis wesi, romelic iqve nimuSze aisaxeba.

Tu printeri mzadyofnaSia, sakuTriv beWdvis procedura daiwyeba OK Rilakze daWeriT.

Mathcad–is dokuments SeiZleba hqondes ormagi sigane da erT gverdze meti

sigrZe, maSin jer ibeWdeba marcxena nawilis yvela gverdi, Semdeg ki marjvena

nawilis.

27

Tavi III dokumentis redaqtirebis meTodebi

3.1 redaqtirebis zogadi xerxebis mokle mimoxilva

gamosaxulebis calkeuli elementebis, misi nawilis an mTlianad

gamosaxulebis gamosayofad viyenebT Semdeg klaviSebs:

klaviSi gadaitans kursors zeviT; gamoTvliT blokSi Sesvlisas viziri

gardaiqmneba lurj kuTxed, romelic moicavs mTel gamosaxulebas;

klaviSi moqmedebs analogiurad, mxolod kursoris gadatana xdeba

qveviT;

klaviSebi da moqmedeben analogiurad, magram maTematikuri aris

SigniT lurji kuTxis markeris gadatanisas icvleba misi forma;

Shift + , Shift + , Shift + , Shift + klaviSebis kombinaciebiT

gamosaxuleba gamoiyofa Setanis markeris adgilidan Sesabamisad zeviT,

qveviT, marcxniv da marjvniv. amasTan Tu vimyofebiT maTematikur an teqstur

areSi, moxdeba Sesabamisi fragmentis gamoyofa da gamoyofili nawilis

gaferadebuli marTkuTxedis saxiT Cveneba.

ganvmartoT marTvis klaviSebis daniSnuleba redaqtirebis procesSi:

Tab – gadaaqvs kursori: SablonSi – mimdinare Wdidan (markeridan)

momdevnoze, Tu yvela Wde Sevsebulia, xdeba kursoris gadatana blokis

gareT da is aRmoCndeba blokis Semdeg;

Shift + Tab – gadaaqvs kursori: SablonSi – mimdinare Wdidan wina Wdeze, Tu

yvela Wde Sevsebulia, xdeba kursoris gadatana blokis gareT, ris Sedegad

is aRmoCndeba blokis win;

Page Up – naxevari fanjriT zeviT gadaadgileba;

Page Down – naxevari fanjriT qveviT gadaadgileba;

Ctrl + Page Up – erTi fanjriT zeviT gadaadgileba;

Ctrl + Page Down – erTi fanjriT qveviT gadaadgileba;

Home – teqstur areSi Setanis markeris teqsturi striqonis dasawyisSi dayeneba;

End – teqstur areSi Setanis markeris teqsturi striqonis boloSi

dayeneba;

Ctrl + Home – dokumentis dasawyisSi gadaadgileba anu kursoris dayeneba

pirveli obieqtris dasawyisSi;

Ctrl + End – dokumentis boloSi gadaadgileba anu kursoris dayeneba

dokumentis bolo oboeqtis dasawyisSi.

teqsturi blokebis redaqtireba ar gansxvavdeba im xerxebisagan, romlebic

miRebulia teqstur redaqtorebSi (WordPad, Word).

28

maTematikuri blokebis redaqtireba detalurad ganxilulia 3.2–Si. aq

aRvniSnoT, rom Insert klaviSis meSveobiT xdeba kursoris gadatana gamoyofili

fragmentis dasawyisSi an bolos, imisda mixedviT Tu saiTken iyo mimarTuli

lurji kuTxis markeri. imisaTvis, rom SevcvaloT ricxvi an aso maTematikur

gamosaxulebaSi, saWiroa davayenoT Setanis markeri Sesabamis adgilas da jer

wavSaloT Sesacvleli simbolo Backspace klaviSis meSveobiT (Tu lurj Setanis

markers aqvs forma) an Delete klaviSiT (Tu lurj Setanis markers aqvs forma),

Semdeg avkriboT axali simbolo. Secvla SesaZlebelia agreTve wasaSleli

fragmentis gamoyofiT Tagvis Cavleba–gadaTrevis (Drag and Drop) teqnikiT da axali

simboloebis akrebiT.DA

qvemoT moyvanilia klaviSebi da maTi kombinaciebi, romelTa meSveobiT

SesaZloa redaqtirebis procesis gamartiveba:

Shift + F5 – Replace dialoguri fanjris gamoZaxeba;

Alt + Backspace – redaqtirebis bolo operaciis gauqmeba;

Ctrl + Insert – gamoyofili obieqtis kopireba monacemTa gacvlis buferSi

(monacemTa gacvlis buferi warmoadgens operatiuli mexsierebis

specialur ares, romelic ixmareba programebs Soris monacemebis

gacvlisaTvis);

Shift + Delete – gamoyofili obieqtis buferSi gadatana;

Insert – Casmis reJimis CarTva;

Shift + Insert – monacemTa kopireba buferidan dokumentSi.

ganvixiloT dokumentebis da fanjrebis marTvis klaviSebi:

Ctrl + Esc – Windows operaciuli sistemis mTavari menius gamoZaxeba (igivea,

rac Start Rilakze dawkapuneba);

Ctrl + F 4 – dokumentis daxurva; Ctrl + P – Print dialoguri fanjris gamoZaxeba;

Alt + F4 – sistemidan gamosvla (Quit); F1 – daxmarebis (Help) fanjris gaxsna.

3.2 maTematikuri gamosaxulebebis redaqtirebis magaliTebi

maTematikur gamosaxulebaze dawkapunebiT SevdivarT redaqtirebis reJimSi,

romelSic SesaZlebelia saWiro cvlilebebis Setana.

saxelis an ricxvis redaqtireba

1) davawkapunoT maTze TagviT. gamoCndeba formis redaqtirebis niSani;

2) da klaviSebiT gadavaadgiloT redaqtirebis niSani saWiro

adgilas;

29

ab

1

a bx d

a b( ) cx d

a bx d

a bx d

c

x

ab

1

3) klaviaturidan Setanili simbolo gamoCndeba redaqtirebis kursoris

marcxniv. Backspace klaviSis daWeriT waiSleba kursoris marcxniv mdgomi

simbolo, xolo Delete klaviSiT marjvniv mdgomi simbolo.

operatoris Casma

I. vTqvaT, identifikatorSi ori simbolos an mudmivSi ori cifris Soris

Casasmelia operatori. mag., gvaqvs ab da gvinda miviRoT a + b. amisTvis:

1) davawkapunoT TagviT a da b simboloebs Soris;

2) avkriboT klaviaturidan + an SevirCioT + operatori Calculator panelidan.

miviRebT sasurvel Sedegs.

II. gvaqvs ab+1. gvinda miviRoT . amisTvis:

1) davayenoT redaqtirebis xazi a da b simboloebs Soris. ekranze vnaxavT

ab+1 ; 2) klaviaturidan an Calculator panelidan gamoviyenoT / niSani. ekranze

miviRebT redaqtirebis Sedegs: .

III. vTqvaT, x gvsurs gadavaqcioT _ad.

1) davawkapunoT gamosaxulebaze da miviyvanoT kursori x_Tan Semdegnairad: x ; 2) davaWiroT \ klaviSs. davinaxavT .

Tu 1 punqtSi kursori moicavda x sxva mxridan _ x , \ klaviSis gamoyeneba

mogvcems Sedegad .

IY. gvaqvs . gvinda miviRoT . amisTvis:

1) davawkapunoT gamosaxulebaze da Semdegnairad davayenoT kursori:

;

2) avriboT *c . miviRebT .

Y. gvaqvs . gvsurs miviRoT (an ).

1) davayenoT lurji kuTxe ise, rom is wilads moicavdes srulad: ;

2) avkriboT *c . miviRebT .

aRvniSnoT, rom Tu meore punqtSi jer davaWerT Insert klaviSs (ekranze

vnaxavT ), xolo Semdeg davbeWdavT *c , miviRebT .

a bx d

a b( ) cx d

a bx d

c

a bx d

a bx d

x

x

ca bx d

ca bx d

30

ab

x

ab

cd

ab

cd

2 x x2 2 x x2

ab

cd

2 x2

a ba b

ca ba b

c

2 x x2

operatoris waSla

I. gvaqvs . wavSaloT operatori da miviRoT ab. amisTvis: 1) davayenoT kursori b_s win: ; 2) davaWiroT Backspace klaviSs. miviRebT .

II. gvaqvs . gadavaqcioT ab _d. 1) davayenoT redaqtirebis lurji kursori Semdegnairad: ;

2) davaWiroT Backspace klaviSs, miviRebT ab . III. gvaqvs erTi operandis mqone operatori, mag., . wavSaloT operatori da

miviRoT x . amisTvis:

1) davayenoT kursori x_is win ; 2) davaWiroT Backspace klaviSs, miviRebT x. operatoris Secvla

I. vTqvaT, gvaqvs , gvsurs miviRoT . amisTvis:

1) davayenoT redaqtirebis kursori Semdegnairad: ;

2) davaWiroT Backspace klaviSs, miviRebT , anu operatoris adgilas

gamoCndeba marTkuTxedi, romelSic Casasmelia sxva operatori;

3) SevitanoT gamoklebis niSani. miviRebT .

II. gvaqvs Setanili . gvinda miviRoT .

1) miviRoT ekranze ;

2) davaWiroT Delete klaviSs. Sedegad moiniSneba da mTlianad gaferaddeba |x| ; 3) davaWiroT Delete klaviSs. miviRebT ;

4) avkriboT x . miviRebT .

Tu kidev erTxel SevirCevT |x| punqts Calculator panelze, miviRebT:

. ra Tqma unda, SesaZlebelia es amocana gadavwyvitoT 1_l punqtSi

miRebiT da me_2 punqtSi Backspace klaviSis daWeriT (me_3 da me_4 punqtebi

ucvlelia).

gamosaxulebis dasawyisSi minusis Casma

gvaqvs sin(a). gvsurs miviRoT _sin(a). 1) davawkapunoT sin(a)_ze da Tu saWiroa gamoviyenoT Space klaviSi. miviRebT

sin(a) . davaWiroT Insert klaviSs. miviRebT sin(a); 2) davbeWdoT gamoklebis niSani. miviRebT sasurvel Sedegs.

frCxilebis Casma

I. vTqvaT, gvaqvs . gvsurs miviRoT .

1) davayenoT kursori Semdegnairad: ;

ab

cd

ab

cd

2 x x2

2 x x2

2 x x2

a ba b

c

ab

x

a ba b

ab

31

2) davbeWdoT apostrofis niSani ‘ an davawkapunoT Calculator panelis ( )

Rilakze . miviRebT .

II. gvaqvs a_b+c. miviRoT a_(b+c): 1) davayenoT redaqtirebis kursori b_s win: a_b+c ; 2) davbeWdoT ( ;

3) davawkapunoT c_ze da davayenoT redaqtirebis xazi c_s ukan a_(b+c ; 4) davbeWdoT ) . frCxilebis waSla

vTqvaT, gvaqvs a_(b+c) . frCxilebis wasaSlelad:

1) davayenoT redaqtirebis kursori b_s win a_( b+c); 2) davaWiroT Backspace klaviSs. miviRebT a_ b+c. anda:

1) davayenoT redaqtirebis kursori c_s ukan a_( b+c ); 2) davaWiroT Delete klaviSs. miviRebT a_b+c . da bolos aRvniSnoT, rom gamosaxulebaze ormagi wkapuni gamoyofs rogorc

mTel obieqts, aseve Sesabamis obieqts mis SigniT.

amrigad, gamosaxulebebis redaqtirebisas redaqtirebis kursoris poziciis

SerCevas principuli mniSvneloba aqvs. unda gvaxsovdes, rom obieqtze

dawkapunebis Semdeg:

Insert klaviSis daWera Secvlis lurji kuTxis formis redaqtirebis niSnis

mimarTulebas: _dan _ze da piriqiT, ase rom Tu lurji kuTxis

kursori moicavda simbolos, gamosaxulebis nawils an mTel

gamosaxulebas, vTqvaT, marjvnidan, Insert klaviSis daWeris Sedegad igive

simbolo, gamosaxulebis nawili an mTeli gamosaxuleba iqneba moculi

marcxnidan ;

da klaviSebiT xdeba erTi simbolodan meoreze gadasvla da

agreTve redaqtirebis kursoris gadaadgileba;

Space (hari) klaviSis gamoyenebis Sedegad lurji kuTxiT iqneba moculi

gamosaxulebis ufro didi nawili. ase rom Space–ze zedized daWeriT

lurji kuTxiT iqneba moculi mTeli gamosaxuleba. Tu kidev davaWerT

Space_s, redaqtirebis kursori dabrundeba Tavdapirvel poziciaSi,

saidanac daviwyeT redaqtirebis procesi. Space klaviSis moqmedeba

ilustrirebulia nax.3.1_Si;

Tab da Shift + Tab klaviSebis daniSnuleba redaqtirebisas ukve iyo

miTiTebuli 3.1_Si;

cvlilebebis Setana SesaZlebelia agreTve wasaSleli fragmentis

gamoyofiT Tagvis Cavleba–gadaTrevis (Drag and Drop) teqnikiT da axali

simboloebis akrebiT. am meTodiT gamoyofili obiqti Delete klaviSze

dawkapunebiT waiSleba.

DA

a ba b

c

32

nax.3.1. Space klaviSis moqmedebis principi

3.3 mTavari menius Edit (redaqtireba) punqtis Semadgenloba

mTavari menius Edit punqti emsaxureba dokumentis redaqtirebas. avirCioT mTavari menius Edit punqti (an davaWiroT klaviSebis kombinacias

Alt + E). is Sedgeba Semdegi qvepunqtebisagan: Undo (gauqmeba) Ctrl+Z _ bolo Sesrulebuli operaciis gauqmeba; Redo (aRdgena) Ctrl+Y _ gauqmebuli operaciis gameoreba; Cut (amoWra) Ctrl+X _ gamoyofili fragmentis amoWra da buferSi

moTavseba; Copy (kopireba) Ctrl+C _ gamoyofili fragmentis aslis buferSi

moTavseba; Paste (Casma) Ctrl+V _ buferis SigTavsis dokumentSi Casma; Paste Special… _ specialuri Casma;

Delete (waSla) Ctrl+D _ gamoyofili fragmentis waSla; Select All (yvelafris gamoyofa) Ctrl+A _ yvela obieqtis moniSvna; Find… (Zebna) Ctrl+F _ teqstis da gamosaxulebis fragmentis Zebna; Replace… (Secvla) Ctrl+H _ teqstis da gamosaxulebis fragmentis

Secvla; Go to Page... (gverdze gadasvla) _ sxva gverdze gadasvla;

Links... (kavSirebi) _ dokumentSi Casmul obieqtTan kavSirebis

redaqtireba; *

Object (obieqti) _ dokumentSi Casmuli obieqtis redaqtireba.

* Links... da Object punqtebi iqneba ganxiluli 5.21 da 5.19_Si.

33

3.4 redaqtirebis operaciis gauqmeba_aRdgena

Edit → Undo brZaneba auqmebs bolo Sesrulebuli operaciis Sedegs. igives

mivaRwevT Standard instrumentTa panelze Undo Rilakze daWeriT.

bolo operaciis gauqmebis Semdeg SesaZlebelia ekranis wina saxis aRdgena,

rasac emsaxureba Edit → Redo brZaneba an Redo Rilaki Standard instrumentTa

panelze. Redo operacia gvaZlevs saSualebas xelmeored SevasruloT bolo

gauqmebuli brZaneba.

3.5 dokumentis fragmentebTan muSaoba

redaqtirebis procesSi xSirad gvesaWiroeba ukve Setanili obieqtis,

obieqtTa jgufis an obieqtis nawilis erTi adgilidan meore adgilze gadatana,

kopireba, waSla an formatis Secvla. amisTvis saWiroa winaswar miTiTebuli iyos

Tu raze unda Catardes moqmedeba anu saWiroa movaxdinoT egreT wodebuli

fragmentis gamoyofa (moniSvna).

ganvixiloT fragmentis gamoyofis wesebi:

calkeuli obieqtis gamoyofa xdeba Tagvis marcxena RilakiT masze

dawkapunebiT. obieqti moiqceva marTkuTxedSi, xolo kursori

aRmoCndeba SigniT da miiRebs saTanado formas (teqstur areSi wiTeli

vertikaluri xazi , maTematikur areSi – lurji kuTxe an ).

calkeuli obieqtis gamoyofa SesaZlebelia aseve obieqtze orjer

dawkabunebiT. is moiqceva marTkuTkuTxedSi, amasTan iqneba gamoyofili da

gaferadebuli obieqtis Sesabamisi nawili. Tu obieqti grafikia, erTi

wkapuni gamoyofs mas, xolo ori _ gamoiZaxebs daformatebis dialogur

fanjaras;

obieqtis an obieqtTa jgufis gamoyofa SesaZlebelia agreTve Tagvis

gadaTrevis (Drag and Drop) teqnikis gamoyenebiT. amisTvis unda

mivitanoT Tagvis maCvenebeli obieqtTan (magram ara mis

SigniT), davaWiroT Tagvis marcxena Rilaks da gadavaTrioT

Tagvi diagonalze. ekranze vnaxavT punqtiriT daxazul

marTkuTxeds. rogorc ki am marTkuTxedSi moxdeba obieqti an

obieqtis nawili, is moiniSneba _ gamoiyofa punqtiruli xazebiT. roca

Tagvis Rilaks avuSvebT xels, ZiriTadi marTkuTxedi gaqreba ekranidan,

magram yvela moniSnuli obieqti darCeba;

taqstur areebSi da maTematikur gamosaxulebebSi SesaZlebelia nebismieri

fragmentis moniSvna Drag and Drop teqnikiT;

calkeuli obieqtebis gamosayofad davawkapunoT jer erT_erT obieqtze,

Semdeg Ctrl klaviSTan erTad davawkapunoT danarCen obieqtebze. Tu

34

daWerili iqneba Shift , sawyis obieqtTan erTad gamoiyofa yvela obieqti,

romlebic mdebareoben sawyis da bolo dawkapunebul obieqtTa Soris.

aRvniSnoT, rom Tu moniSvnisas obieqti gamoyofilia markerebiani

marTkuTxediT, markerTan Tagvis maCveneblis mitanisas ukanaskneli miiRebs

ormxrivi isris formas. TagviT isris gadaweva gamoiwvis obieqtis zomebis

Secvlas.

Edit → Cut brZanebiT an Standard instrumentTa panelze Cut Rilakze

daWeriT xdeba gamoyofili fragmentis amoWra da gadatana buferSi.

Edit → Copy brZanebiT an Standard instrumentTa panelze Copy Rilakze

daWeriT xdeba gamoyofili fragmentis aslis moTavseba buferSi, amasTan TviTon

fragmenti rCeba dokumentSi Tavis adgilze.

Edit → Paste brZanebiT an Standard instrumentTa panelze Paste Rilakze

daWeriT xdeba buferSi mdebare obieqtis dokumentSi Casma kursoris adgilas.

am dros buferis SigTavsi SenarCundeba da SesaZlebelia Casmis operaciis

gameoreba.

gamoyofili obieqtis gadatana da kopireba SesaZlebelia gacvlis buferis

gamouyenebladac _ Drag and Drop meTodiT anu im dros, rodesac Tagvis maCvenebels

xelisgulis forma aqvs, xdeba obieqtis TagviT Cavleba da gadaTreva erTi

adgilidan meoreze (kopirebisas – Ctrl klaviSze erTdrouli daWeriT).

Cut, Copy da Paste brZanebebiT fragmentis gadatana da kopireba

SesaZlebelia ara mxolod erTi dokumentis farglebSi, aramed erTi dokumentidan

meoreSic. fragmentis gadanacvleba erTi fanjridan meoreSi xorcieldeba agreTve

Tagvis meSveobiT uSualod erTi fanjridan meore fanjris sasurvel adgilas

fragmentis gadaTreviT (kopirebisas erTdroulad vaWerT Ctrl klaviSs).

Edit → Paste Special... brZaneba gvaZlevs dokumentSi sxvadasxva formatis

nax.3.2. dialoguri fanjara Paste Special

35

(teqsturi, Mathcad, RTF, Bitmap) failebis Casmis saSualebas. gamoCndeba dialoguri

fanjara (nax.3.2), sadac amoirCeva saWiro formati.

Edit → Delete brZanebiT xdeba gamoyofili fragmentis waSla anu iseTi

moSoreba, romlis dros ar xdeba misi gadatana buferSi.

Edit → Select All brZanebiT xdeba yvela obieqtis gamoyofa punqtiruli

marTkuTxedebiT. am dros Cven naTlad vxedavT Tu rogor arian

urTierTganlagebuli blokebi da saWiroebisamebr vaxdenT maT gadanacvlebas.

ra Tqma unda, brZanebebi SeiZleba SeirCes konteqsturi meniudanac.

3.6 teqstis an gamosaxulebis fragmentis Zebna da Secvla

Edit → Find... brZanebiT xdeba Zebnis dialoguri fanjris gamoZaxeba (nax3.3).

am fanjris Find what: teqstur velSi unda SevitanoT teqstis an

gamosaxulebis saZebni fragmenti. Zebnis gasagrZeleblad davaWiroT Find Next Rilaks, xolo operaciis gasauqmeblad – Cancel Rilaks.

nax.3.3. Zebnis dialoguri fanjara

winaswari SeTanxmebiT Mathcad_i axorcielebs Zebnas mxolod teqstur

areebSi.

Tu saWiroa, SegviZlia CavrToT almebi: Match whole word only (am dros saZebni fragmenti calkeul sityvas warmoadgens), Match case (zeda da qveda registrebis gaTvaliswineba anu am almis dayenebiT Mathcad–i gansxvavebulad aRiqvams mcire

da mTavrul asoebs Zebnis procesSi), Find in Text Regions (teqstur areebSi Zebna), Find in Math Regions (maTematikur areebSi Zebna).

Zebnis mimarTuleba (Direction) SeiZleba iyos kursoris zeviT (Up) an qvevviT (Down).

Edit → Replace… brZanebiT xdeba Secvlis dialoguri fanjris gamoZaxeba

(nax.3.4), romelsac Find what: teqsturi velis garda gaaCnia teqsturi veli

Replace with: , sadac Caiwereba Semcvleli fragmenti.

36

nax.3.4. Secvlis dialoguri fanjara

Secvlis dialoguri fanjris Replace All Rilaks viyenebT, Tu gvsurs Find

what: velSi miTiTebul yvela saZebni monacemis Secvla Replace with: velSi

Cawerili monacemiT; Replace da Find Next Rilakebs viyenebT, Tu Secvla gvsurs

amorCeviT. Secvlis dialogur fanjaraSi gvxvdeba igive gadamrTvelebi, rac Find dialogSi.

3.7 dokumentis sasurvel gverdze gadasvla

Edit → Go to Page… brZanebiT gamoiZaxeba Go to Page dialoguri fanjara

(nax.3.5), sadac unda mivuTiToT, romel gverdze gvsurs gadasvla: pirvelze (First Page), boloze (Last Page) Tu gverdze, romlis nomers mivuTiTebT Page Number: gadamrTvelis cifrul velSi. am dialoguri fanjris qveda nawilSi Cans ori

Setyobineba: Number of Pages: (gverdebis raodenoba) da Current Page: (mimdinare gverdis nomeri).

nax.3.5. dialoguri fanjara Go to Page

37

Tavi IV menius punqti View (xedi)

4.1 mTavari menius View punqtis Semadgenloba

avirCioT mTavari menius View punqti (an davaWiroT klaviSebis kombinacias

Alt + V). davinaxavT qvemenius Semdeg punqtebs:

Toolbars (instrumentTa panelebi) _ instrumentTa panelebis moxsna_dayeneba;

Ruler (saxazavi) _ saxazavis Cveneba_damalva ekranze;

Status Bar (mdgomareobis striqoni) _ mdgomareobis striqonis

Cveneba_damalva ekranze; Header and Footer… (zeda da qveda kolontitulebi) _ kolontitulebis

Seqmna da gaformeba;

Regions (areebi) _ areebis TeTri foniT gamoyofa;

Refresh (ganaxleba) Ctrl + R _ samuSao furclis ganaxleba;

Zoom... (masStabi) _ masStabis Secvla.

4.2 instrumentTa panelebi

View → Toolbars brZanebiT, rogorc ukve viciT, xdeba ama Tu im panelis

moxsna_dayeneba. Toolbars CamonaTvalSi Sedis:

Standard _ standartuli paneli; Formatting _ daformatebis paneli; Math _ maTematikuri paneli; Controls _ marTvis paneli; Resources _ resursebis paneli;

Calculator _ gamoTvlebis Catarebis operatorebis paneli; Graph _ grafikebis agebis paneli; Matrix _ matricebTan muSaobisaTvis gankuTvnili operatorebis paneli; Evaluation _ miniWebis, tolobis, simboluri gardaqmnebis operatorebis

paneli. aq agreTve ganlagebulia momxmareblis mier operatoris

ganmsazRvreli punqtebi;

Calculus _ maTanalizis operatorebis paneli; Boolean _ bulis algebris operatorebis paneli; Programming _ daprogramebis paneli;

Greek _ berZnuli anbanis paneli;

Modifier _ modifikaciis paneli.

38

4.3 saxazavi, mdgomareobis striqoni da areebi

View menius Ruler da Status Bar punqtebiT xdeba saxazavisa da mdgomareobis

striqonis Cveneba_damalva ekranze. es punqtebic, iseve rogorc panelebis saxelebi

Toolbars CamonaTvalSi, arsebiTad alams warmoadgenen.

Mathcad_is dokumenti Sedgeba calkeuli blokebisagan, romelTa Soris

sazRvrebi Cveulebrivad ar Cans ekranze. View → Regions brZaneba yvela ares

TeTrad gamoyofs, xolo maT Soris Sualedebs – ruxad, rac mogvcems saSualebas

naTlad davinaxoT maTi urTierTganlageba. Tu saWiroa, Format → Separate Regions brZanebiT xdeba areebis urTierTgadafarvis mocileba.

4.4 masStabis Secvla da ganaxleba

View menius Zoom... punqti gamoitans ekranze Zoom dialogur fanjaras

(nax.4.1). am fanjaraSi gadamrTvelis ama Tu im poziciaSi dayenebiT (200%, 100%,

75%, 50%, 25%) xdeba Sesabamisi masStabis dafiqsireba da OK Rilakze

daWeris Semdeg am masStabiT gamosaxulebis danaxva. Custom punqtis arCevisas

misawvdomi xdeba mis marjvniv mdebare veli, sadac SegviZlia mivuTiToT

sasurveli masStabi.

nax.4.1. masStabis Secvlis fanjara

View → Refresh brZanebiT xdeba mimdinare samuSao furclis ganaxleba. saqme

imaSia, rom obieqtebTan muSaobis dros, mag., maTi zomebis Secvlisas, gamoyofisas,

gadaadgilebisas da a.S., ekranze xandaxan Cndeba arasasurveli obieqtebi (mag.,

jvaredini wiTeli kursori SeiZleba Candes ramdenime adgilas an teqsturi aris

nawili ar Candes, radgan is nawilobriv maTematikuri ariT aris gadafaruli).

Refresh brZaneba moiSorebs am zedmet obieqtebs, amasTan dokumentis obieqtebi

xeluxlebeli darCeba.

39

4.5 gverdis kolontitulebis Seqmna da gaformeba

zeda (Header) da qveda (Footer) kolontitulebi (TavsarTi da qvesarTi) es

aris teqsti, romelic avtomaturad gameordeba yvela gverdze Sesabamisad zeda da

qveda mindvris areSi. es SeiZleba iyos dokumentis saTauri, organizaciis

dasaxeleba, avtoris gvari da sxv. aq SeiZleba agreTve moTavsdes gverdis nomeri,

TariRi, dro da a.S.

View → Header and Footer brZanebiT ekranze gamoitaneba kolontitulebis

dialoguri fanjara (nax.4.2) ori CanarTiT: Header da Footer, romlebSic xdeba

Sesabamisad TavsarTis da bolosarTis Seqmna da gaformeba.

nax.4.2. kolontitulebis dialoguri fanjara

avirCioT romelime, vTqvaT, Header CanarTi. fanjris zeda nawilSi davinaxavT

sam seqcias: Left (marcxena), Center (centraluri), Right (marjvena). blokebSi

klaviaturidan SeiZleba SevitanoT sasurveli teqsti. teqstis garda, blokebSi

survilisamebr Seitaneba sxva informaciac Tools (instrumentebi) ganyofilebis

Rilakebis meSveobiT:

– Insert File Name (failis saxelis Casma);

_ Insert File Path (failis sruli misamarTis Casma);

_ Insert Page Number (mimdinare gverdis nomris Casma);

_ Insert Number of Pages (gverdebis raodenobis Casma);

_ Insert Date Last Saved (failis bolo Senaxvis TariRis Casma);

_ Insert Time Last Saved (failis bolo Senaxvis drois Casma);

40

_ Insert Date (mimdinare TariRis Casma);

_ Insert Time (mimdinare drois Casma). Tools ganyofilebaSi aris agreTve Rilakebi Format… , romelic gaxsnis

daformatebis dialogur fanjaras, da Image... (gamosaxulebis Casma), romelic

gaxsnis naxatebis Casmis dialogur fanjaras.

Format dialogur fanjaraSi (nax.4.3) SesaZlebelia Sriftis, misi stilis da

zomis dayeneba. am fanjris Alignment ganyofilebaSi SeiZleba mivuTiToT sworebis

tipi, xolo Effects ganyofilebaSi efeqtebi: Strikeout (gadaxazva), Underline (xazgasma) da Color: (feri).

nax.4.3. dialoguri fanjara Format

kolontitulebis dialogis Options (parametrebi) ganyofilebaSi SeiZleba

mivuTiToT Tu romeli cifriT gvsurs numeraciis dawyeba da davayenoT alami

Different header and footer on first page – pirveli gverdisaTvis gansxvavebuli TavsarTis

da qvesarTis Seqmna. Frame (CarCo) ganyofilebaSi SegviZlia davayenoT almebi

mTeli gverdis (Page), zeda (Header) da qveda (Footer) kolontitulebis CarCoSi

mosaTavseblad.

Use full width for each section almis dayenebiT kolontituli daikavebs Sesabamisi

seqciis (marcxena, centraluri da marjvena) mTel siganes da mxolod Semdeg

gadaitaneba Tavisi seqciis Semdeg striqonze.

OK Rilakze daWeris Semdeg kolontituli Caismeba dokumentSi, magram

Cveulebriv reJimSi Cven mas ver davinaxavT. misi danaxva SesaZlebelia Print Preview reJimSi da rasakvirvelia, is daibeWdeba beWdvisas.

41

Tavi V menius punqti Insert (Casma)

5.1 mTavari menius Insert punqtis Semadgenloba

avirCioT mTavari menius Insert punqti (an davaWiroT klaviSebis kombinacias

Alt + I). davinaxavT qvemenius Semdegi punqtebiT:

Graph (grafiki) _ sxvadasxva tipis grafikebis Casma; Matrix... (matrica) Ctrl + M _ matricis Casma; Function... (funqcia) Ctrl + E – funqciis Casma; Unit... (sazomi erTeuli) Ctrl + U – sazomi erTeulis Casma;

Picture (naxati) Ctrl + T – naxatis Casma; Area (ubani) _ ubnis formireba; Page Break – gverdis gawyveta; Math Region (maTematikuri are) _ maTematikuri aris Casma;

Text Region (teqsturi are) “ _ teqsturi aris Casma; Component... (komponenti) _ komponentis Casma; Data (monacemebi) _ monacemebis Casma; Control (marTva) _ mmarTveli komponentebis Casma;

Object... (obieqti) _ obieqtis Casma; Reference... (miTiTeba) _ sxva dokumentze miTiTebis Casma;

Hyperlink... (hipermimarTva) Ctrl + K _ hipermimarTvis damyareba.

5.2 grafikis Casma

Insert → Graph brZaneba Seicavs Semdeg qvepunqtebs: X_Y Plot (X_Y grafiki) Shift + @ – dekartis koordinatTa sistemaSi

grafikis ageba;

Polar Plot (polaruli grafiki) Ctrl + 7 – polaruli grafikis ageba;

Surface Plot (zedapiris grafiki) Ctrl + 2 – zedapiris grafikis ageba; Contour Plot (konturuli grafiki) Ctrl + 5 – konturuli grafikis ageba;

3D Scatter Plot (samganzomilebiani wertilovani grafiki) – samganzomilebiani

wertilovani grafikis ageba;

3D Bar Plot (samganzomilebiani svetovani grafiki) – samganzomilebiani

svetovani grafikis ageba;

Vector Field Plot (veqtoruli velis grafiki) – veqtoruli velis grafikis

ageba;

42

Plot Wizard... (grafikis ostati) – grafikis agebis ostatis dialoguri

fanjris gamoZaxeba.

grafikebis asagebad iyeneben agreTve Graph instrumentTa panels (nax.5.1)

Semdegi RilakebiT: X_Y Plot, Zoom(masStabi), Trace(trasa), Polar Plot, Surface Plot, Contour Plot, 3D Bar Plot, 3D Scatter Plot, Vector Field Plot.

nax.5.1. Graph instrumentTa paneli

5.3 organzomilebiani X_Y grafikis ageba da redaqtireba

Insert → Graph → X_Y Plot brZanebiT (an Graph instrumentTa panelze

Sesabamisi Rilakis daWeriT) viziris adgilas Seiqmneba organzomilebiani X_Y grafikis Sabloni dekartis koordinatTa sistemaSi (nax.5.2).

nax.5.2. X_Y grafikis Sabloni

grafikis asagebad:

1) davawkapunoT markerze, romelic mdebareobs ordinatTa RerZis marcxniv da

SevitanoT funqcia, cvladi an gamosaxuleba;

2) davawkapunoT markerze, romelic mdebareobs abscisTa RerZis qveS da

SevitanoT funqcia, cvladi an gamosaxuleba.

markeridan markerze gadasasvlelad SeiZleba visargebloT agreTve

klaviaturis kursoris gadaadgilebis klaviSebiT.

3) gadavitanoT kursori grafikuli obieqtis gareT da davawkapunoT an

davaWiroT Enter klaviSs, grafiki aigeba gamoTvlebis avtomatur reJimSi. Tu

gamoTvlebis avtomaturi reJimi gamorTulia, grafikis asagebad saWiroa F9 funqcionaluri klaviSis gamoyeneba.

43

grafikis agebisas Mathcad_i TviTon irCevs X da Y RerZebis zRvrul

mniSvnelobebs. saWiroebisamebr momxmarebels SeuZlia sxva mniSvnelobebis

miTiTeba.

erT grafikul areSi SesaZlebelia miviRoT ramdenime wiri. am SemTxvevaSi X da Y RerZebis markerebis adgilas Setanili funqciebi, cvladebi an

gamosaxulebebi gamovyoT erTimeorisagan mZimiT.

Tagvis marcxena RilakiT dawkapuneba grafikze gamoyofs mas. davinaxavT

marTkuTxeds, romelic moicavs mTel grafiks. mivitanoT Tagvis kursori

CarCosTan da rodesac is miiRebs xelisgulis formas, gadavaadgiloT grafiki

sasurvel adgilas.

grafikis zomis Sesacvlelad gamovyoT grafiki da mivitanoT Tagvis

maCvenebeli CarCoze mdebare marTkuTxedis formis patara Sav markerebTan. roca

Tagvis maCvenebeli miiRebs ormimarTuliani isris formas, Tagvis gadaTreviT

SesaZlebelia grafikis dapataraveba_gadideba. zomis Secvla xdeba vertikaluri,

horizontaluri da diagonaluri mimarTulebiT.

grafikis parametrebis Sesacvlelad SevasruloT mis areSi ormagi wkapuni

Tagvis marcxena RilakiT. gamoCndeba organzomilebiani grafikis parametrebis

Secvlis dialoguri fanjara (nax.5.3). igives mivaRwevT konteqsturi meniudan

Format... punqtis arCeviT an Format → Graph → X_Y Plot... brZanebiT.

nax.5.3. X_Y grafikis daformatebis dialoguri fanjara

X_Y grafikis daformatebis dialogur fanjaraSi X_Y Axes (X_Y RerZebi) CanarTis X_Axis da Y_Axis ganyofilebebSi gvaqvs almebi:

Log Scale – logariTmuli skalis dayeneba;

44

Grid Lines (badis xazebi) – RerZidan gamomavali xazebis dayeneba grafikis

badiT dafarvisaTvis; Numbered – RerZis numeracia; Autoscale – RerZis masStabis avtomaturi dayeneba; Show Markers – markerebis Cvenebis reJimis dayeneba; Auto Grid _ RerZidan gamomavali xazebis avtomaturi dayeneba; Number of Grids: – RerZidan gamomavali xazebis raodenobis miTiTeba. es almebi SeiZleba davayenoT cal_calke X da Y RerZebisaTvis.

Axis Style ganyofilebaSi Boxed gadamrTveli gamoiyvans grafiks CarCoSi da

RerZebis gareSe, Crossed _ uCarCod, magram RerZebiT, xolo None – uCarCod da

RerZebis gareSe. alami Equal Scales daayenebs erTnair masStabs orive RerZisaTvis.

Grid Color… Rilakis meSveobiT dayendeba badis xazebis sasurveli feri.

amave dialoguri fanjris Traces CanarTSi miTiTebulia wirebis parametrebi

(mag., xazis feri, stili da a.S.), romlebic SegviZlia survilisamebr SevcvaloT.

dialoguri fanjris Labels (warwerebi) CanarTSi Title ganyofilebis teqstur

velSi SeiZleba SevitanoT grafikis saTauri. aqve gadamrTveli Above an Below aCvenebs, grafikis zeviT Tu qveviT gvsurs saTauris ganlageba. Show Title alami

daayenebs saTauris Cvenebis reJims. amave CanarTis Axis Labels ganyofilebaSi

davayenoT, Tu gvsurs, almebi X_Axis da Y_Axis RerZebze warwerebis Sesaqmnelad da

SevitanoT es warwerebi Sesabamis teqtur velebSi.

Formatting Currently Selected X_Y Plot dialoguri fanjris Defaults CanarTSi

SeiZleba davayenoT alami Use for Defaults, ris Sedegad grafikis mimdinare

parametrebi iqneba damaxsovrebuli rogorc winaswari SeTanxmebis (by Default) parametrebi, xolo alami Change to Defaults winaswari SeTanxmebis parametrebs

Secvlis mimdinare parametrebiT am dokumentisaTvis.

nax.5.4_ze naCvenebia dekartis koordinatTa sistemaSi agebuli sxvadasxva

grafiki:

1. grafikis SablonSi X RerZis markerSi Setanilia x , Y RerZis – 2x2+5x_6. redaqtirebisas Setanilia saTauri, dayenebulia alami Show Title da

miTiTebulia saTauris adgilmdebareoba Above (zeviT).

2. grafikis agebamde gansazRvrulia diskretuli cvladi z , romelic

miuTiTebs z–is zRvrul mniSvnelobebs da Secvlis bijs, da y(z) funqcia.

grafikis SablonSi abscisTa RerZis markeris adgilas Setanilia z , xolo

ordinatTa RerZis _ y(z). redaqtirebisas dayenebulia gadamrTveli Crossed. 3. grafikis SablonSi abscisTa RerZis markerSi Setanilia r , ordinatTa sin(r).

Setanilia agreTve ordinatis zRvruli mniSvnelobebi: _0.5 da 1.

4. grafikis SablonSi abscisTa RerZis markerSi Setanilia sin(a), xolo

ordinatTa – cos(a). miRebulia e.w. parametruli grafiki anu grafiki,

romelic aCvenebs erTi funqciis (gamosaxulebis) damokidebulebas meore

funqciaze (gamosaxulebaze).

45

nax.5.4. dekartis sakoordinato sistemaSi agebuli grafikebi

5. grafikis SablonSi abscisTa RerZis markerSi Setanilia , xolo

ordinatTa – sin( ) , sin( ) + 1. dayenebulia gadamrTveli Crossed. Sedegad erT

koordinatTa sistemaSi miRebulia ori wiri, romelTa ordinatebi erT

cvladze arian damokidebuli.

6. grafikis SablonSi abscisTa RerZis markerSi Setanilia c , d , xolo

ordinatTa RerZis markerSi sin(c)2 , d + 3 . dayenebulia gadamrTveli Crossed. Sedegad erT koordinatTa sistemaSi miRebulia ori wiri, romelTa

ordinatebis mniSvnelobebi sxvadasxva cvladebze arian damokidebuli.

7. Seqmnilia matrica N da veqtorebi X da Y , romlebic warmoadgenen

Sesabamisad matricis pirvel da meore svets. grafikis SablonSi abscisTa

RerZis markeris adgilas miTiTebulia X , xolo ordinatTa _ Y. miRebulia

erTi veqtoris meoreze damokidebuleba.

yvela grafiks aqvs warwera: graph.1 , graph.2 da a.S. warwerebi Seqmnilia

calke da Drag and Drop tenikiT ganlagebulia sasurvel adgilze.

46

5.4 polaruli grafikis ageba da redaqtireba

Insert → Graph → Polar Plot brZanebiT (an Graph instrumentTa panelze

Sesabamisi Rilakis daWeriT) viziris adgilas Seiqmneba polaruli grafikis

Sabloni koordinatTa polarul sistemaSi (nax.5.5).

nax.5.5. polaruli grafikis Sabloni

koordinatTa polarul sistemaSi wertili moicema Tavisi kuTxis da R radius_veqtoris mniSvnelobebiT. grafiki aigeba kuTxis sxvadasxva

mniSvnelobebisaTvis, yvelaze xSirad icvleba 0–dan 2 –mde. saWiroebisamebr

momxmarebels winaswar SeuZlia sxva mniSvnelobebis miTiTeba (vTqvaT, kuTxes

diskretuli cvladis saxiT gamosaxviT: ). SesaZlebelia agreTve

uSualod grafikis Sablonze radius_veqtoris minimaluri da maqsimaruri

mniSvnelobebis miTiTeba.

polaruli grafikis daformatebisaTvis gamoiZaxeba dialoguri fanjara

Formatting Currently Selected Polar Plot, sadac Polar Axes CanarTis Radial (radialuri

RerZi) da Angular (kuTxis RerZi) ganyofilebebSi gvaqvs almebi: radialuri

RerZisaTvis _ Log Scale, Grid Lines, Numbered, Show Markers, Auto Grid, Number of Grids: da kuTxisaTvis _ Grid Lines, Numbered, Auto Grid, Number of Grids:. almebis

daniSnuleba ar gansxvavdeba X_Y grafikis daformatebis fanjris analogiuri

almebis daniSnulebisagan. Axes Style ganyofilebaSi gadamrTveli Perimeter gamoiyvans wrewiriT

SemosazRvrul grafiks, Crossed _ wrewiris gareSe da RerZebiT, None _ wrewiris da RerZebis gareSe.

Grid Color... RilakiT dayendeba badis xazebis sasurveli feri.

am dialoguri fanjris Traces, Labels da Defaults CanarTebs gaaCniaT igive

datvirTva, rac X_Y grafikis daformatebisas.

nax.5.6_ze naCvenebia polarul koordinatTa sistemaSi Seqmnili ramdenime

grafiki:

47

nax.5.6. polarul koordinatTa sistemaSi agebuli grafikebi

1. polaruli grafikis SablonSi qveda markeris adgilas Setanilia , xolo

marcxena markeris – sin ( ) + 1. dayenebulia bade kuTxis RerZisaTvis da

miTiTebulia misi feri (Savi).

2. polaruli grafikis SablonSi qveda markeris adgilas Setanilia , xolo

marcxena markeris – 2sin( ), cos( )2. redaqtirebisas dayenebulia bade kuTxis

RerZisaTvis da miTiTebulia misi feri (Savi). Traces CanarTSi meore wiris

feri Secvlilia lurjidan Savze, xolo misi moxazulobis stili

Secvlilia dash_ze ( ). miRebulia erT polarul koordinatTa sistemaSi

ori wiri.

3. polaruli grafikis SablonSi qveda markeris adgilas Setanilia x , xolo

marcxena markeris – sin(x), cos(x). redaqtirebisas dayenebulia Savi feris bade

kuTxis RerZisaTvis da Traces CanarTSi _ dash moxazuloba kosinusoidasTvis.

Sedegad erT polarul koordinatTa sistemaSi miRebulia ori wiri. isrebi

Seqmnilia Word_Si da Casmulia Mathcad_is dokumentSi. 4. polaruli grafikis SablonSi qveda markeris adgilas Setanilia y, xolo

marcxena markeris – cos(2y), sin(2y). daformatebisas orive miRebuli

wirisaTvis Traces CanarTSi miTiTebulia 4_is toli wona (Weight) da xazis tipi Solid.

48

5.5 3_ganzomilebiani zedapiris grafikis ageba da redaqtireba

3_ganzomilebiani zedapiris grafikis Sesaqmnelad saWiroa:

1) ganvsazRvroT orcvladiani funqcia funqciis an matricis saxiT;

2) Tu saWiroa, mivuTiToT cvladebis zRvruli mniSvnelobebi;

3) mivceT brZaneba Insert → Graph → Surface an Graph panelze davaWiroT

Sesabamis Rilakze. Seiqmneba zedapiris grafikis Sabloni (nax.5.7);

nax.5.7. zedapiris grafikis Sabloni

4) Sablonis qveda marcxena kuTxeSi ganlagebul markerSi SevitanoT

funqciis an matricis saxeli;

5) davaWiroT Enter klaviSs an davawkapunoT TagviT grafikis gareT.

Tu 3_ganzomilebiani grafikis Sesaqmnelad viyenebT funqcias da ara

matricas, aseT grafiks ewodeba swrafad miRebadi grafiki (Quick Plot). misi Seqmnisas Mathcad_i iyenebs winaswari SeTanxmebiT gansazRvrul damoukidebeli cvladebis

mniSvnelobebs (isini icvlebian _5_dan 5_mde) da am mniSvnelobebis Secvlis bijs

(0,5). Tu saWiroa, 3_ganzomilebiani grafikis daformatebis Sesabamis CanarTSi

(Quick Plot Data) SeiZleba am parametrebis Secvla.

funqcia SeiZleba iyos mocemuli sxvadasxvanairad, mag.:

)cos()sin(:),( yxyxF an

)sin(3)cos(3

3:),(

qpqp

pqpA

.

pirveli funqciis grafikis Seqmnisas x da y cvladebis zRvruli

mniSvnelobebi iqneba _5 da 5, xolo biji 0,5. Sablonis markerSi Sesatania F .

meore funqcia A(p,q) warmoadgens veqtor_funqcias. grafikis Seqmnisas p da q cvladebi icvleba _5_dan 5_mde bijiT 0,5 . x, y da z koordinatebi icvleba

veqtor_funqciaSi mocemuli formulebis mixedviT. Sablonis markerSi Sesatania

A.

49

funqcia SeiZleba agreTve ganvsazRvroT rogorc x, y da z koordinatebis damokidebuleba damoukidebel cvladebze, mag.:

vvux 2:),( aaR :)(

vuvuy :),( an 2:)( aaS

vuvuz 2:),( 23:)( aaaT .

aq pirvel SemTxvevaSi x, y da z warmoadgenen ori (u da v) cvladis funqcias,

romelnic icvlebian _5_dan 5_mde bijiT 0,5 ; Sablonis gamoZaxebis Semdeg

markerSi Sesatania (x, y, z). meore SemTxvevaSi R ,S da T warmoadgenen erTi cvladis

funqcias, damoukidebeli cvladi aseve icvleba _5_dan 5_mde bijiT 0,5 , Sablonis

markerSi unda SevitanoT (R,S,T). rodesac ori cvladis damokidebuleba mocemulia ara funqciiT, aramed

matricis saxiT, saWiroa ganvsazRvroT x da y cvladebis zRvruli mniSvnelobebi

da warmovidginoT Z(x,y) funqcia M matricis saxiT. mag.:

50..0:i , 51..0:j ,

iix 210: , jy j 41: ,

22:),( yxyxZ ,

),(:, jyixZjiM .

am magaliTSi x icvleba _10_dan 90_mde bijiT 2, y icvleba _4_dan 200_mde

bijiT 4. Seiqmneba 51_striqoniani da 52_svetiani M matrica, romlis i-_uri

striqonis da j_uri svetis gadakveTaze myofi elementi udris 22 jyix .

aqve aRvniSnoT, rom 3_ganzomilebiani grafikic, rogorc 2_ganzomilebiani,

SeiZleba iyos parametruli.

gamovyoT grafiki. davaWiroT Tagvis marcxena Rilaks da aseT

mdgomareobaSi gavwioT_gadmovwioT Tagvi grafikis areSi. davinaxavT, rom

rakursi, romliT Cans grafiki, Tagvis moZraobisas icvleba. am xerxiT advilad

SeirCeva CvenTvis sasurveli xedvis kuTxe.

grafikis Seqmnis Semdeg SesaZlebelia misi daformateba. grafikze TagviT

marcxena ormagi wkapuniT an konteqsturi meniudan Format... punqtis arCeviT an

mTavari menius Format → Graph → 3D Plot... brZanebiT gamoitaneba 3_ganzomilebiani

grafikis daformatebis dialoguri fanjara (nax5.8).

aq General CanarTis Display As: ganyofilebaSi gvaqvs gadamrTveli, romelic

iqneba CarTuli Surface Plot poziciaSi. Tu gadavrTavT gadamrTvels sxva poziciaSi

(Data Points – wertilovani grafiki, Bar Plot – svetovani grafiki, Contour Plot – konturuli grafiki, Vector Field Plot – veqtoruli velis grafiki, Patch Plot – calkeuli elementebisagan Sedgenili grafiki), igive funqcia sxva saxis grafikad

iqneba warmodgenili.

General CanarTis View ganyofilebis pirvel sam velSi miTiTebuli ricxvebi

aCveneben ra rakursiT Cans grafiki, xolo Zoom_Si miTiTebulia misi masStabi.

50

nax.5.8. 3_ganzomilebiani

grafikis daformatebis dialoguri fanjara

Axes Style ganyofilebaSi aris gadamrTveli Semdegi SesaZlo poziciebiT:

Perimeter (aCvenebs grafiks zomebiT perimetrze); Corner (aCvenebs grafiks zomebiT RerZebze); None (aCvenebs grafiks zomebis gareSe). alami Equal Scales daayenebs yvela

RerZze erTnair masStabs.

Frames ganyofilebaSi SeiZleba davayenoT ori alami: Show Border _ aCvenebs grafikis sazRvrebs, Show Box _ aCvenebs grafiks da marTkuTxa paralelepipeds,

romelSic is moqceulia.

Title CanarTis Graph Title ganyofilebis teqstur velSi SeiZleba SevitanoT

grafikis saTauri, ris Semdeg davayenoT gadamrTveli poziciaSi Above (zemoT),

Below (qvemoT) an Hide (damalva).

Axes CanarTSi xdeba TiToeuli RerZisaTvis badis dayeneba xazebis

raodenobis, sisqis da feris arCeviT.

aRvniSnoT, rom Quick Plot grafikis ageba SesaZlebelia ara mxolod dekartis,

aramed agreTve sferul da cilindrul koordinatTa sistemebSi. amisaTvis Quick Plot grafikis daformatebisas Quick Plot Data CanarTis Coordinate System ganyofilebaSi unda avirCioT ara Cartesian (dekartis koordinatTa sistema),

romelic dayenebulia winaswari SeTanxmebiT, aramed Spherical (sferuli) an

Cylindrical (cilindruli).

nax.5.9_ze (a,b,c,d magaliTebi) naCvenebia 3_ganzomilebiani zedapiris

grafikebi, xolo e magaliTSi moyvanilia 3_ganzomilebiani wertilovani grafiki,

romelic miRebulia d_dan gadamrTvelis Display As: Sesabamis poziciaSi dayenebiT.

51

nax.5.9. 3_ganzomilebiani grafikebis magaliTebi

a da b grafikebi warmoadgenen Quick Plot tipis zedapiris grafikebs. a_Si gamoyenebulia winaswari SeTanxmebiT mocemuli zRvruli mniSvnelobebi, xolo

b_Si es mniSvnelobebi da biji, romliTac icvleba damoukidebeli cvladebi,

Secvlilia. amisaTvis Quick Plot grafikebisaTvis arsebobs Semdegi wesi:

1. grafikze ormagi wkapuniT SevideT 3D Plot Format dialogur

fanjaraSi, sadac avirCioT QuickPlot Data CanarTi;

2. Range 1 (1_li diapazoni) velSi davayenoT X RerZisaTvis sawyisi da bolo

mniSvnelobebi (Cven magaliTSi esaa Sesabamisad 0 da 5), xolo # of Grids (badis danayofTa raodenoba) velSi mivuTiToT sasurveli raodenoba

(Cven magaliTSi 5);

3. Range 2 (me_2 diapazoni) velSi davayenoT Y RerZisaTvis sawyisi da bolo

mniSvnelobebi (0 da 5) da mivuTiToT badis danayofTa raodenoba (15).

aqve aRvniSnoT, rom Mathcad_i “dagveTanxmeba” Cvens mier miTiTebul

cvladebis zRvrul mniSvnelobebs mxolod im SemTxvevaSi, rodesac dekartis

(Cartesian) koordinatTa sistemaSi asagebia grafiki, romelic asaxavs Cveulebriv

orcvladian funqcias. danarCen SemTxvevebSi Mathcad_i TviTon airCevs zRvrul

mniSvnelobebs X, Y da Z RerZebisaTvis, romlebic Seesabameba mocemul funqcias.

52

c grafikis redaqtirebisas 3D Plot Format dialoguri fanjris Appearance CanarTis Fill Options (Sevsebis ofciebi) ganyofilebaSi dayenebulia Fill Surface (zedapiris Sevseba) gadamrTveli, ris Semdeg Color Options (ferebis ofciebi)

ganyofilebaSi dayenebulia Solid Color gadamrTveli. marjvniv mdgom patara

marTkuTxedze dawkapunebiT gamoZaxebulia ferTa palitra, sadac arCeulia

stafilosferi; Line Options (wirebis ofciebi) ganyofilebaSi dayenebulia

gadamrTveli Contour Lines da Weight_Si (wona) miTiTebulia wiris sisqe 2.0; Color Options ganyofilebaSi dayenebulia gadamrTveli Solid Color da datovebulia

winaswari SeTanxmebiT mocemuli Savi feri.

d grafikis redaqtirebisas 3D Plot Format dialoguri fanjris Axes CanarTSi X RerZisaTvis Grids (bade) velSi dayenebulia alami Draw Lines, xolo Line Color_Si badis xazebis ferad aRebulia ruxi.

e grafikis redaqtirebisas 3D Plot Format dialoguri fanjris Appearance CanarTSi Points Options (wertilebis ofciebi) velSi, sadac winaswari SeTanxmebiT am

tipis grafikisaTvis dayenebulia simboloebis Cvenebis reJimi anu dayenebulia

alami Draw Points, Secvlilia simboloebis moxatuloba: winaswari SeTanxmebiT iyo

dots (wertilebi), dayenda Boxes (yuTebi) zomiT 1.5. Color Options–Si CarTulia

gadamrTveli Colormap (ferebis sqema), ris Sedegad miRebulia grafiki, romelSic

funqciis sxvadasxva dones sxvadasxva feri aqvs.

5.6 konturuli grafikis Seqmna

Insert → Graph → Contour Plot brZanebiT an Graph panelze Sesabamisi Rilakis

daWeriT Seiqmneba 3_ganzomilebiani konturuli grafikis Sabloni. konturuli

grafiki – erTnairi donis wirebis ruka – farTod gamoiyeneba, magaliTad,

kartografiaSi. is xSirad Seicavs met informacias, vidre zedapiris grafiki,

romelSic zedapiris erTi nawili sakmaod xSirad dafarulia sxva nawilebiT. am

grafikis Seqmnis da redaqtirebis procesi arsebiTad ar gansxvavdeba zedapiris

grafikisagan. nax.5.10_is a magaliTSi moyvanilia konturuli grafiki. 3_ganzomilebiani grafikebisTvisac SeiZleba erT grafikul areSi ramdenime

funqciis grafikis ageba. praqtikuli gamoyeneba hpova mxolod konturuli (an

veqtoruli velis) da zedapiris (wertilovani an svetovani) erTi da igive

funqciis amsaxveli grafikebis erT grafikul areSi Seqmna.

ganvixiloT konturuli da Data Points tipis erTi funqciis grafikebis erT

sakoordinato sistemaSi warmodgena magaliTze:

53

nax.5.10. konturuli, wertilovani, svetovani da veqtoruli velis grafikebi

1) ganvsazRvroT funqcia:

22

4041

40411:),(

yxyxP ;

2) Insert → Graph → Contour Plot brZanebiT miviRebT Sablons, sadac markerSi

SevitanoT P,P; 3) davaWiroT Enter klaviSs. Sedegad erT grafikul areSi miiReba ori

grafiki: konturuli da meore – by Default – zedapiris (nax.5.11 a). 4) SevideT daformatebis reJimSi;

5) General CanarTis Display As: ganyofilebaSi avirCioT Plot2 da davayenoT

grafikis tipebis gadamrTveli Data Plot_ze; 6) davaWiroT OK Rilaks.

miviRebT 2 grafiks erT sakoordinato sistemaSi: konturul da Data Plot tipis (nax.5.11 b).

nax.5.11 c_zec agebulia 2 grafiki erT grafikul areSi: veqtoruli velis da

zedapiris grafikebi. Tagvis gawev_gamoweviT Secvlilia xedvis rakursi.

54

nax.5.11. erT sakoordinato sistemaSi ori grafikis agebis magaliTebi

5.7 wertilovani da svetovani grafikebis Seqmna

Insert → Graph → 3D Scatter Plot brZanebiT an Graph panelze Sesabamisi Rilakis

daWeriT Seiqmneba 3_ganzomilebiani wertilovani grafikis Sabloni. wertilovani

grafikis agebis da redaqtirebis procesi ar gansxvavdeba sxva tipis

3_ganzomilebiani grafikebis Seqmnis da redaqtirebis procesisagan. aRvniSnoT,

rom wertilovani grafikis redaqtirebisas SeiZleba SevcvaloT wertilebis zoma,

maTi gamosaxuleba (mag., SevcvaloT wertilebi jvaredina formis simboloebiT,

wrewirebiT, kvadratebiT da a.S.) da feri. nax5.10 b_ze moyvanilia wertilovani

grafiki. redaqtirebis reJimSi Secvlilia gamoyenebuli simbolo (3D Plot Format dialogur fanjris Appearance CanarTis Points Options ganyofilebaSi miTiTebulia

simbolo x’s da simboloebis feri – wiTeli).

Insert → Graph → 3D Bar Chart brZanebiT an Graph panelze Sesabamisi Rilakis

daWeriT Seiqmneba 3_ganzomilebiani svetovani grafikis (histogramis) Sabloni.

histogramaSi svetebis simaRle X da Y RerZebis koordinatebis mniSvnelobebze

damokidebulia. svetovani grafikis magaliTi moyvanilia nax.5.10 c_ze.

55

5.8 veqtoruli velis grafikis Seqmna

Insert → Graph → Vector Field Plot brZanebiT an Graph panelis igive

saxelwodebis Rilakis daWeriT Seiqmneba veqtoruli velis grafikis Sabloni. es

grafiki warmoadgens mokle isrebis – veqtorebis erTobliobas. isari mimarTulia

zedapiris simaRlis zrdis mxares, xolo isrebis ganlagebis simkvrive zrdis

siCqarezea damokidebuli. grafikis aseTi forma xSirad gamoiyeneba

eleqtromagnituri, siTburi da gravitaciuli velebis warmodgenisaTvis.

veqtoruli velis grafiki moyvanilia nax.5.10 d_ze.

5.9 grafikebis Seqmna ostatis meSveobiT

Insert → Plot Wizard brZanebiT gamoiZaxeba grafikis Seqmnis ostati. ostatis

muSaobis pirvel safexurze Plot Type dialogSi xdeba grafikis tipis SerCeva

(nax.5.12).

nax.5.12. grafikis Seqmnis ostatis muSaobis pirveli safexuri

ostats SeuZlia Seqmnas Semdegi tipis grafikebi: Surface Plot, Contour Plot, Vector Field Plot, Bar Plot an Scatter Plot. aqve vnaxavT SerCeuli tipis nimuSs. Rilak

Next>_ze daWeriT xdeba me_2 safexurze gadasvla, sadac SeirCeva grafikis

garegnuli saxe.

nax.5.13_ze moyvanilia me_2 safexuris Appearance dialogi, sadac gvaqvs ga-damrTveli: Draw lines (xazebis Cveneba), Fill surface with color (zedapiris Sevseba feriT), Fill surface and draw lines (zedapiris Sevseba da xazebis Cveneba). marjvniv vnaxavT

Sesabamis nimuSs. <Back Rilakze daWeriT gadavdivarT wina safexurze, sadac Tu

gvsurs SeiZleba movaxdinoT saWiro cvlilebebi, xolo Next> Rilakze daWeriT

gadavdivarT bolo, me_3 safexurze.

56

nax.5.13. grafikis Seqmnis ostatis muSaobis meore safexuri

nax.5.14_ze naCvenebia me_3 safexuris Coloring dialogi, sadac gadamrTveli

gvaZlevs gaferadebis stilis erT_erT Semdeg variants: Color by height (feris Secvla simaRlis cvlasTan erTad), Color using lighting (feri ganaTebiT), Solid color (feri ar icvleba). Tu arCeulia gaferadebis stili Solid color , marjvniv naCvenebi

iqneba feri, romelzec dawkapunebiT gamoiZaxeba palitra, sadac SeiZleba

SevarCioT sxva feri. Finish Rilakze daWeriT ostatis muSaoba dasruldeba.

nax.5.14. grafikis Seqmnis ostatis muSaobis mesame safexuri

samuSao furcelze davinaxavT grafikis Sablons, sadac markerSi Sesatania

funqciis an matricis saxeli. Enter klaviSze daWeriT an grafikis gareT

dawkapunebiT davinaxavT ostatis mier Seqmnil grafiks.

57

5.10 matricis Casma dokumentSi

rogorc ukve iyo naTqvami, Insert → Matrix... brZanebiT, Ctrl + M swrafmoqmedebis klaviSebiT Man Matrix panelze matricis Sablonze dawkapunebiT

gamoiZaxeba matricis Casmis dialoguri fanjara Insert Matrix (nax.5.15), romelSic

Rows: da Columns: velebSi misaTiTebelia matricis striqonebisa da svetebis

raodenoba.

nax.5.15. matricis Casmis dialoguri fanjara

amis Semdeg Tu avirCevT Insert Rilaks (am dros dialoguri fanjara rCeba

ekranze) an davaWerT OK Rilaks an klaviaturis Enter klaviSs (am dros dialoguri

fanjara ixureba), viziris adgilas Caismeba matricis an veqtoris Sabloni.

SablonSi Sesatania matricis (veqtoris) elementebis mniSvnelobebi. matricis

(veqtoris) elementebi SeiZleba iyon ricxvebi, mudmivebi, cvladebi da

maTematikuri gamosaxulebebi.

Tu Cven davasrulebT matricis Sevsebas ise, rom yvela markeri ar iqneba

Setanili, Seuvsebeli markerebi gawiTldebian.

Insert Matrix dialoguri fanjris meSveobiT SeiZleba gavadidoT an

SevamciroT matricis zoma. amisaTvis SevideT am dialogSi, roca kursori

imyofeba matricis Sablonis an Sevsebuli matricis SigniT. Rows: da Columns: velebSi SevitanoT Casasmeli (wasaSleli) striqonebis da svetebis raodenoba.

davaWiroT Insert (Delete) Rilaks. Mathcad_i Casvams striqonebs gamoyofili

elementis qveviT, xolo svetebs _ gamoyofili elementis marjvniv. striqonebis

(svetebis) waSlas Mathcad_i iwyebs gamoyofili elementis striqonidan (svetidan)

da agrZelebs striqonebis waSlas qveviT, xolo svetebis marjvniv.

mag., Tu gvsurs wavSaloT romelime sveti, davayenoT kursori am svetis

romelime elementSi, SevideT Insert Matrix dialogSi, Rows: velSi SevitanoT 0,

Columns: velSi _ 1 da davaWiroT Delete Rilaks.

58

5.11 funqciebis Casma

Insert → Function... brZanebiT an Ctrl + E swrafmoqmedebis klaviSebiT

gamoiZaxeba Insert Function dialoguri fanjara (nax.5.16).

nax.5.16. funqciis Casmis dialoguri fanjara

fanjris marcxena nawilSi moyvanilia funqciebis kategoriebis CamonaTvali.

saWiro kategoriaze dawkapunebis Semdeg fanjris marjvena nawilSi vnaxavT am

kategoriis funqciebis sias. Tu Cven ar viciT, romel kategorias ekuTvnis

funqcia, is moiZebneba All kategoriaSi, romelSic moyvanilia yvela funqcia

alfabetis mixedviT. dialoguri fanjris Qqveda nawilSi mokled moyvanilia

arCeuli funqciis aRwera. OK an Insert Rilakebis arCeviT an klaviaturis Enter klaviSze dawkapunebiT kursoris adgilas Caismeba funqciis Sabloni.

5.12 sazomi erTeulis Casma

Insert → Unit... brZanebiT an Ctrl + U swrafmoqmedebis klaviSebiT gamoiZaxeba

sazomi erTeulebis Casmis dialoguri fanjara (nax.5.17).

Insert Unit dialoguri fanjris Dimension (ganzomileba) ganyofilebaSi

moyvanilia ganzomilebis mqone sidideebis CamonaTvali, xolo Unit ganyofilebaSi

ganzomilebebi. winaswari SeTanxmebiT gamoyenebulia SI sistema. Tu Mathcad_i muSaobs ganzomilebis mqone sidideebTan, cvladebis mniSvnelobebi iqneba

gamoTvlili da gamotanili saWiro ganzomilebebis miTiTebiT.

59

nax.5.17. sazomi erTeulebis Casmis dialoguri fanjara

5.13 naxatis Casma

Mathcad_s SeuZlia moaxdinos sxva programebSi (AutoCAD, PCAD da a.S.) Seqmnili grafikuli failebis importireba.

Insert → Picture brZanebiT an Matrix panelze Picture Rilakze dawkapunebiT an

Ctrl + T swrafmoqmedebis klaviSebiT xdeba naxatis Sablonis Casma. Sablons aqvs

erTaderTi markeri qveda marcxena kuTxeSi, sadac Tu Casasmeli faili mimdinare

direqtoriaSi imyofeba, Sesatania failis saxeli, winaaRmdeg SemTxvevaSi ki _

failis sruli misamarTi. es monacemebi striqonuli tipisaa da amitom saWiroa

maTi brWyalebSi Casma. amis Semdeg Tagvis marcxena RilakiT naxatis gareT

dawkapunebiT moxdeba naxatis importireba.

ra Tqma unda, SesaZlebelia agreTve movaxdinoT sxva programebiT Seqmnili

naxatebis kopireba gacvlis buferidan (brZanebebiT Edit → Copy an Edit → Cut naxatis Semqmnel programaSi, Semdeg Edit → Paste an Edit → Paste Special Mathcad_Si).

nebismier matricas SeiZleba SevusabamoT nacrisferi skalis gradaciebSi

Sesrulebuli naxati. amisaTvis:

1. davawkapunoT furclis cariel adgilas;

2. Insert → Picture brZanebiT an Matrix panelze Picture Rilakze dawkapunebiT an

Ctrl + T swrafmoqmedebis klaviSebiT SevqmnaT naxatis Sabloni;

3. SevitanoT markerSi matricis saxeli. Sedegad miviRebT matricis amsaxvel naxats. matricis yoveli elementi

Seesabameba naxatis erT piqsels, amasTan matricis 0_is toli elementi aisaxeba

Sav ferad, xolo 255_is toli _ TeTr ferad. ricxvebs, romlebic ar Sedian 0 _

255 diapazonSi, Mathcad_i naxatis Sesaqmnelad “Secvlis” da “miiyvans” zRvrul

mniSvnelobebamde, xolo ricxvebis wiladur nawilebs ar miiRebs mxedvelobaSi.

60

Tu gvaqvs erTi da igive ganzomilebis mqone 3 matrica, Mathcad_s SeuZlia am

matricebis safuZvelze Fferadi naxatis Seqmna, vTqvaT, erTi matricis wiTeli,

meore – mwvane, xolo mesame – lurji komponentad warmodgeniT.

naxatis konteqsturi meniudan Picture toolbar punqtis SerCeviT SesaZlebelia

misi redaqtireba. redaqtirebisas SeiZleba SevcvaloT naxatis zomebi, masStabi,

kontrastuloba, sikaSkaSe da a.S.

5.14 ubnis formireba da gverdis gawyveta

Insert → Area brZanebiT Mathcad_i Casvams dokumentSi wirebis wyvils,

romlebic aCveneben ubnis sazRvrebs.

Format menius punqtebis meSveobiT SeiZleba ubnisaTvis saxelis miniWeba,

misi Caketva, gaReba, SekumSva da gafarToeba. ubnis sazRvari moiniSneba masze

dawkapunebiT an Tagvis waTreviT mis gaswvriv. moniSnuli sazRvari SeiZleba

gadavaadgiloT ubnis gasazrdelad an Sesamcireblad.

ubnebis raodenoba dokumentSi ar aris SezRuduli, magram ar aris

daSvebuli ubnis Casma arsebuli ubnis farglebSi.

ubnis wasaSlelad gamovyoT misi orive sazRvari da mivceT Edit → Delete an Edit → Cut brZaneba an davaWiroT Standard panelis Cut Rilaks.

gverdis gawyveta xdeba Insert → Page Break brZanebiT. es brZaneba gamoiyeneba

im situaciaSi, rodesac Print Preview reJimSi gamoCndeba, rom gverdis qveda nawilSi

ganlagebuli romelime grafiki an cxrili ar eteva am gverdze an paragrafis

saTauri aRmoCndeba erT gverdze, xolo TviT paragrafi iwyeba meoreze.

5.15 maTematikuri da teqsturi areebis Casma

maTematikuri da teqsturi areebis Casma xdeba Insert → Math Region da Insert → Text Region brZanebebiT.

rodesac teqsturi are aqtiuria, SesaZlebelia misi daformateba Format → Text... brZanebis meSveobiT, Tumca am dialogur fanjaraSi gvaqvs teqstur

redaqtorebTan SedarebiT (mag., MSWord_Tan) mwiri SesaZleblobani.

teqstur areSi teqstis Setanis Semdeg dokumentis cariel adgilze

dawkapunebiT komentarebis Seqmnis procesi dasruldeba.

Mathcad_Si SesaZlebelia teqstur areSi maTematikuri formulebis Casma.

amisaTvis teqsturi markeri davayenoT teqsturi aris im adgilas, sadac unda

CavweroT formula. brZaneba Insert → Math Region gamoiyvans am adgilas

maTematikuri aris Sablons patara Savi kvadratis saxiT. am SablonSi SeiZleba

CavweroT formulebi Mathcad_Si arsebuli Cveulebrivi xerxebiT. cxadia, teqsturi

61

aris formulebi ar gamoiTvlebian. arsebuli maTematikuri gamosaxulebebis Casma

teqstur areSi SesaZlebelia Edit → Copy, Edit → Paste brZanebebiT.

5.16 komponentebis Casma

Insert → Component... brZanebiT gamoiZaxeba komponentebis Casmis ostati.

ostati warmoadgens ramdenime safexurebian dialogs, romlis pirvel safexurze

(nax.5.18) xdeba im komponentis anu sxva programis SerCeva, romelic gvsurs

mivuerToT Mathcad_s. amasTan SerCeva xdeba mxolod arsebuli siidan.

nax.5.18. komponentebis Casmis ostatis muSaobis pirveli safexuri

avirCioT, vTqvaT, Microsoft Excel_i. Next> Rilakze dawkapunebiT gadavalT

Semdeg safexurze – Excel Setup Wizard (Excel_is dayenebis ostati) dialogSi (nax.5.19).

masSi gvaqvs gadamrTveli: Create an empty Excel worksheet (Excel_is carieli

samuSao furclis Seqmna) an Create from file: (failidan Seqmna). avirCioT saWiro,

vTqvaT, Create an empty Excel worksheet. aqve SegviZlia davayenoT alami Display as Icon (gamoaCine piqtogramis saxiT). Next> Rilakze dawkapunebiT gadavalT Semdeg

safexurze (nax.5.20), xolo <Back Rilakze dawkapunebiT davbrundebiT wina

fanjaraSi, sadac SegviZlia SevitanoT sasurveli koreqtireba. Excel_is dayenebis ostatis me_2 dialogur fanjaraSi Inputs da Outputs

velebSi misaTiTebelia Sesabamisad Mathcad_dan Excel_Si Sesatani da Excel_dan Mathcad_Si gamosatani monacemebis raodenoba. amasTan es raodenoba (Excel_is SemTxvevaSi) ar aris limitirebuli da SeizRudeba praqtikulad mxolod

kompiuteris mexsierebis moculobiT da siCqariT. Starting Cell areSi Sesatania

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nax.5.19. Excel_is dayenebis ostatis dialoguri fanjara (I)

sawyisi ujredis nomeri. mag., Tu Input cvladi warmoadgens 44 _ ganzomilebian

matricas da sawyis ujredad mivuTiTebT A1, matricis mniSvnelobebi daikaveben

Excel_is A1 : B4 diapazons. Range areSi Sesatania ujredebis diapazoni, sadac

moTavsdeba Output cvladebi.

nax.5.20. Excel_is dayenebis ostatis dialoguri fanjara (II)

davaWiroT Finish Rilaks. Mathcad_is samuSao furcelze davinaxavT Excel_is eleqtronuli cxrilis Sablons. Input cvladebis saxelebi SevitanoT qveda

markerSi, xolo Output cvladebis _ miniWebis simbolos marcxniv mdebade markerSi.

Tu davawkapunebT Casmuli komponentis gareT, Input cvladebi aRmoCndebian Excel_is

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cxrilSi. komponentze ormagi wkapuniT moxdeba misi gaaqtiureba da davinaxavT

komponentis meniusa da panelebs, ase rom Mathcad_idan gamousvlelad SevZlebT

muSaobasK Excel_Si. Excel_Tan muSaobis damTavrebis Semdeg Mathcad_Si dafiqsirdeba Output cvladebis mniSvnelobebi.

komponentebis Casma xdeba aseve Insert → Data da Insert → Controls brZanebebis meSveobiT.

5.17 monacemebis Casma

Insert → Data brZanebis qvebrZanebebia: Table _ eleqtronuli cxrilis Casma;

File Input _ monacemTa failebis importireba;

File Output _ monacemTa failebis eqsportireba.

Casmuli eleqtronuli cxrilis monacemebis gamoyeneba Mathcad_Si Insert → Data → Table brZanebiT SesaZlebelia Mathcad_is samuSao furcelSi

nax.5.21. Mathcad_is samuSao furcelSi Casmuli cxrilidan monacemTa

gamoyenebis magaliTi

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CavsvaT eleqtronuli cxrili, romelic arsebiTad masivs warmoadgens. marcxena

zeda kideSi arsebuli markeris adgilas avkriboT sasurveli saxeli da SevavsoT

cxrili monacemebiT. nax.5.21_ze mocemulia Mathcad_is samuSao furcelSi Casmuli

cxrilidan monacemTa gamoyenebis magaliTi.

Casmuli cxrilis ganzomilebis Sesacvlelad gamovyoT cxrili da

mivitanoT Tagvis maCvenebeli marTkuTxedis formis patara Sav markerebTan. roca

Tagvis maCvenebeli miiRebs ormimarTuliani isris formas, Tagvis gadaTreviT

SesaZlebelia cxrilis dapataraveba_gadideba.

monacemTa eqsportireba da importireba menius Insert → Data punqtiT SesaZlebelia monacemTa failebis importireba

da eqsportireba. Insert → Data → File Input brZanebis gamoyenebis Semdeg gamodis File Options dialoguri fanjara (nax.5.22), romlis meSveobiT xdeba monacemTa

importireba.

nax.5.22. dialoguri fanjara File Options

monacemTa importirebisaTvis:

1. File Format: siisebur velSi moTavsebulia im programebis CamonaTvali,

saidanac SesaZlebelia monacemebis importireba. avirCioT sasurveli

programa am siidan;

2. teqstur velSi avkriboT sasurveli failis sruli saxeli an gamoviyenoT

Browse... Rilaki, romelic gadagviyvans Read from file dialogSi; am dialogis

Look in: velSi avirCioT katalogi, sadac aris Cawerili Cveni faili,

movZebnoT faili da movaxdinoT masze orjeradi wkapuni. teqstur velSi

Caiwereba failis sruli saxeli;

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3. Next Rilakis meSveobiT gadavideT meore safexurze, sadac xdeba

importirebul monacemTa adgilis dakonkreteba (mag., Excel_is failis

arCevisas samuSao furclis da ujredebis misamarTebis miTiTeba);

4. Tu saWiroa, davayenoT alami Use comma as decimal symbol (aTobiT wiladebSi

mTeli nawilis wiladuri nawilisagan mZimiT gamoyofa);

5. davayenoT, Tu saWiroa, alami Use relative file path. amiT failis sxva misamarTze

gadaadgilebis Semdegac Mathcad_i SeZlebs misi axali adgilmdebareobis

gansazRvras.

6. davaWiroT Finish Rilaks.

Mathcad_is samuSao furclis moniSnul adgilas Caismeba piqtograma failis

sruli saxeliT, romlis marcxena zeda kideSi, miniWebis operatoris win

arsebuli markeris adgilas unda mivuTiToT sasurveli saxeli. Casmuli regionis

gareT Tagvis dawkapunebis Semdeg Mathcad_i kiTxulobs Casmuli failis monacemebs

da SesaZlebloba gveZleva es monacemebi gamoviyenoT Mathcad_is matricebSi an

ricxviT diapazonebSi. nax.5.23_ze naCvenebia Casmuli failidan (Cven SemTxvevaSi

aRebulia Excel_is faili) monacemebis gamoyenebis magaliTi.

nax.5.23. importirebuli failidan monacemebis gamoyenebis magaliTi

analogiurad sruldeba Mathcad_idan monacemTa eqsportireba, mxolod

amisaTvis viyenebT Insert → Data → File Output brZanebas.

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samuSao furcelze arsebuli monacemebis saxeli unda Caiweros Casmuli

piqtogramis marcxena qveda kideSi arsebuli markeris adgilas. monacemebi

dafiqsirdeba im failSi, sadac movaxdineT eqsportireba. nax.5.24_ze naCvenebia

eqsportirebis magaliTi.

nax.5.24. Mathcad_idan monacemTa eqsportirebis magaliTi

5.18 mmarTveli komponentebis Casma

Insert → Control brZanebiT SesaZlebelia Mathcad_is samuSao furcelSi Caisvas

mmarTveli komponentebi rogoricaa:

damoukidebeli gadamrTveli _ alami (Check Box); erTmaneTze damokidebuli gadamrTveli (Radio Button);

Rilaki (Push Button); slaidi (Slider);

teqsturi veli (Text Box); siiseburi veli (List Box).

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igive moqmedebebis Sesruleba SesaZlebelia Controls panelis (nax.5.25)

Rilakebis meSveobiT.

nax.5.25. Controls panelis Rilakebi

5.19 Mathcad_is dokumentSi sxva obieqtis Casma

Mathcad_s aqvs SesaZlebloba gamoiyenos OLE (Object Link Embedding) meqanizmi sxva gafarToebis failebTan kavSiris damyarebisaTvis CaSenebuli (Embedding) an

bmulis (Link) saxiT. Oobieqti warmoadgens ZiriTad dokumentSi gadatanil

monacemTa nebismier tips anu es SeiZleba iyos teqstis fragmenti, formula an

misi nawili, grafiki, eleqtronulo cxrili, videoklipi, faili da a.S. obieqtis

Casma ZiriTad dokumentSi SesaZlebelia rogorc kopirebiT da specialuri

CasmiT, aseve Insert → Object... brZanebiT. Aam ukanasknels xmaroben, rodesac

romelime faili mTlianad Casasmelia ZiriTad dokumentSi. aRvniSnoT, rom

dokuments, sadac xdeba obieqtis Casma, uwodeben klients, xolo obieqts, romlis

CaSeneba an mibma xdeba, uwodeben servers. gansxvaveba am or operaciaTa Soris

Semdegia:

Mathcad_is dokumentSi sxva gafarToebis failis CaSenebisas masSi

Semdgomi cvlilebebi ar aisaxeba Mathcad_is dokumentSi; Mathcad_is dokumentSi sxva gafarToebis failis mibmis SemTxvevaSi

cvlilebebi (redaqtireba) aisaxeba rogorc Mathcad_is dokumentSi, aseve serverSi anu mibmul failSic.

Mathcad_Si sxva obieqtis CaSeneba 1. avirCioT menius Insert → Object... brZaneba. gamova dialoguri fanjara Insert

Object (nax.5.26); 2. dialoguri fanjris Create New gadamrTvelis arCevisas Object Type velidan

sasurveli programis miTiTebiT Caismeba sruliad axali dokumenti, xolo

Create from File gadamrTvelis arCeviT SesaZlebelia ukve arsebuli failis

Casma. am ukanasknelis arCeviT Seicvleba dialoguri fanjris saxe (nax.5.27).

Browse... Rilakis meSveobiT SesaZlebelia katalogTa da failebis xeze

sasurveli failis moZebna;

3. davaWiroT OK Rilaks. Sedegad im adgilas, sadac manamde iyo aqtiuri

kursori, Mathcad_Si CaSendeba sxva obieqti.

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nax.5.26. obieqtis Casmis dialoguri fanjara (I)

nax.5.27. obieqtis Casmis dialoguri fanjara (II)

Mathcad_Si sxva obieqtis mibma. 1. avirCioT menius Insert → Object... brZaneba. gamova dialoguri fanjara Insert

Object (nax.5.26); 2. avirCioT gadamrTveli Create from File. obieqtis Casmis dialoguri fanjara

Seicvleba (nax.5.27). Browse... Rilakis meSveobiT sasurveli failis miTiTebis

Semdeg davayenoT Link alami, rac mogvcems bmuli kontaqtis damyarebis saSualebas.

Tu ar gvsurs Mathcad_Si CaSenebuli an bmuli dokumentis srulad danaxva,

Display As Icon almis dayenebiT SesaZlebelia obieqtis piqtogramis saxiT warmoCena.

obieqtis Casma piqtogramis saxiT SesaZlebelia agreTve misi iarliyis TagviT

gadaTreviT, vTqvaT, Windows Explorer_is fanjridan.

CaSenebuli obieqtis redaqtireba.

movniSnoT CaSenebuli obieqti masze TagviT erTjer dawkapunebiT. Mmenius

Edit → Object brZaneba xelmisawvdomi gaxdeba. Mmisi saxe (Edit → Document Object, Edit → Object Equation da a.S.) damokidebulia obieqtis tipze. mas gaaCnia Edit da Open

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qvebrZanebebi. Edit qvebrZanebis gamoyenebiT SesaZlebelia Mathcad_is programaSive CaSenebuli failis redaqtireba. Open qvebrZanebis arCevisas gadavalT CaSenebuli

failis programaSi da iq vaxdenT redaqtirebas.

CaSenebuli obieqtis redaqtireba SesaZlebelia agreTve masze TagviT

orjeradi dawkapunebiT, romelic faqtobrivad Edit → Document Object (an am punqtis sxva saxecvla) → Edit brZanebis tolfasia.

aRsaniSnavia, rom redaqtireba, romelsac SevasrulebT CaSenebul obieqtze,

ar aisaxeba mis wyaroze (igulisxmeba obieqti, romlis CaSenabac moxda).

5.20 miTiTebebis Casma

zog SemTxvevaSi saWiroa erTi da igive gansazRvrebebis da gamoTvlebis

xSiri gameoreba. ra Tqma unda, amas advilad mivaRwevT Edit → Copy da Edit → Paste brZanebebiT an Sesabamisi areebis Drag and Drop teqnikiT kopirebiT erTi

dokumentidan meoreSi, magram im SemTxvevaSi, roca ganmeorebadia mTeli

dokumentis gansazRvrebebi da gamoTvlebi, umjobesia mTavar dokumentSi CavsvaT

e.w. miTiTeba (Reference) meore dokumentze. am dros meore dokumenti misaRwevadi xdeba misi gaxsnis gareSe.

miTiTebebis Casasmelad:

1. davawkapunoT mTavari dokumentis Tavisufal adgilas – iq, sadac gvsurs

miTiTebis Casma;

2. mivceT Insert → Reference... brZaneba, gamoCndeba Insert Reference dialoguri

fanjara (nax.5.28);

nax.5.28. miTiTebis Casmis dialoguri fanjara

3. Insert reference to file velSi CavweroT im failis misamarTi, romelzec miTiTeba

xdeba. misamarTi Caiwereba klaviaturidan an Browse... Rilakis meSveobiT. am velSi

SesaZlebelia agreTve Web_qselSi ganlagebul Mathcad_is failis saxelis Cawera.

4. davaWiroT OK Rilaks. Sedegad Mathcad_i Casvams miTiTebas, rasac Cven

davinaxavT marTkuTxedSi Casmuli patara Canaweris saxiT. am Canaweris marjvniv da

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qveviT moqmedebs miTiTebuli dokumentis gansazRvrebebi da gamoTvlebi, xolo

masze ormagi wkapuni gaxsnis miTiTebul dokuments Tavis fanjaraSi –

redaqtirebisaTvis. nebismieri sxva obieqtis msgavsad, SesaZlebelia am Canaweris

gadaadgileba an, vTqvaT, waSla. miTiTebis Casmis Semdeg Cven ver vxedavT

miTiTebuli dokumentis obieqtebs da formulebs, magram mTavari dokumenti

“xedavs” da muSaobs maTTan ise rogorc am dokumentSi Setanil monacemebTan.

aRvniSnoT, rom winaswari SeTanxmebiT miTiTebuli dokumentis sxva

misamarTze gadaadgilebis Semdeg Mathcad_i ver SeZlebs misi axali

adgilmdebareobis gansazRvras. Tu gvsurs, rom Mathcad_ma SeZlos amis gakeTeba,

saWiroa Insert Reference dialogur fanjaraSi Use relative path for reference almis

dayeneba.

Tu miTiTebuli dokumenti saWiroebs modifikacias, mTavari dokumentis

ganaxlebisaTvis:

1. movaxdinoT saWiro cvlilebebi miTiTebul dokumentSi;

2. SevinaxoT miTiTebuli dokumenti;

3. davawkapunoT mTavari dokumentis miTiTebaze da davaWiroT F9 klaviSs.

5.21 hipermimarTvis damyareba

hiperlinki (hipermimarTva) es aris moniSnuli sityva an sityvebis jgufi,

romelzec orjer dawkapunebiT gadavdivarT sxva samuSao furcelze an sxva

failSi. SesaZlebelia agreTve internetis sasurvel misamarTze gadasvla.

hiperlinkis dasamyareblad:

1. movniSnoT sasurveli regioni an sityvaTa jgufi; 2. mivceT Insert → Hyperlink… brZaneba. Ggamova hiperlinkis Casmis dialoguri

fanjara (nax.5.29);

nax.5.29. hipermimarTvis Casmis dialoguri fanjara

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3. Link to file or URL: velSi avkriboT im failis misamarTi, romelzec gadavalT

hiperlinkis meSveobiT (mag., C:\David’s_documents\file1.mcd) an movZebnoT

sasurveli faili katalogTa da failebis xeze Browse... Rilakis

gamoyenebiT. arCeuli misamarTi Caiwereba Link to file or URL: velSi. Tu

gvsurs internetis misamarTze hiperlinkis damyareba, unda avkriboT

misamarTi srulad (mag., http://www.mathsoft.com/text.swk da ara

www.mathsoft.com/text.swk); 4. davayenoT, Tu gvsurs, alami Use relative path for hyperlink. amiT miTiTebuli

failis sxva misamarTze gadaadgilebis Semdegac Mathcad_i moaxerxebs misi axali adgilmdebareobis gansazRvras.

5. Message that appears on the status line when mouse is over link: velSi SegviZlia

CavweroT raime teqsturi Setyobineba, romelic gamoCndeba moniSnul

obieqtTan Tagvis miaxlovebisas; 6. OK Rilakis gamoyeneba brZanebas gauSvebs Sesrulebaze.

SesaZlebelia gamoZaxebuli dokumentis ara mxolod wakiTxva, aramed

redaqtirebac.

Tu gvsurs hiperlinkis waSla, movniSnoT sityva an sityvaTa jgufi,

romelzec iyo ganxorcielebuli hiperlinki, da mivceT Insert → Hyperlink... brZaneba. gamoCndeba Edit Hyperlink dialoguri fanjara (nax.5.30). davaWiroT Remove Link Rilaks. hipermimarTva waiSleba.

Nnax.5.30. hipermimarTvis redaqtirebis dialoguri fanjara

Oobieqtis Casmis Semdeg (Edit → Paste Special... an Insert → Object... brZanebebis

meSveobiT) menius Edit punqtis Links... qvepunqtiT gaixsneba dialoguri fanjara, romlis GRilakebi gvaZleven hipermimarTvis ganaxlebis da waSlis, obieqtis

wyaros gaxsnis da Secvlis saSualebas.

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Tavi VI simboluri operaciebi Mathcad_Si

6.1 Symbolics menius da Symbolic panelis Semadgenloba

simboluri operaciebi – es iseTi operaciebia, romelTa Sedegi ZiriTadad

moicema ara ricxobrivad, aramed simboloebis saxiT.

avirCioT mTavari menius Symbolics punqti (an davaWiroT Alt + S klaviSebs).

davinaxavT qvemenius:

Evaluate – gamoTvla;

Simplify (gamartiveba) – gamoyofili gamosaxulebis gamartiveba;

Expand (gaSla) – gamoyofili gamosaxulebis gaSla;

Factor (mamravli) – gamoyofili gamosaxulebis martiv mamravlebad daSla;

Collect (Segroveba) – gamoyofili gamosaxulebis mwkrivad gaSla da msgavsi

wevrebis dayvana (SeerTeba);

Polynomial Coefficients (polinomis koeficientebi) – polinomis koeficientebis

gansazRvra gamoyofil gamosaxulebaSi;

Variable – cvladi;

Matrix – matrica; Transform – transformireba; Evaluation Style... (gamoTvlebis stili) – gamoTvlebis stilis formireba.

Symbolics → Evaluate brZanebis qvebrZanebebia: Symbolically (simbolurad) _ gamoyofili gamosaxulebis simboluri

gardaqmna;

Floating Point... (mcocavi wertili) – gamoTvlebis Sedegis mcocavi wertiliT

warmodgena;

Comlex (kompleqsuri) – gamoTvlebis Sesruleba kompleqsur areSi da

Sedegis warmodgena kompleqsur formaSi.

Symbolics → Variable brZanebis qvebrZanebebia: Solve (amoxsna) – amocanis amoxsna miTiTebuli cvladis mimarT; Substitute (Casma) – gamosaxulebis Casma miTiTebuli cvladis magivrad; Differentiate (diferencireba) – diferencireba miTiTebuli cvladis mimarT; Integrate (integreba) – integreba miTiTebuli cvladis mimarT; Expand to Series... (mwkrivad gaSla) _ teiloris mwkrivad gaSla; Convert to Partial Fraction (wiladebad gardaqmna) _ gamosaxulebis warmodgena

elementaruli wiladebis jamis saxiT. Symbolics → Matrix brZanebis qvebrZanebebia:

Transpose (transponireba) – matricis transponireba; Invert (Sebruneba) – matricis Sebruneba; Determinant (determinanti) – matricis determinantis gamoTvla.

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Symbolics → Transform brZanebis qvebrZanebebia:

Fourier – furies gardaqmna miTiTebuli cvladis mimarT; Inverse Fourier – furies Sebrunebuli gardaqmna miTiTebuli cvladis

mimarT; Laplace – laplasis gardaqmna miTiTebuli cvladis mimarT; Inverse Laplace _ laplasis Sebrunebuli gardaqmna miTiTebuli cvladis

mimarT; Z _ Z_gardaqmna miTiTebuli cvladis mimarT; Inverse Z – Sebrunebuli Z_gardaqmna miTiTebuli cvladis mimarT.

nax.6.1_ze moyvanilia instrumentTa paneli Symbolic Semdegi punqtebiT:

nax.6.1. instrumentTa paneli Symbolic

→ _ simboluri tolobis niSani, sxvanairad mas simboluri gardaqmnebis

operators eZaxian; gamoiZaxeba Sabloni maTematikuri gamosaxulebis Sesatanad da

misi analizuri saxiT warmosadgenad;

_ gafarToebuli simboluri gardaqmnebis operatori; gamoiZaxeba

Sabloni maTematikuri gamosaxulebisa da simboluri operaciis saxelis

Sesatanad;

Modifiers _ gamoiZaxeba instrumentTa paneli Modifier; float _ gamoiZaxeba Sabloni Sedegis mcocavi wertilis formatSi

warmosadgenad;

complex _ am operatoriT xdeba gamoTvlebis Sesruleba kompleqsur areSi,

Sedegic Caiwereba kompleqsur formaSi;

assume _ gamoiZaxeba Sabloni cvladisaTvis SezRudvebis dasawesad;

solve _ gamoiZaxeba Sabloni gantolebis da utolobis amosaxsnelad

miTiTebuli cvladis mimarT;

simplify _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis gasamartiveblad;

substitute _ gamoiZaxeba Casmis Sabloni;

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factor _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis martiv mamravlebad

dasaSlelad;

expand _ gamoiZaxeba maTematikuri gamosaxulebis gaSlis Sabloni;

coeffs _ gamoiZaxeba Sabloni polinomis koeficientebis gansazRvrelad

miTiTebuli cvladis mimarT;

collect _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis mwkrivad

gasaSlelad (miTiTebuli cvladis mimarT) msgavsi wevrebis SeerTebiT;

series _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis teiloris mwkrivad

gasaSlelad miTiTebuli cvladis mimarT;

parfrac _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis elementaruli

wiladebis jamis saxiT warmosadgenad miTiTebuli cvladis mimarT;

fourier _ gamoiZaxeba Sabloni furies gardaqmnis Sesasruleblad miTiTebuli

cvladis mimarT;

laplace _ gamoiZaxeba Sabloni laplasis gardaqmnis Sesasruleblad miTiTebuli

cvladis mimarT;

ztrans _ gamoiZaxeba Sabloni Z_gardaqmnis Sesasruleblad miTiTebuli

cvladis mimarT;

invfourier _ gamoiZaxeba Sabloni furies Sebrunebuli gardaqmnis

Sesasruleblad miTiTebuli cvladis mimarT;

invlaplace _ gamoiZaxeba Sabloni laplasis Sebrunebuli gardaqmnis

Sesasruleblad miTiTebuli cvladis mimarT;

invztrans _ gamoiZaxeba Sabloni Sebrunebuli Z_gardaqmnis Sesasruleblad

miTiTebuli cvladis mimarT;

MT→ _ gamoiZaxeba Sabloni matricis transponirebisaTvis;

M_1 → _ gamoiZaxeba Sabloni matricis SebrunebisaTvis; |M |→ _ matricis determinantis gansazRvra.

6.2 maTematikuri gamosaxulebebis warmodgena analizuri saxiT

rogorc ukve iyo naTqvami, maTematikuri gamosaxulebis warmodgena

analizuri saxiT SeiZleba miviRoT Evaluation an Symbolic panelebis → (simboluri

toloba) operatoris meSveobiT. amisaTvis:

davayenoT kursori maTematikur gamosaxulebaSi, gamoviyenoT → operatori

(an Ctrl + . klaviSebis kombinacia) da Semdeg klaviaturis Enter klaviSi;

gamoviyenoT simboluri tolobis operatori an klaviaturis Ctrl + . klaviSebi. ekranze gamoCndeba simboluri tolobis niSani da mis marcxniv markeri. markeris adgilas SevitanoT maTematikuri gamosaxuleba da Enter klaviSiT

davadasturoT brZaneba.

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maTematikuri gamosaxulebis analizuri saxiT warmodgenis miReba

SesaZlebelia agreTve Symbolics → Evaluate → Symbolically brZanebiT. amisaTvis jer

gamovyoT maTematikuri gamosaxuleba anu Setanis markeri – lurji kuTxe –

davayenoT ise, rom is moicavdes gamosaxulebas mTlianad, Semdeg ki mivceT

Symbolics → Evaluate → Symbolically brZaneba (an Shift + F9). ekranze davinaxavT Sedegs.

aRvniSnoT, rom maTematikuri gamosaxulebis analizuri saxiT warmodgenisas

Mathcad_i Seecdeba miiRos pasuxi rac SeiZleba martivi formiT. aRsaniSnavia

agreTve, rom Tu gamoyofili iyo maTematikuri gamosaxulebis nawili, Symbolics menius brZanebebi am nawils exeba.

Tu Mathcad_ma ver SeZlo gamosaxulebis warmodgena analizuri saxiT,

ekranze sawyisi gamosaxuleba gameordeba (nax.6.2_5), rac niSnavs, rom amocana

dasmulia koreqtulad, magram misi warmodgena analizuri saxiT ver moxerxda.

Nnax.6.2. maTematikuri gamosaxulebebis analizuri saxiT warmodgenis

magaliTebi

nax.6.2_ze (1,2,3,4,5 magaliTebi) marcxniv moyvanilia sxvadasxva saxis

maTematikuri gamosaxulebebi, marjvniv (amisaTvis dialogur fanjaraSi Evaluation Style arCeulia gadamrTveli Horizontally) Symbolics → Evaluate → Symbolically brZanebiT

76

miRebuli am gamosaxulebebis analizuri saxe. nax.6.2_ze (6,7,8,9,10,11)

gamosaxulebebis analizuri saxe miRebulia Symbolic panelis → operatoris

meSveobiT.

6.3 maTematikuri gamosaxulebebis gamartiveba

(simplify)

maTematikuri gamosaxulebebis gasamartiveblad gamoiyeneba Symbolic panelis simplify operatori.

amisaTvis arsebobs sami xerxi.

I xerxi:

1. avirCioT Symbolic panelis simplify punqti; 2. miRebul SablonSi markeris adgilas SevitanoT gasamartivebeli

gamosaxuleba;

3. davaWiroT klaviaturis Enter klaviSs.

II xerxi:

1. avkriboT gasamartivebeli maTematikuri gamosaxuleba;

2. avirCioT Symbolic an Evaluation panelebis punqti (an davaWiroT klaviSebis

kombinacias Ctrl + Shift + . ). gamosaxulebis marjvniv Caismeba markeri da simboluri

tolobis → niSani; 3. markeris adgilas avkriboT klaviaturidan sityva simplify ; 4. davaWiroT klaviaturis Enter klaviSs.

III xerxi:

1. avirCioT Symbolic an Evaluation panelebis punqti (an davaWiroT klaviSebis

kombinacias Ctrl + Shift + . ). Caismeba Sabloni ori markeriT → niSnis win; 2. pirveli markeris adgilas SevitanoT gasamartivebeli maTematikuri

gamosaxuleba;

3. meore markeris adgilas avkriboT klaviaturidan sityva simplify ; 4. davaWiroT klaviaturis Enter klaviSs.

aqve aRvniSnoT, rom Symbolic panelis sxva operatorebis arCevisas aseve am

meTodebs viyenebT. pirvel meTodSi miRebuli Sablonis saxe operatorzea

damokidebuli. umetes SemTxvevaSi Sabloni or markers Seicavs da me_2 punqtis

Semdeg emateba Sablonis marjvena markeris waSlis aucilebloba (Tu cvladis

miTiTeba ar aris saWiro) an marjvena markerSi cvladis (an gamosaxulebis) Setana,

romlis mimarT gvsurs operaciis Sesruleba. xolo meore da mesame xerxSi me_3

punqtSi sityva_gasaRebis dabeWdvis Semdeg, Tu saWiroa, aikribeba mZime da cvladi,

romlis mimarT sruldeba operacia.

77

Symbolic panelis simplify operatoriT ganxorcielebuli maTematikuri

gamosaxulebebis gamartiveba moyvanilia nax.6.3_ze (3,4,6,7 magaliTebi), amasTan me_6

da me_7 magaliTebSi gamartivebis Semdeg gamoyenebulia float operatori. maTematikuri gamosaxulebebis gamartiveba SesaZlebelia agreTve Symbolics →

Simplify brZanebiT. gamovyoT gamosaxuleba da gamoviyenoT Symbolics → Simplify brZaneba. Nnax.6.3_ze (1,2,5 magaliTebi) moyvanilia sxvadasxva gamosaxulebebi, xolo

gamosaxulebebis marjvniv Symbolics → Simplify brZanebiT miRebuli maTi gamartivebis

Sedegi. gamartivebis es meTodi sasargebloa, rodesac Cven gvsurs SevasruloT

gamosaxulebis nawilis gamartiveba. saqme imaSia, rom zogjer Mathcad_s ar ZaluZs

moaxdinos mTliani gamosaxulebis gamartiveba, xolo gamosaxulebis calkeuli

nawilebis gamartiveba SesaZlebelia. amisTvis unda gamovyoT gamosaxulebis

nawili da mivceT brZaneba Symbolics → Simplify. Tu Mathcad_ma ver SeZlo gamosaxulebis gamartiveba, ekranze sawyisi

gamosaxuleba gameordeba (nax.6.3_5), rac niSnavs, rom amocana dasmulia

koreqtulad, magram misi gamartiveba ver moxerxda.

gamartivebis operacia xSirad ixmareba modifikatorebTan erTad.

nax.6.3. maTematikuri gamosaxulebebis gamartivebis

(simplify) magaliTebi

78

6.4 maTematikuri gamosaxulebis gaSla

(expand)

maTematikuri gamosaxulebis gaSla xdeba Symbolics → Expand brZanebiT. es

brZaneba, SeiZleba iTqvas, warmoadgens gamartivebis sapirispiro brZanebas. misi

meSveobiT rTuli funqciebi ufro martivi funqciebiT gamoisaxebian da xdeba

algebruli gamosaxulebis warmodgena gaSlili formiT.

maTematikuri gamosaxulebis gaSla SesaZlebelia agreTve Symbolic panelis

expand operatoriT.

nax.6.4_ze moyvanilia maTematikuri gamosaxulebebis gaSlis magaliTebi,

Symbolics → Expand brZanebiT (magaliTebi 1,2) da Symbolic panelis expand operatoriT

(3,4,5,6) ganxorcielebuli. Mme_4 magaliTSi gaSla ver moxerxda.

nax.6.4. maTematikuri gamosaxulebebis gaSlis

(expand) magaliTebi

aRvniSnoT, rom Symbolic panelis punqtebiT simboluri operaciebis

Sesrulebisas Mathcad_i jer amowmebs hqonda Tu ara masSi Sesul cvladebs da

funqciebs ufro adre miniWebuli raime mniSvnelobebi, Tu ki, Mathcad_i iyenebs am mniSvnelobebs. es debuleba ilustrirebulia nax.6.5_ze (magaliTebi 1,2). rac

79

Seexeba Symbolics menius brZanebebs, isini ar amowmeben masSi Sesuli cvladebis da

funqciebis wina mniSvnelobebs da amitomac ar iyeneben maT. am cvladebis wina

mniSvnelobebis Secvla ar gamoiwvevs Sesabamisi simboluri gamoTvlebis

Sedegebis Secvlas (nax.6.5, mag.3).

nax.6.5. gansxvaveba Symbolic panelis operatorebsa da

Symbolics menius brZanebebs Soris

6.5 maTematikuri gamosaxulebebis da ricxvebis

martiv mamravlebad daSla (factor)

maTematikuri gamosaxulebebis da ricxvebis daSla martiv mamravlebad

xdeba Symbolics → Factor brZanebiT da Symbolic panelis factor operatoris meSveobiT.

nax.6.6_ze (1,2,3,4,5 magaliTebi) moyvanilia Symbolics → Factor brZanebiT

ganxorcielebuli gamosaxulebebis daSlis magaliTebi, xolo me_6 da me_7

80

magaliTebSi daSla ganxorcielebulia Symbolic panelis factor operatoriT. Mme_2@

magaliTSi daSla ver ganxorcielda.

nax.6.6. maTematikuri gamosaxulebebis da ricxvebis

martiv mamravlebad daSlis (factor) magaliTebi

6.6 maTematikuri gamosaxulebis mwkrivad gaSla

msgavsi wevrebis SeerTebiT (collect)

imisaTvis rom movaxdinoT maTematikuri gamosaxulebis mwkrivad gaSla

(miTiTebuli cvladis mimarT), saWiroa Seyvanil maTematikur gamosaxulebaSi

gamovyoT saWiro cvladi an funqcia (kuTxis formis lurji kursoriT), Semdeg ki

avirCioT brZaneba Symbolics → Collect. moxdeba gamosaxulebis gaSla da msgavsi

wevrebis SeerTeba. igives miviRebT Symbolic panelis collect operatoriT. orive

meTodiT Sesrulebuli mwkrivad gaSla da msgavsi wevrebis SeerTeba naCvenebia

nax.6.7_ze. 1 magaliTSi mwkrivad gaSla ganxorcielebulia Symbolics → Collect brZanebiT, xolo 2,3,4,5 magaliTebSi _ Symbolic panelis collect operatoriT.

81

Nnax.6.7. maTematikuri gamosaxulebis mwkrivad gaSla

da msgavsi wevrebis SeerTeba (collect)

6.7 polinomis koeficientebis gansazRvra miTiTebuli

cvladis mimarT (coeffs)

Tu sawyisi maTematikuri gamosaxuleba polinomia, misi koeficientebis

gansazRvra SesaZlebelia Symbolics → Polynomial Coefficients brZanebiT (nax.6.8,

magaliTebi 1,2) an Symbolic panelis coeffs (koeficientebi) operatoriT (nax.6.8,

magaliTebi 3,4).

koeficientebis gansazRvra xdeba gamoyofili (miTiTebuli) cvladis

mimarT. Sedegad miiReba veqtor_sveti, romlis nulovani elementi warmoadgens

Tavisufali wevris koeficients, xolo bolo – gamoyofili (miTiTebuli) cvladis

maqsimaluri xarisxis mqone wevris koeficients.

rogorc Cans me_4 magaliTidan, polinomis koeficientebis gansazRvra

SeiZleba ganxorcieldes agreTve gamosaxulebis mimarT.

82

nax.6.8. polinomis koeficientebis gansazRvris

(coeffs) magaliTebi

6.8 gantolebebis da utolobebis amoxsna

miTiTebuli cvladis mimarT (solve)

gantolebebis da utolobebis amoxsna miTiTebuli cvladis mimarT xdeba

Symbolics → Variable → Solve brZanebiT an Symbolic panelis solve operatoriT.

Tu maTematikur gamosaxulebaSi ar Sedis tolobis an utolobis niSani,

Mathcad_i awarmoebs cvladis iseTi mniSvnelobis moZebnas, romlisTvis sawyisi

gamosaxuleba utoldeba nuls, winaaRmdeg SemTxvevaSi Cveulebriv amoxsnis

moyvanil gantolebas.

nax.6.9_ze (magaliTebi 1,2) moyvanilia Symbolics → Variable → Solve brZanebiT

gantolebebis amoxsnis magaliTebi, xolo 3,4,5 magaliTebSi gantolebebi da

utolobebi amoxsnilia ^ Symbolic panelis solve operatoriT, amasTan 2,3 da 5

magaliTebSi gantolebebi da utolobebi Cawerilia sruli saxiT, xolo 1 da 4

magaliTebSi nagulisxmevia, rom moyvanili gamosaxuleba udris nuls.

83

nax.6.9. gantolebebis da utolobebis amoxsnis magaliTebi

(solve)

Mathcad_Si SesaZlebelia agreTve gantolebaTa sistemis amoxsna. imisaTvis

rom amovxsnaT gantolebaTa sistema solve operatoris meSveobiT, unda SevqmnaT

veqtor_sveti, romlis striqonebSi Caiwereba sawyisi monacemebi gantolebebis an

utolobebis saxiT. cvladebi, romlis mimarT xdeba amoxsna, aseve Caiwereba

veqtor_svetis saxiT. pasuxic miiReba veqtor_svetis saxiT. nax.6.10_ze (magaliTebi

1,2) moyvanilia gantolebaTa sistemis amoxsna solve operatoris meSveobiT, xolo

magaliTSi 3 _ wrfiv gantolebaTa sistemis amoxsna Given _ Find funqciebiT.

6.9 gamosaxulebis Casma miTiTebuli cvladis

Mmagivrad (substitute)

imisaTvis rom ganvaxorcieloT maTematikuri gamosaxulebis Casma Symbolics menius meSveobiT, saWiroa:

1) avkriboT maTematikuri gamosaxuleba, romliTac unda Seicvalos

cvladi;

84

nax.6.10. gantolebaTa sistemis amoxsna

2) gamovyoT es gamosaxuleba da SevasruloT Edit → Cut an Edit → Copy brZaneba. Sedegad gamosaxuleba iqneba Senaxuli buferul mexsierebaSi

misi amoWriT an amoWris gareSe;

3) SevitanoT is maTematikuri gamosaxuleba, sadac saWiroa ganvaxorcieloT

Casma;

4) gamovyoT (lurji kuTxiT) cvladi, romlis magivrad Caismeba

gamosaxuleba buferidan;

5) SevasruloT Symbolics → Variable → Substitute brZaneba. Symbolic panelis substitute operatori axorcielebs maTematikuri

gamosaxulebis Casmas buferidan miTiTebuli cvladis magivrad an, rac gacilebiT

ufro moxerxebulia, rogorc cvladi, ise Casasmeli gamosaxuleba Caiwereba

uSualod substitute operatorSi. nax.6.11_ze naCvenebia maTematikuri gamosaxulebebis Casmis magaliTebi,

ganxorcielebuli Symbolics → Variable → Substitute brZanebiT (magaliTebi 1,2) da

Symbolic panelis substitute punqtis SerCeviT (magaliTebi 3,4,5,6). rogorc Cans me_5

magaliTidan, simboluri operacia SeiZleba ganxorcieldes miRebuli Sedegis

mimarT. am dros Cven vxedavT Sualedur Sedegebsac. Tu ramdenime simboluri

85

operacia miTiTebulia erTdroelad (nax.6.11, magaliTi 4), ekranze davinaxavT

mxolod saboloo Sedegs.

nax.6.11. gamosaxulebis Casma miTiTebuli cvladis

Mmagivrad (substitute)

6.10 maTematikuri gamosaxulebebis diferencireba

da integreba

maTematikuri gamosaxulebebis diferencireba gamoyofili cvladis mimarT

xdeba Symbolics → Variable → Differentiate brZanebiT. Sedegi iqneba miRebuli simboluri

saxiT.

imisaTvis, rom miviRoT meore rigis warmoebuli, saWiroa gavimeoroT

brZaneba, mesame rigis – gamoviyenoT is kidev erTxel da a.S.

maTematikuri gamosaxulebebis integreba gamoyofili cvladis mimarT xdeba

Symbolics → Variable → Integrate brZanebiT. Setanili maTematikuri gamosaxuleba

integralqveSa funqcias warmoadgens. Sedegad miiReba ganusazRvreli integralis

mniSvneloba simboluri saxiT.

86

ra Tqma unda, diferencirebis da integrebis operaciebis Sesruleba

SesaZlebelia agreTve Calculus panelis meSveobiT gamosaxulebis CaweriT da Semdeg

→ operatoriT. nax.6.12_ze da nax.6.13_ze naCvenebia diferencirebisa da integrebis

magaliTebi.

nax.6.12. maTematikuri gamosaxulebebis diferencirebis

magaliTebi

6.11 maTematikuri gamosaxulebebis teiloris

mwkrivad gaSla (series)

imisaTvis, rom movaxdinoT maTematikuri gamosaxulebebis teiloris

mwkrivad gaSla Symbolics menius meSveobiT, saWiroa:

1) SevitanoT maTematikuri gamosaxuleba;

2) gamovyoT lurji kuTxiT cvladi, romlis mimarT moxdeba mwkrivad

gaSla;

3) avirCioT Symbolics → Variable → Expand to Series... brZaneba.

87

nax.6.13. maTematikuri gamosaxulebebis integrebis

magaliTebi

gamoCndeba dialoguri fanjara, romelSic unda mivuTiToT

aproqsimaciis rigi;

4) davaWiroT OK Rilaks.

Tu aproqsimaciis rigi ar iqneba miTiTebuli, Mathcad_i winaswari

SeTanxmebis Tanaxmad CaTvlis mas 6_is tolad. es niSnavs, rom mwkrivis bolo

wevris xarisxis maCvenebeli 6_ze naklebia.

aRvniSnoT, rom Symbolics → Variable → Expand to Series... brZanebiT teiloris

mwkrivad gaSla xorcieldeba erTi cvladis mimarT, xolo Symbolic panelis series operatorSi SeiZleba mivuTiToT ramdenime cvladi. am dros aproqsimaciis rigi

Tu udris, mag., 8_s, es niSnavs, rom mwkrivis bolo wevris xarisxis maCveneblebis

jami unda iyos 8_ze naklebi. Tu aproqsimaciis rigi miTiTebuli ar iqneba,

Mathcad_i CaTvlis mas 6_is tolad. aRsaniSnavia agreTve, rom series operatorSi SeiZleba mivuTiToT cvladis ra wertilis midamoSi xdeba teiloris mwkrivad

gaSla, xolo Tu es informacia ar aris moyvanili, igulisxmeba, rom gaSla xdeba

cvladis 0 wertilis midamoSi.

nax.6.14_ze naCvenebia teiloris mwkrivad gaSla Symbolics → Variable → Expand to Series... brZanebiT (magaliTebi 1,3) da Symbolic panelis series operatoriT

88

(magaliTebi 2,4,5). me_5 magaliTSi gaSla ganxorcielebulia X=1 wertilis

midamoSi, xolo danarCen magaliTebSi _ cvladis 0 wertilis midamoSi.

nax.6.14. maTematikuri gamosaxulebebis teiloris

mwkrivad gaSla (series)

6.12 maTematikuri gamosaxulebebis warmodgena elementaruli

wiladebis jamis saxiT (parfrac)

Symbolics → Variable → Convert to Partial Fraction brZanebiT xdeba maTematikuri

gamosaxulebis gaSla elementarul nawilebad gamoyofili cvladis mimarT.

Sedegad miiReba maTematikuri gamosaxuleba, romelic warmoadgens elementaruli

wiladebis jams.

igives mivaRwevT Symbolic panelis parfrac operatoriT. Nnax.6.15_ze naCvenebia

maTematikuri gamosaxulebebis elementarul nawilebad gaSla ganxorcielebuli

Symbolics → Variable → Convert to Partial Fraction brZanebiT (magaliTi 1) da Symbolic panelis parfrac operatoriT (magaliTebi 2,3).

89

nax.6.15. maTematikuri gamosaxulebebis warmodgena elementaruli

wiladebis jamis saxiT (parfrac)

6.13 matricebis transponireba, Sebruneba da

determinantis gansazRvra

Symbolics → Matrix menius aqvs sami punqti: Transpose, Invert, Determinant, romlebic xdebian aqtiurni (Sesrulebadi) romelime matricis gamoyofisas.

matricis transponireba anu striqonebisa da svetebis urTierTSecvla

xdeba Symbolics → Matrix → Transpose brZanebiT. transponireba xorcieldeba agreTve

Symbolic panelis MT → operatoriT, Matrix panelis MT operatoriT an klaviaturis

Ctrl + 1 klaviSebiT.

Sebrunebuli matrica es aris iseTi matrica, romlis gamravlebiT sawyis

matricaze miiReba erTeulovani matrica (erTeulovani matrica aris matrica,

romlis diagonaluri elementebi erTis tolia, xolo danarCeni elementebi

nulis). Sebrunebuli matrica miiReba Symbolics → Matrix → Invert brZanebiT. igive

xorcieldeba Symbolic an Matrix panelebis Sesabamisad M_1→ da X_1 operatorebiT

90

an ^ _ 1 klaviSebis rigrigobiT akrebiT. cxadia, sawyisi matrica unda iyos

kvadratuli.

matricis determinantis gansazRvra xdeba Symbolics → Matrix → Determinant brZanebiT an Symbolic an Matrix panelebis Sesabamisad |M|→ da |X| operatorebiT.

SeiZleba agreTve gamoviyenoT | klaviSi.

aRvniSnoT, rom Tu matrica Seicavs simbolur elementebs, mizanSewonilia

visargebloT Symbolic panelis MT → , M_1→ da |M|→ operatorebiT, xolo Matrix panelis punqtebiT sargeblobisas Sesabamisi punqtis Semdeg saWiroa simboluri

tolobis niSnis SerCeva.

nax.6.16_ze naCvenebia matricebis transponirebis, Sebrunebis da

determinantis povnis magaliTebi.

nax.6.16. matricebis transponireba, Sebruneba da

determinantis gansazRvra

91

6.14 maTematikuri gamosaxulebebis gardaqmnebi

Mathcad_Si SeiZleba Sesruldes furies pirdapiri da Sebrunebuli

gardaqmna, laplasis pirdapiri da Sebrunebuli gardaqmna, Z_gardaqmna da

Sebrunebuli Z_gardaqmna. rogorc cnobilia, furies pirdapiri da Sebrunebuli gardaqmna moicema

formulebiT:

dtiwtetfwF )()(

da

dwiwtewFtf

)(21)(

.

mag., rodesac procesi aRwerilia droSi cvladi funqciiT, furies

pirdapiri gardaqmniT miiReba misi aRwera sixSireze damokidebuli funqciiT da

piriqiT.

Mathcad_i asrulebs furies gardaqmnebs gamoyofili cvladis mimarT

Symbolics → Transform → Fourier da Symbolics → Transform → Inverse Fourier brZanebebiT an

Symbolic panelis fourier da invfourier operatorebis meSveobiT.

laplasis pirdapiri da Sebrunebuli gardaqmna moicema formulebiT:

dtetfSF St

0

)()(

da

i

i

StdteSFtf

)(21)( .

laplasis pirdapiri da Sebrunebuli gardaqmna gamoiyeneba, mag.,

eleqtronul wredebSi gardamavali procesebis daTvlisas.

Mathcad_i asrulebs laplasis gardaqmnebs gamoyofili cvladis mimarT

Symbolics → Transform → Laplace da Symbolics → Transform → Inverse Laplace brZanebebiT

an Symbolic panelis laplace da invlaplace operatorebis meSveobiT.

...),,( 210 xxxX mimdevrobis pirdapiri Z_gardaqmna moicema formuliT:

...)( 221

0 zx

zxxzF .

92

is asrulebs iseTive rols diskretuli mimdevrobebisaTvis (vTqvaT,

diskretuli signalebisaTvis), rogorc furies da laplasis gardaqmnebi uwyveti

funqciebisaTvis.

Z_gardaqmna SeiZleba Sesruldes uwyveti funqciisaTvisac, romelic

warmodgenilia Tavisi mniSvnelobebiT sxvadasxva wertilebSi _ damoukidebeli

cvladis diskretuli bijiT cvlilebisas:

0

)()(n

nznfzF .

Sebrunebuli Z_gardaqmna moicema formuliT:

dzzFzi

f nn )(

21 1

.

Mathcad_i asrulebs pirdapir da Sebrunebul Z_gardaqmnebs gamoyofili

cvladis mimarT Symbolics → Transform → Z da Symbolics → Transform → Inverse Z brZanebebiT an Symbolic panelis ztrans da invztrans operatorebis meSveobiT.

nax.6.17_ze moyvanilia furies, laplasis da Z pirdapiri da Sebrunebuli

gardaqmnebis magaliTebi.

nax.6.17. furies, laplasis da Z_gardaqmnebi

93

6.15 simboluri gamoTvlebis Sedegebis gamotanis

stilis dayeneba

Symbolics → Evaluation Style... brZanebiT gamoiZaxeba Sedegebis gamotanis stilis

dialoguri fanjara (nax.6.18).

Nnax.6.18. dialoguri fanjara Evaluation Style Evaluation Style dialoguri fanjris Show evaluation steps (gamoTvlebis

safexurebis Cveneba) ganyofilebaSi gvaqvs gadamrTvelis dayenebis sami varianti:

Vertically, inserting lines – Sedegebis ganlageba ZiriTadi gamosaxulebis qveS,

carieli striqonebis CasmiT marjvniv;

Vertically, without inserting lines – Sedegebis ganlageba carieli striqonebis

Casmis gareSe;

Horizontally – Sedegebis ganlageba ZiriTadi gamosaxulebis marjvniv.

am dialogur fanjaraSi gvaqvs ori alami:

Show Comments – komentarebis Cveneba; Evaluate In Place – adgilze gamoTvla anu sawyisi gamosaxulebis Secvla

simboluri operaciis SedegiT. Nnax. 6.19_ze naCvenebia simboluri gamosaxulebis Sedegebis sxvadasxva stiliT

gamotanis magaliTebi.

6.16 cvladebis mniSvnelobebis SezRudva da instrumentTa

paneli Modifier (modificikacia)

Symbolic panelis assume punqtiT xdeba cvladis wina mniSvnelobis ignorireba

da masze SezRudvis daweseba. tipiuri SezRudvebia, mag., 10 , 5b da sxv.

qvemoT moyvanil magaliTSi

94

nax.6.19. simboluri gamoTvlebis Sedegebis gamotanis stili

simboluri gamoTvla Sesrulebulia im pirobiT, rom namdvili dadebiTi

ricxvia.

Symbolic panelis Simplify operatorSi SesaZlebelia cvladebis

mniSvnelobebze damatebiTi SezRudvebis daweseba, rac xorcieldeba Modifier instrumentTa panelis assume, real, RealRange, trig punqtebiT:

assume punqtiT viziris adgilas Caismeba sityva_gasaRebi cvladis

mniSvnelobebze SezRudvebis dasawesad;

real SezRudva niSnavs, rom cvladi namdvili tipisaa;

RealRange SezRudva gansazRvravs namdvili tipis cvladis

mniSvnelobaTa ares. mag., c = RealRange(a,b) Canaweri niSnavs, rom c_s

mniSvnelobebi unda iyos a_s da b_s Soris, sadac a da b namdvili

ricxvebia an usasruloba;

trig modifikatori zRudavs gamartivebis process trigonometriuli

formulebiT (sin2(x)+cos2(x)=1; cosh(x)2_sinh(x)2=1). am dros Mathcad_i ar

xmarobs logariTmebTan, xarisxebTan an radikalebTan dakavSirebul

formulebs.

95

aRvniSnoT, rom rodesac gvaqvs SezRudva assume=real, simboluri gamoTvlebi

Sesruldeba im pirobiT, rom maTematikur gamosaxulebaSi Sesuli yvela

cvladi namdvili tipisaa, xolo Tu dawesebulia assume=RealRange(a,b) SezRudva, simboluri gamoTvlebi Sesruldeba im pirobiT, rom maTematikur

gamosaxulebaSi Sesuli yvela cvladi namdvili tipisaa da am cvladebis

mniSvnelobaTa intervalia (a,b). nax.6.20_ze moyvanilia Modifier panelis operatorebis magaliTebi.

nax.6.20. Modifier panelis operatorebi

6.17 simboluri gamoTvlebis Sedegebis warmodgena

kompleqsuri ricxvis saxiT da mcocavi wertiliT

(complex, float)

Symbolic panelis complex operatoriT simboluri gamoTvlebi Sesruldeba

kompleqsur areSi da misi Sedegebi Caiwereba kompleqsuri ricxvis saxiT. am

miznisaTvis SesaZlebelia gamoviyenoT agreTve Symbolics → Evaluate → Complex brZaneba.

96

Symbolic panelis float operatoriT Sedegi Caiwereba mcocavi wertilis saxiT.

igives miviRebT Symbolics → Evaluate → Floating Point... brZanebiT.

nax. 6.21_ze moyvanil magaliTebSi Sedegebi warmodgenilia kompleqsuri

ricxvis saxiT da mcocavi wertiliT Symbolic panelis operatorebis da Symbolics menius Sesabamisi brZanebebis gamoyenebiT.

nax.6.21. simboluri gamoTvlebis Sedegebis warmodgena

kompleqsuri ricxvis saxiT da mcocavi wertiliT

97

Tavi VII daformateba Mathcad_Si

7.1 Format menius da Formatting panelis Semadgenloba

mTavari menius Format punqtiT an Alt + O klaviSebis kombinaciiT gamoiZaxeba

Semdegi qvemeniu:

Equation... (gantoleba) _ maTematikuri gamosaxulebebis daformateba; Result... (Sedegi) _ ricxviTi Sedegebis daformateba; Text... (teqsti) _ teqstis daformateba; Paragraph... (abzaci) _ abzacis daformateba; Tabs... (tabulacia) _ tabulaciis poziciebis dayeneba; Style... (stili) _ stilis daformateba; Properties... (Tvisebebi) _ Tvisebebis dayeneba; Graph (grafiki) _ grafikebis daformateba; Color (feri) _ ferebis dayeneba; Area (ubani) _ ubnebis daformateba; Separate Regions _ areebis gancalkeveba; Align Regions _ areebis sworeba; Repaginate Now _ dokumentis gverdebad xelmeore dayofa.

Formatting instrumentTa paneli Sedgeba 3 velisagan da 10 Rilakisagan

(nax.7.1).

nax.7.1. Formatting instrumentTa paneli

pirvel siisebur velSi (Style) Cawerilia mimdinare stilis saxeli. Tu

saWiroa, am velis marjvniv mdebare Rilakis isarze dawkapunebiT SegviZlia

gavxsnaT stilebis CamonaTvali da avirCioT sasurveli.

Semdegi veli – Sriftebis siiseburi velia (Font). aq Cawerilia mimdinare

Sriftis saxeli. am velis marjvniv mdebare Rilakis isarze dawkapunebiT

gaixsneba Sriftebis CamonaTvali, saidanac survilisamebr airCeva saWiro.

mesame velSi (Font Size) Cawerilia Sriftis mimdinare zoma. Font Size velis marjvniv mdebare Rilakis isarze dawkapunebiT gaixsneba Sriftis zomebis

CamonaTvali, saidanac SeirCeva sasurveli zoma.

Bold Rilakze (B) daWeriT CairTveba sqeli moyvanilobis simboloebis

akrebis reJimi, Italic (I) _ aikribeba daxrili teqsti (kursivi), Underline (U) _

aikribeba xazgasmuli teqsti.

98

Align Left Rilakze daWeriT xdeba abzacis sworeba teqstis aris marcxena

sazRvarze, Center _ abzacis centrireba anu misi moTavseba sazRvrebs Soris SuaSi,

Align Right _ abzacis sworeba teqstis aris marjvena sazRvarze.

Bullets Rilakze daWeriT CairTveba markerebis Casmis reJimi, xolo

Numbering _ punqtebis numeraciis. Ees ori punqti emsaxureba siebis Seqmnis

process. siis erTi punqtis akrebis Semdeg Enter klaviSis daWerisas avtomaturad

gadavalT siis momdevno punqtze. imisaTvis rom davamTavroT siis Seqmnis procesi,

axal punqtze gadasvlis Semdeg isev davaWiroT Bullets Rilaks an siis bolo

punqtis akrebis Semdeg orjer davawkapunoT Enter klaviSze. siis Sesaqmnelad

SesaZlebelia agreTve jer misi punqtebis akreba da moniSvnis Semdeg Bullets an Numbering Rilakebze dawkapuneba.

Superscript (zeda indeqsi) RilakiT simboloebi ganlagdebian striqonis

zedoneze, xolo Subscript (qveda indeqsi) RilakiT _ qvedoneze.

7.2 maTematikuri gamosaxulebebis daformateba

Format → Equation… brZanebiT gamoiZaxeba Equation Format dialoguri fanjara

(nax.7.2), romelic emsaxureba maTematikuri gamosaxulebebis daformatebas.

nax.7.2. Equation Format dialoguri fanjara

maTematikur gamosaxulebaSi Sedian cvladebi, mudmivebi, specialuri

simboloebi da operatorebi. Mathcad_i iyenebs or maTematikur stils, romelTa

parametrebi dayenebulia winaswari SeTaxmebiT. es stilebia Variables (cvladebisaTvis, simboloebisaTvis da operatorebisaTvis) da Constants (ricxvebisaTvis). survilisamebr SeiZleba stilebis parametrebis Secvla.

Equation Format dialoguri fanjris Style Name (stilis saxeli) velSi iseve

rogorc Formatting panelis Sesabamis velSi avtomaturad Caiwereba aqtiuri

obieqtis stilis saxeli: Variables (cvladebi), Constants (mudmivebi) an momxmareblis

99

mier Seqmnili stilis saxeli. mag., ricxvze dawkapunebis Semdeg am velSi iqneba

Cawerili Constants. obieqtis stilis parametrebis Sesacvlelad:

1. gamovyoT obieqti da mivceT Format → Equation… brZaneba an gamoviZaxoT

Equation Format dialoguri fanjara obieqtis gaaqtiurebis gareSe da Style Name velis CamonaTvalidan avirCioT sasurveli stili;

2. gamoviyenoT Modify… Rilaki. gamoCndeba obiqtis dialoguri fanjara,

romelSic airCeva Srifti, misi moyvaniloba, zoma, feri, simboloebis

nakrebi da dayendeba survilisamebr alami Underline; 3. davaWiroT OK Rilaks.

Sedegad Mathcad_i Secvlis dokumentSi yvela am tipis obieqtis gaformebas.

nax.7.3_ze moyvanilia dialoguri fanjara Variables.

nax.7.3. dialoguri fanjara Variables

maTematikuri gamosaxulebis obieqtebis formatis Secvla SesaZlebelia

agreTve Formatting panelis daxmarebiT. Mmag., Tu gvsurs mudmivebis formatis

Secvla, jer gamovyoT ricxvi (an Formatting panelis stilebis CamonaTvalidan

avirCioT stili Constants), Semdeg davawkapunoT Formatting panelis sasurvel

Rilakebze. ase SeiZleba SevcvaloT Srifti, misi zoma da moyvaniloba. Equation Format dialogis Default Equation Color velis CamonaTvalidan SeirCeva

garkveuli stilis obieqtebis gaformebis feri. mag., Tu gvsurs maTematikur

gamosaxulebebs da komentarebs (teqsts) hqondeT gansxvavebuli feri, Default Equation Color velis CamonaTvalidan avirCioT sasurveli feri, romliTac iqneba

gaformebuli, vTqvaT, yvela maTematikuri gamosaxuleba da davaWiroT OK Rilaks.

100

momxmarebels SeuZlia Seqmnas damatebiTi maTematikuri stilebi. Sedegad

rogorc Formatting panelis, aseve Equation Format dialoguri fanjris stilebis

CamonaTvalSi iqneba Sesuli axali stilebis saxelebi.

ganvixiloT axali stilis Seqmnis procesi. vTqvaT, gvsurs matricebis

identifikatorebis gaformeba sqeli moyvanilobis xazgasmuli SriftiT. amisaTvis:

1. gamovyoT elementi, romlisTvisac vqmniT axal stils (Cven magaliTSi

matricis saxeli) da mivceT Format → Equation… brZaneba an gamoviZaxoT

Equation Format dialoguri fanjara obieqtis gaaqtiurebis gareSe;

2. davawkapunoT Style Name velis marjvniv mdebare isarze da gavxsnaT

stilebis CamonaTvali;

3. avirCioT maTematikuri stilebis CamonaTvalidan romelime gamouyenebeli

saxeli (mag., User 1), romelic Caiwereba New Style Name (axali stilis

saxeli) teqstur velSi;

4. davayenoT kursori am teqstur velSi da SevcvaloT User 1, vTqvaT,

Matrix_iT;

5. davaWiroT Modify… Rilaks da gaxsnil dialogur fanjaraSi davayenoT

sasurveli maxasiaTeblebi: Bold da Underline; 6. davaWiroT OK Rilaks Variables dialogur fanjaraSi;

7. davaWiroT OK Rilaks Equation Format dialogur fanjaraSi.

Seiqmneba axali maTematikuri stili saxelad Matrix. SemdgomSi SeiZleba

SevusabamoT axali stili saWiro obieqtebs.

aRvniSnoT, rom zemoaRwerili moqmedebebiT SeiZleba gamosaxulebis

calkeul cvladebs an mudmivebs SevusabamoT garkveuli maTematikuri stili,

magram es ar exeba gamoTvlebis ricxviT Sedegebs, romlis stilia yovelTvis

Constants. dayenebuli stilebis sxva dokumentSi gamosayeneblad saWiroa jer

SevinaxoT dokumenti rogorc Sabloni anu .mct gafarToebiT, Semdeg ki gavxsnaT

axali dokumenti Sablonis saxiT da SevavsoT is arCeul SablonSi.

7.3 ricxviTi Sedegebis daformateba

gamoTvlebis ricxviTi Sedegis miRebisas Mathcad_i aCvenebs mas winaswari

SeTanxmebiT gaTvaliswinebul formatSi. am formatis Sesacvlelad davawkapunoT

gamosaxulebis nebismier adgilas da mivceT Format → Result… brZaneba an

movaxdinoT ormagi wkapuni gamoTvlebis Sedegze. gamova Result Format dialoguri

fanjara (nax.7.4), romelic Sedgeba ramdenime CanarTisagan:

Number Format (ricxvebis formati) CanarTis Format areSi SeirCeva sasurveli

formati. Number of decimal places (aTobiTi Tanrigebis raodenoba) da

Exponential threshold (eqsponentis zRurbli) mTvlelebis velebSi winaswari

101

SeTanxmebiT miTiTebulia 3. saWiroebisamebr SegviZlia es ricxvi

SevcvaloT. Tu saWiroa, davayenoT almebi: Show trailing zeros (bolo aTobiTi

Tanrigebis nulebis Cveneba), Show exponents in engineering format (eqsponentebis Cveneba inJinrul formatSi).

nax.7.4. dialoguri fanjara Result Format

Mathcad_Si arsebobs ricxvis warmodgenis 5 formati: o General (zogadi). am formatSi SeiZleba dayendes Tanrigebis raodenoba

aTobiTi wertilis marjvniv, eqsponentis zRurbli da bolo aTobiTi

Tanrigebis nulebis Cvenebis reJimi. Tu eqsponentis zRurblis

mniSvneloba gadametebulia, pasuxi iqneba warmodgenili

eqsponencialur an inJinrul formatSi. bolo aTobiTi Tanrigebis

nulebi iqneba naCvenebi mxolod 15 Tanrigis CaTvliT aTobiTi

wertilis Semdeg;

o Decimal (aTobiTi). am formatis arCevisas pasuxis warmodgena

eqsponencialuri formiT ar xdeba. aqac SeiZleba dayendes aTobiTi

Tanrigebis raodenoba da bolo aTobiTi Tanrigebis nulebis Cvenebis

reJimi, xolo ricxvis warmodgenis sizustea 15 aTobiTi Tanrigi;

o Scientific (samecniero anu eqsponencialuri formati) da Engineering (inJinruli). am formatebSi pasuxis warmodgena xdeba yovelTvis

eqsponencialuri formiT. Scientific da Engineering formatebSi Show exponents as E 000 almis dayenebiT xarisxis maCveneblis Tanrigebis

raodenoba gaxdeba 3_is jeradi ricxvi. orive formatSi SeiZleba

dayendes aTobiTi Tanrigebis raodenoba da bolo aTobiTi Tanrigebis

nulebis Cvenebis reJimi.

o Fraction (wiladuri). am formatSi xdeba Sedegis Cveneba wiladis saxiT.

nax.7.5_ze warmodgenilia cxrili, romelSic moyvanilia ricxvebis

sxvadasxva formatSi warmodgenis magaliTebi.

vTqvaT, x=8.25891, y=π*105, z=150 000 000, a=1.25.

102

x=8.26 General formati, Exponential threshold=15, Number of decimal places=2

x=8.2589 Decimal formati, Number of decimal places=4

x=8.2589100 Decimal formati, Number of decimal places=7, dayenebulia alami Show trailing zeros

z=1.50x108 General formati, Exponential threshold=6, Number of decimal places=2, dayenebulia alami Show trailing zeros

y=3.142x105 Scientific formati

y=31.416x104 Engineering formati

x=8.259E+000

y=31.416E+004

Engineering formati, dayenebulia alami

Show exponents as E 000

a=411 Fraction formati

a=45 Fraction formati, dayenebulia alami

Use mixed numbers nax.7.5. ricxvebis warmodgena sxvadasxva formatSi

Display Options (Cvenebis ofciebi) CanarTSi SeiZleba mivuTiToT kompleqsuri

ricxvis warmosaxviTi nawilis warmodgenisaTvis gamosayenebeli aso (i an j), aTvlis sistema, Matrix display style siidan SeiZleba avirCioT masivebis Cvenebis

stili: matricis saxiT (Matrix) an cxrilis saxiT (Table), Expand nested array almis gaaqtiurebiT SesaZlebelia rTuli masivebis gafarToebiT Cveneba. im

SemTxvevaSi, rodesac rTul masivs anu masivs, romlis elementebi Tavis

mxriv masivebia, matricis forma aqvs da ar aris gaTvaliswinebuli

gafarToebis SesaZlebloba, ekranze davinaxavT ara TviT masivs Tavis

elementebiTurT, aramed frCxilebSi Casmul Canawers, romelSic aRniSnulia

rTuli masivis calkeuli elementebis striqonebisa da svetebis raodenoba.

nax.7.6_ze naCvenebia rTuli masivis warmodgenis magaliTebi.

aRvniSnoT, rom imisaTvis, rom davinaxoT cxrilis elementi srulad,

elementis moniSvnis Semdeg avirCioT konteqsturi meniudan Down One Level (erTi doniT dabla) punqti, xolo aragafarToebuli formis aRsadgenad _

Up One Level (erTi doniT maRla).

Tu gvsurs dokumentis yvela masivi iyos naCvenebi matricis an

cxrilis saxiT anu maTi Cvenebis forma ar iyos damokidebuli masivis

zomaze (zogadad, Tu matricis an veqtoris striqonebis (svetebis)

raodenoba 9_s aRemateba, is avtomaturad cxrilis saxiT aris

warmodgenili), Display Options CanarTSi Sesabamisi miTiTebebis Semdeg saWiroa

davayenoT Set as Default alami.

103

Tolerance (daSveba) CanarTSi dayendeba kompleqsuri ricxvis zRurbli

(Complex threshold) da xdeba imis miTiTeba Tu ra sididis mcire ricxvi unda

iyos aRqmuli rogorc nuli (Zero threshold). Unit Display (sazomi erTeulebis Cveneba) CanarTSi SesaZlebelia sazomi

erTeulebis wiladis saxiT warmodgenis (Format units) da maTi gamartivebis

reJimebis (Simplify units when possible) dayeneba.

nax.7.6. rTuli masivis warmodgenis magaliTebi

yvela Sedegis parametrebis Sesacvlelad:

1. davawkapunoT dokumentis cariel adgilas;

2. mivceT Format Result… brZaneba;

3. SevcvaloT parametrebi;

4. OK

mTel dokumentSi dayendeba Sedegebis Cvenebis axali parametrebi da

Seicvleba im Sedegebis warmodgenis forma, romelTa formati ar iyo

individualurad specificirebuli.

igives mivaRwevT calkeuli Sedegis parametrebis SecvliT da Set as Default almis dayenebiT.

104

7.4 teqstisa da abzacis daformateba

teqstis daformateba gulisxmobs Sriftis tipis, zomis, moyvanilobis

stilisa da simboloTa feris SerCevas.

teqstis daformatebisaTvis gamoiyeneba Formatting panelis Sesabamisi velebi

da Rilakebi da menius Format → Text… brZaneba (an konteqsturi menius teqstis daformatebis punqtebi), romliTac gamoiZaxeba Text Format dialoguri fanjara

(nax.7.7).

Text Format dialoguri fanjris Font: velSi SeirCeva teqstis akrebis

sasurveli Srifti, Font Style: velSi – moyvanilobis stili: Regular (Cveulebrivi),

Italic (daxrili), Bold (sqeli), Bold Italic (sqeli daxrili), xolo Size: velSi _

Sriftis zoma. simboloTa feris arCeva xdeba Color: siiseburi velis

CamonaTvalidan. Effects areSi gvaqvs almebis jgufi, romelTa dayenebiT SeirCeva

daformatebis Semdegi reJimebi: Strikeout _ xazgadasmuli teqstis akreba, Underline _ xazgasma, Subscript _ qveda indeqsis akreba anu teqstis ganlageba striqonis

qvedoneze, Superscript _ zeda indeqsis akreba anu teqstis ganlageba striqonis

zedoneze. Sample areSi aisaxeba SerCeuli Sriftis nimuSi Tavisi maxasiaTeblebiT.

nax.7.7. teqstis daformatebis dialoguri fanjara

daformatebis maxasiaTeblebis dayeneba SesaZlebelia rogorc teqstis

akrebamde, aseve akrebis Semdeg _ moniSnuli fragmentisaTvis.

Tu Tagvis kursori imyofeba teqstur areSi, SesaZlebeli xdeba ara mxolod

teqstis, aramed abzacis daformatebac. amas emsaxureba Formatting panelis

Sesabamisi Rilakebi da Format → Paragraph Format… brZaneba. am brZanebiT da

105

agreTve konteqsturi menius Paragraph... punqtiT gamoiZaxeba abzacis daformatebis

dialoguri fanjara (nax.7.8).

nax.7.8. abzacis daformatebis dialoguri fanjara

Paragraph Format dialoguri fanjris Indent (wanacvleba, dacileba)

ganyofilebis Left: (marcxena) da Right: (marjvena) velebSi SeirCeva abzacis yvela

striqonis dacileba teqstis aris marcxena da marjvena sazRvrebidan. Special: velis CamonaTvalSi SeirCeva, xolo By: velSi dayendeba abzacis pirveli

striqonis (First Line) an danarCeni striqonebis (Hanging) dacileba teqstis aris

marcxena sazRvridan. standartulad aq gvaqvs reJimi none. wanacvlebis dayeneba

SesaZlebelia agreTve saxazavis meSveobiT. amisaTvis davawkapunoT abzacis

nebismier adgilas (an movniSnoT abzaci) da mivceT View → Ruler brZaneba. saxazavis zeda isris gadaadgilebiT dayendeba abzacis pirveli striqonis, xolo qveda

isriT – danarCeni striqonebis dacileba.

Bullets: velSi airCeva markerebis an cifrebis stili mimdinare da momdevno

abzacebis siebis saxiT gasaformeblad, xolo Alignment ganyofilebaSi

gadamrTveli unda iyos CarTuli erT_erT poziciaSi: Left – abzacis sworeba

teqstis marcxena sazRvarze, Right _ abzacis sworeba teqstis marjvena sazRvarze, Center – abzacis centrireba anu misi moTavseba marcxena da marjvena sazRvrebidan

Tanabari daSorebiT.

Tabs… (tabulacia) Rilakze dawkapunebiT gamoiZaxeba Tabs dialoguri

fanjara, sadac SesaZlebelia tabulaciis poziciebis dayeneba (ix. 7.5).

abzacebis daformateba SesaZlebelia rogorc teqstis akrebamde, aseve

akrebis Semdeg _ moniSnuli abzacebisaTvis, amasTan erTi abzacis maxasiaTeblebis

misaTiTeblad sakmarisia movaTavsoT teqsturi kursori abzacis nebismier

adgilas.

106

7.5 tabulaciis poziciebis dayeneba

klaviaturis Tabs klaviSze daWeriT xdeba garkveuli manZiliT kursoris

poziciis gadaadgileba. tabulaciis poziciis dayeneba xdeba Tabs dialogur

fanjaraSi, romlis gamoZaxeba SesaZlebelia Format → Tabs… brZanebiT an Paragraph Format dialoguri fanjris Tabs… Rilakze dawkapunebiT (nax.7.9).

Tabs dialogis Tab stop position velSi sasurveli ricxvis Setanis Semdeg unda

davaWiroT Set (dayeneba) Rilaks, tabulaciis meore poziciisaTvis isev SevitanoT

ricxvi da davaWiroT Set_s da a.S. tabulaciis poziciebis dayeneba SesaZlebelia aseve saxazavis meSveobiT.

amisaTvis davawkapunoT abzacis nebismier adgilas (an movniSnoT erTi an

ramdenime abzaci) da mivceT View → Ruler brZaneba. saxazavze dawkapuneba daayenebs am adgilas tabulaciis pozicias da saxazavze gamoCndeba Sesabamisi simbolo. Tu

gvsurs tabulaciis poziciis gadaadgileba, davaWiroT saxazavze tabulaciis

simbolos da Tagvis marcxena RilakiT Drag and Drop teqnikiT gadavasrialoT

sasurvel adgilas.

nax.7.9. Tabs dialoguri fanjara

aRvniSnoT, rom saxazavze Tagvis marjvena RilakiT dawkapuneba gamoitans

mis konteqstur menius, romelSic SeirCeva is sazomi erTeuli, romelic iqneba

gamoyenebuli Mathcad_is dialogebSi: Inches (diumebi), Centimeters (santimetrebi),

Points (wertilebi) an Picas (piqselebi).

7.6 stilis daformateba

teqstur areSi teqstis Setana winaswari SeTanxmebiT xorcieldeba Normal (Cveulebrivi) stiliT. survilisamebr SesaZlebelia sxva stilis SerCeva Formatting

107

panelis stilebis siidan an Text Styles dialogidan, romelSic SevdivarT Format → Style… brZanebiT (nax.7.10).

nax.7.10. Text Styles dialoguri fanjara

arCeuli stilis modifikaciisaTvis:

1. mivceT brZaneba Format → Style…;

2. Styles: velis CamonaTvalidan avirCioT sasurveli stili da davaWiroT

Modify… Rilaks;

3. gamoCndeba stilis parametrebis gansazRvris Define Style dialoguri fanjara

(nax.7.11), romelSic xdeba stilis parametrebis Secvla.

nax.7.11. Define Style dialoguri fanjara

Define Style dialoguri fanjris Font... RilakiT SevalT dialogSi, sadac

SesaZlebelia sxva Sriftis, misi parametrebis da specefeqtebis dayeneba, xolo

Paragraph... RilakiT SevalT dialogSi, sadac SesaZlebelia wanacvlebis, sworebis

da abzacis sxva parametrebis Secvla. modifikaciis Semdeg Seicvleba im teqsturi

areebis gaformeba, sadac es stili iyo gamoyenebuli.

axali stilis formirebisaTvis:

1. mivceT brZaneba Format → Style…;

2. Text Styles dialogur fanjaraSi davaWiroT New… Rilaks. gamoCndeba Define Style dialoguri fanjara (nax.7.11);

108

3. Name: velSi SevitanoT axali stilis saxeli. Tu axali stilis Seqmnas

romelime arsebuli stilis safuZvelze vapirebT, Based On: velis

CamonaTvalidan avirCioT saWiro stili;

4. Font... da Paragraph... RilakebiT SevideT Sesabamis dialogebSi da davayenoT

axali stilis sasurveli parametrebi.

Define Style dialoguri fanjris daxurvisas axali stilis saxels vnaxavT

stilebis siaSi, amasTan im stilis saxeli, romlis safuZvelze axali stili iyo

Seqmnili, aseve darCeba siaSi.

stilis wasaSlelad:

1. mivceT brZaneba Format → Style…;

2. Styles: velis CamonaTvalSi davawkapunoT wasaSlel stilze;

3. davaWiroT klaviaturis Delete Rilaks.

7.7 obieqtis Tvisebebis dayeneba

Mathcad_is obieqtebs: maTematikur gamosaxulebas Tu teqsts, komponents Tu

ubans _ iseve rogorc Windows 95/XP operaciuli sistemis nebismieri gamoyenebiTi programis obieqtebs, gaaCnia Tavisi Tvisebebi, romlebic damokidebulia moniSnuli

obieqtis tipze.

avirCioT obieqtad maTematikuri are da Format → Properties… brZanebiT an

konteqsturi menius Properties… punqtiT gamoviZaxoT Properties dialoguri fanjara

(nax.7.12), romelic Sedgeba ramdenime CanarTisagan:

nax.7.12. maTematikuri gamosaxulebis Tvisebebis

dialoguri fanjara

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Display CanarTis Highlight Region almis dayenebiT xdeba gamoyofili areebis

feriT gaformeba. Highlight Region almis dayenebisas gaaqtiurdeba Choose Color… (feris SerCeva) Rilaki. masze daWeriT gamoiZaxeba ferTa palitra,

sadac SeirCeva sasurveli feri.

Show Border almiT xdeba CarCos dayeneba gamoyofili gamosaxulebis an

rastris irgvliv.

Display at Original Size almis dayenebiT xdeba gamosaxulebis an rastris

Cveneba pirvandel zomebSi.

Tag (etiketi) velSi SesaZlebelia gamoyofili aris markireba etiketiT,

romelic warmoadgens asoebis, cifrebis da harebis krebuls, sadac

dauSvebelia zogi specialuri simboloebi.

Calculation CanarTis Calculation Options areSi gvaqvs ori alami: Disable Evaluation (gamoTvlebis gamorTva) da Enable Optimization (optimizaciis SesaZlebloba).

Disable Evaluation almis CarTviT gamoyofili maTematikuri are kargavs

Tavis Tvisebebs da ar monawileobs gamoTvlebSi. programa aRiqvams mas

rogorc komentars. am dros aris marjvena zeda kideSi Cndeba Savi markeri.

imisaTvis, rom maTematikuri are gaxdes xelmisawvdomi gamoTvlebisaTvis,

davawkapunoT masze, Format → Properties… brZanebiT SevideT Properties dialogSi, romlis Calculation CanarTSi movxsnaT alami Disable Evaluation an gavxsnaT amave aris konteqsturi meniu da avirCioT Enable Evaluation brZaneba.

Enable Optimization almis CarTva moaxdens gamoyofili maTematikuri aris

optimizacias.

Protect CanarTSi SeiZleba davayenoT alami Protect region from editing (aris dacva redaqtirebisagan). dacva SeiZleba ganxorcieldes im SemTxvevaSi, Tu

redaqtirebisagan daculia TviT dokumentic.

Tu obieqtad arCeulia teqsturi are, Properties dialogi Sesabamisad

nax.7.13. teqsturi aris Tvisebebis dialogis Text CanarTi

optimizaciis ganxilva moxdeba 8.7_Si

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Seicvleba, kerZod, Calculation CanarTis magivrad gveqneba Text CanarTi (nax. 7.13)

almebiT: Occupy Page Width da Push Regions Down As You Type. Occupy Page Width almiT teqsturi are daikavebs gverdis mTel siganes,

xolo Push Regions Down As You Type almis dayenebiT xdeba beWdvisas areebis qveviT

Caweva raTa ar moxdes areebis zeddeba.

Tu obieqtad arCeulia ubani, Format → Properties… brZanebiT gamoviZaxebT

ubnis Tvisebebis dialogs CanarTebiT: Display, Area da Protect. Area CanarTSi

SesaZlebelia ubnisaTvis saxelis miniWeba (Area name), ubnis sazRvris (Line), miniWebuli saxelis (Name), piqtogramis (Icon) da Caketvis TariRisa da drois

(Timestamp) Cvenebis reJimebis dayeneba.

7.8 grafikebis daformateba

Format → Graph brZanebas aqvs Semdegi qvebrZanebebi: X_Y Plot… (dekartis grafiki), Polar Plot… (polaruli grafiki), 3D Plot… (3_ganzomilebiani grafiki), Trace… (kvali, traeqtoria) da Zoom… (masStabi).

dekartis, polaruli da 3_ganzomilebiani grafikebis daformateba iyo

ganxiluli 5.3 _ 5.8 _Si.

Trace qvebrZanebiT xdeba traeqtoriis wertilebis koordinatebis amokiTxva.

amisaTvis:

1. davawkapunoT grafikis nebismier adgilas;

2. mivceT Format → Graph → Trace… brZaneba. gamoCndeba Sesabamisi tipis

grafikis (dekartis an polarulis) traeqtoriis dialoguri fanjara.

nax.7.14_ze naCvenebia X_Y Trace dialogi;

nax.7.14. X_Y Trace dialogi

3. davayenoT Track Data Points alami, romliTac xdeba mxolod uSualod

traeqtoriaze mdebare (da ara nebismieri) wertilebis koordinatebis

amokiTxva;

4. gadavataroT Tagvi im traeqtoriis gaswvriv, romlis wertilebis

koordinatebis amokiTxva gvsurs. punqtiruli gadajvaredinebuli

wrfewirebic gadainacvlebian erTi wertilidan meoreze. mimdinare

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wertilis X da Y koordinatebi (an radiusis da kuTxis mniSvnelobebi)

iqneba dafiqsirebuli Sesabamis velebSi (nax.7.15);

nax.7.15. grafikis wertilebis koordinatebis amokiTxva

5. Tu davaWerT klaviaturis marjvena an marcxena mimarTulebis klaviSs,

gadavaadgildebiT traeqtoriis momdevno an wina wertilze, xolo zeda da

qveda mimarTulebis klaviSebis gamoyenebiT gadavalT sxva traeqtoriebze.

dafiqsirebuli koordinatebis mniSvnelobebi SeiZleba traeqtoriis

dialoguri fanjris Copy X, Copy Y (an Copy Radius, Copy Angle) RilakebiT

gadavitanoT buferul mexsierebaSi.

ori punqtiruli gadajvaredinebuli wrfewiri darCeba grafikze dialoguri

fanjris daxurvamde.

ganvixiloT Format → Graph → Zoom… brZaneba;

1. movniSnoT grafiki masze TagviT dawkapunebiT;

2. mivceT Format → Graph → Zoom… brZaneba. gamova nax.7.16_ze moyvanili X_Y Zoom dialoguri fanjara (an Polar Zoom _ Tu moniSnuli iyo polaruli

grafiki);

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nax.7.16. X_Y Zoom dialoguri fanjara

3. gamovyoT Tagvis gadaTrevis teqnikiT grafikis is regioni, romlis

masStabirebas vapirebT. Min: da Max: teqstur velebSi davinaxavT

gamoyofili regionis X da Y RerZebis koordinatebs (polaruli grafikis

SemTxvevaSi am tipis grafikis Sesabamis koordinatebs);

4. davaWiroT Zoom Rilaks. davinaxavT grafiks axali masStabiT. RerZebis

koordinatebis minimaluri da maqsimaluri mniSvnelobebi iqnebian iseTebi,

romlebic dafiqsirebulia Min: da Max: velebSi;

5. Tu gvsurs am masStabis gauqmeba, davaWiroT Unzoom Rilaks;

6. OK Rilakze daWeriT moxdeba axali masStabis dafiqsireba.

Tu gvaqvs grafiki, romlis masStabis Secvla ukve moxda, SesaZlebelia

sawyisi masStabis aRdgena. amisaTvis X_Y Zoom dialogSi davaWiroT Full View Rilaks.

7.9 ferebis dayeneba

Format → Color brZanebas aqvs Semdegi qvebrZanebebi:

Background… _ samuSao furclis fonis feris Secvla;

Highlight… _ gamoyofili areebis feris dayeneba;

Annotation… _ anotaciis feris dayeneba;

Use Default Palette _ winaswari SeTanxmebis palitris gamoyeneba;

Optimize Palette _ palitris optimizacia.

pirveli sami qvebrZanebiT gamoiZaxeba Sesabamisi dialoguri fanjrebi,

sadac warmodgenil ferTa palitraSi SevirCevT CvenTvis sasurvel fers da OK Rilakis meSveobiT cvlilebas davadasturebT.

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7.10 ubnebis daformateba

arsebobs SemTxvevebi, rodesac saWiroa movaxdinoT samuSao furclis ubnis

Caketva raTa davicvaT Cveni dokumenti (Tundac sxva momxmareblisagan) an SekumSva.

Format → Area brZanebas aqvs Semdegi punqtebi: Lock… (Caketva), Unlock… (Caketvis moxsna), Collaps (SekumSva), Expand (gafarToeba).

ubnis Casaketad:

1. davawkapunoT ubnis SigniT;

2. mivceT Format → Area → Lock… brZaneba. gamoCndeba Lock Area dialoguri

fanjara (nax.7.17);

nax.7.17. ubnis Caketvis dialoguriFfanjara

3. Tu gvsurs ubnis Caketva paroliT, avkriboT paroli (asoebis, cifrebis da

sxva simboloebis kombinacia) dialogis pirvel velSi;

4. parolis Setanis SemTxvevaSi gavimeoroT is Reenter password: velSi;

5. Collapse when locked almis dayenebiT xdeba Caketili ubnis SekumSva, xolo

Show lock timestamp almis dayenebiT _ ubnis bolo Caketvis TariRis da

drois Cveneba;

6. SekumSuli ubnis dasamalad masze marjvena wkapuniT gamoviZaxoT

konteqsturi meniu, avirCioT Properties... punqti, SevideT Properties dialogis

Area CanarTSi, sadac Sesabamisi almebis moxsniT moxdeba ubnis sruli

damalva;

7. davaWiroT OK Rilaks.

Caketili ubnis sazRvrebze davinaxavT boqlomis gamosaxulebas da Caketvis

TariRsa da dros (Tu Show lock timestamp alami iyo dayenebuli), xolo SekumSul

ubans winaswari SeTanxmebiT vnaxavT erTi wrfewiris saxiT.

damalul areze Tagvis gadatarebiT gamoCndeba ori punqtiruli wrfewiri –

ubnis zeda da qveda sazRvrebi.

ubnis SesakumSad Caketvis gareSe:

1. davawkapunoT masze;

2. mivceT Format → Area → Collapse brZaneba.

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ubnis Caketvis moxsna Semdegnairad xdeba:

1. davawkapunoT Caketil ubanze;

2. avirCioT Format → Area → Unlock… brZaneba (Tu ubani iyo Caketili paroliT,

saWiroa misi Setana);

3. davaWiroT OK Rilaks.

ubnis blokireba moixsneba da SesaZlebeli gaxdeba misi redaqtireba. Tu

ubani iyo Caketili parolis gareSe, nebismier momxmarebels SeuZlia blokirebis

moxsna Format → Area → Unlock… brZanebiT.

SekumSuli ubnis misi pirvandeli saxiT dasanaxad saWiroa misi gafarToeba.

amisaTvis:

1. davawkapunoT sazRvris wrfewirze;

2. avirCioT Format → Area → Expand brZaneba.

7.11 areebis gancalkeveba da sworeba.

gverdebis xelmeore numeracia

areebis urTierTgadafarvis SemTxvevaSi saWiro xdeba maTi gancalkeveba,

rac Format → Separate Regions brZanebiTExorcieldeba. igives mivaRwevT calkeuli

areebis individualuri gadaadgilebiTac da, Tu saWiroa, Sesabamis adgilebSi

damatebiTi striqonebis CasmiT. amasTan ar unda daviviwyoT, rom zogjer Format → Separate Regions brZaneba ise gadaadgilebs areebs, rom gamoTvlebis mimdevroba

Seicvleba, amitom ufro xelsayrelia areebis gancalkeveba movaxdinoT xeliT.

areebis sworebisaTvis:

1. gamovyoT areebi;

2. avirCioT Format → Align Regions → Across brZaneba (sworeba horizontalis

gaswvriv) an Format → Align Regions → Down (sworeba vertikalis gaswvriv).

igives mivaRwevT Standard panelis da RilakebiT.

areebis vertikaluri sworeba SesaZlebelia agreTve saxazavis meSveobiT.

amisaTvis:

1. mivceT View → Ruler brZaneba; 2. davawkapunoT saxazavis im adgilas, romelic areebis marcxena kideebis

sasurvel daSorebas Seesabameba. saxazavze gamoCndeba tabulaciis simbolo;

3. tabulaciis simboloze marjvena wkapuni gamoitans konteqstur menius.

avirCioT Show Guideline punqti. gamoCndeba mwvane vertikaluri xazi, romlis

adgilmdebareobis Secvla SesaZlebelia tabulaciis simbolos gadaTreviT;

4. gamovyoT da gadavaadgiloT areebi mwvane xazTan.

Format → Repaginate Now brZanebiT xdeba dokumentis gverdebad xelmeore

dayofa. Mathcad_i avtomaturad dayofs dokuments gverdebad ise, rom arc erTi

are ar gadakveTs gverdis sazRvrebs.

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Tavi VIII mTavari menius Tools (instrumentebi) punqti

8.1 mTavari menius Tools punqtis Semadgenloba

mTavari menius Tools punqtiT an Alt + T klaviSebis kombinaciiT gamoiZaxeba

Semdegi qvemeniu:

Spelling... – marTlweris Semowmeba;

Animation – animaciuri klipebis Seqmna da aRwarmoeba;

Protect Worksheet... – samuSao furclis dacva;

Calculate _ gamoTvlebis reJimis dayeneba; Optimize _ gamoTvlebis optimizacia; Disable Evaluation _ calkeuli maTematikuri aris gaangariSebis procesidan

gamoricxva; Trace Error (Secdomis kvali) – Secdomis wyaros gamovlineba; Worksheet Options... _ samuSao furclis ofciebi; Preferences… (upiratesobani) _ parametrebis momarTva.

8.2 marTlweris Semowmeba da koreqtireba

marTlweris Semowmeba da koreqtireba xdeba Tools → Spelling… brZanebiT an

Standard panelis Rilakze daWeriT. amisaTvis:

1. davawkapunoT im adgilas, saidanac gvsurs daviwyoT marTlweris

Semowmeba. Mathcad_i daiwyebs Semowmebas am adgilidan da gaagrZelebs

dokumentis bolomde, ris Semdeg SesaZlebelia procesis Sewyveta an

gagrZeleba dokumentis dasawyisidan;

2. mivceT Tools → Spelling brZaneba an davaWiroT Standard panelis

Rilaks.

Mathcad_i daiwyebs marTlweris Semowmebas, risTvisac iyenebs

inglisuri enis leqsikons, gamdidrebul maTematikuri terminologiiT da

momxmareblis personaluri leqsikoniT. Tu dokumentSi aRmoCndeba

Mathcad_isaTvis ucnobi sityva, gaixsneba Check Spelling (marTlweris

Semowmeba) dialoguri fanjara (nax.8.1), sadac Not Found: velSi davinaxavT

am sityvas da Change To: velSi savaraudo cvlilebebis CamonaTvals. Tu

programa ver gvTavazobs Secvlis rekomendacias, naCvenebi iqneba

mxolod misTvis ucnobi sityva;

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nax.8.1. marTlweris Semowmebis dialoguri fanjara

3. Tu Secvlis rekomendaciebis CamonaTvali Seicavs sityvis swor variants,

movniSnoT is, Tu ara _ avkriboT is Change To: velSi. davaWiroT Change Rilaks. Suggest Rilaks viyenebT, Tu gvsurs Secvlis damatebiTi, magram

naklebi albaTobis variantebis daTvaliereba. Tu Mathcad_s ara aqvs

damatebiTi SeTavazebebi, Suggest Rilaki ar iqneba aqtiuri.

Tu sityvis Secvla ar gvsurs, viyenebT Ignore (ignorireba) Rilaks. am

SemTxvevaSi Tu Mathcad_s momavalSi es sityva kidev Sexvdeba, is ar

iqneba aRqmuli rogorc arasworad dawerili.

Add RilakiT sityva iqneba Setanili momxmareblis personalur

leqsikonSi.

SeiZleba agreTve movaxdinoT marTlweris Semowmeba teqstis gamoyofili

fragmentisaTvis.

aRvniSnoT, rom marTlweris Sesamowmeblad SesaZlebelia inglisuris

sasurveli dialeqtis miTiTeba. amisaTvis Tools → Preferences… brZanebiT SevdivarT

dialogSi, romlis Language CanarTSi moyvanilia xelmisawvdomi dialeqtebis

CamonaTvali.

8.3 animaciuri klipebis Seqmna da aRwarmoeba

Tools → Animation punqts gaaCnia ori qvebrZaneba: Record… (Cawera) da

Playback… (aRwarmoeba). animaciuri klipebis Sesaqmnelad Mathcad_i iyenebs Frame (kadri) CaSenebul

cvlads, romelic Rebulobs mTel mniSvnelobebs (winaswari SeTanxmebiT 0_dan

9_mde bijiT 1). SesaZlebelia ara mxolod grafikebis animacia, aramed yvelafris,

rac Frame cvladzea damokidebuli. Frame cvladi arsebiTad mimdinare kadris

nomers warmoadgens. kadrebis mimdevrobiTi aRwarmoeba gansazRvruli siCqariT

(winaswari SeTanxmebiT – 10 kadri 1 wuTSi) qmnis moZrav gamosaxulebas.

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animaciuri klipis Sesaqmnelad:

1. SevqmnaT gamosaxuleba an gamosaxulebaTa jgufi, romelTa mniSvnelobebi

saboloo jamSi arian Frame cvladze damokidebuli;

2. mivceT Tools → Animation → Record… brZaneba. gamoCndeba Record Animation dialoguri fanjara (nax.8.2);

3. punqtiruli marTkuTxediT gamovyoT dokumentis is nawili (nawilebi),

romelTa animaciur klips vqmniT. Tu klipi iqmneba grafikisaTvis, gamovyoT

uSualod grafiki (wina gansazRvrebebis gareSe);

nax.8.2. grafikisaTvis klipis Seqmna

4. Record Animation dialoguri fanjris For FRAME ganyofilebis From: da To: cifrul velebSi ganvsazRvroT FRAME cvladis mniSvnelobebis qveda da

zeda sazRvrebi, xolo At: velSi – kadrebis aRwarmoebis siCqare; 5. davaWiroT Animate Rilaks. daiwyeba klipis Seqmnis procesi. dialoguri

fanjris SuaSi – daTvalierebis zonaSi – gamoCndeba dokumentis

gamoyofili nawilebis miniaturuli gamosaxuleba. daTvalierebis zonaSi

davinaxavT yovel axal Seqmnil kadrs warweriT zonis qveviT (mag., FRAME =5), romelic aCvenebs mimdinare kadris nomers.

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aRvniSnoT, rom axali kadrebis gamoCenis siCqare ar aris damokidebuli

dialogis At: velSi miTiTebul cifrze, radgan Animation RilakiT xdeba

kadrebis Seqmna da ara aRwarmoeba;

6. Seqmnili animaciuri klipis Sesanaxad davaWiroT Save As… Rilaks.

gamoCndeba dialoguri fanjara, romelSic Sesatania klipis saxeli da

asarCevia saqaRalde, sadac is iqneba ganlagebuli.

klipi Seinaxeba gafarToebiT .avi (Audio_Video Interleaved) da misawvdomi iqneba Windows operaciuli sistemis garemos yvela programisaTvis.

animaciuri klipebi xSirad moiTxoven did mexsierebas, amitom maTi Senaxva

xdeba SekumSuli formiT. Record Animation dialoguri fanjris Options… Rilakze

daWeriT gamoiZaxeba dialogi, romelSic SesaZlebelia SekumSvis meTodis SerCeva.

aRvniSnoT, rom grafikebis animaciis Seqmnis dros umjobesia gamovrToT

grafikebis avtomaturi masStabirebis parametrebi da davayenoT Sesabamisi

parametrebi xeliT, radgan avtomaturi masStabirebisas grafikis zomebi xSirad

icvleba naxtomisebr FRAME cvladis diskretuli mniSvnelobebis Sesabamisad.

rogorc ki animaciuri klipis Seqmna damTavrdeba, gamoCndeba Play Animation (animaciis aRwarmoeba) fanjara, romelSic Cans klipis pirveli kadri (nax.8.3).

nax.8.3. animaciis aRwarmoebis fanjara

Seqmnili animaciuri klipis aRwarmoebisaTvis davawkapunoT fanjris

marcxena qveda kuTxis isarze.

dialogis meore Rilaki (isris marjvniv) warmoadgens aRwarmoebis marTvis

Rilaks. masze daWeriT gamoCndeba Semdegi meniu:

View (xedi) _ klipis fanjris zomis marTva. menius am punqts aqvs

qvepunqtebi: Half Size (fanjris zomis ganaxevreba), Normal Size (Cveulebrivi

zoma), Double Size (ormagi zoma); Speed (siCqare) – sasurveli siCqare dayendeba mcocis meSveobiT; Open… – avi–failebis gaxsnis dialogis gamotana; Close – mimdinare fanjris daxurva; Copy – buferul mexsierebaSi kopireba;

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Configure... (konfiguraciis dayeneba) – dialoguri fanjris gamoZaxeba,

romelSic xdeba daTvalierebis reJimis dayeneba – mTel ekranze an

garkveuli zomis fanjaraSi; Command… (brZaneba) – marTva brZanebaTa striqonidan.

nebismieri arsebuli animaciuri klipis aRwarmoebisaTvis:

1. mivceT Tools → Animation → Playback… brZaneba. gamoCndeba Play Animation

dialogi, romelic jer SekumSulia, radgan ar aris gaxsnili avi_faili;

2. aRwarmoebis marTvis dialogSi meore Rilakis menius Open… punqtze

dawkapunebiT gavxsnaT Open File dialoguri fanjara, sadac avirCioT saWiro

avi_faili; 3. davaWiroT Play Animation dialogis pirvel Rilaks.

aRvniSnoT, rom Tu dokumentSi iyo damyarebuli hiperlinki avi_failTan an

Casmuli avi_failis iarliyi, iarliyze an hipermimarTvaze orjeradi dawkapunebiT

moxdeba animaciuri klipis aRwarmoeba.

8.4 samuSao furclis dacva

dokumentis dacvisaTvis avirCioT Tools → Protect Worksheet... brZaneba. gamova Protect Worksheet dialoguri fanjara (nax.8.4).

nax.8.4. Protect Worksheet dialogi

Protect Worksheet dialoguri fanjris Protection Level ganyofilebaSi arsebuli

gadamrTvelebidan avirCevT sasurvels:

File – failis sruli dacva. am dros SeuZlebelia failis sxva gafarToebiT

Senaxva;

Content _ arsebuli areebis, ubnebis, teqsturi velebis dacva. SesaZlebelia

axali monacemebis Seyvana da daculi areebis kopireba;

Editing – samuSao furclis dacva redaqtirebisagan. am dros SeuZlebelia

redaqtireba, kopireba da axali areebis Seqmna.

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Password (optional): velSi avkriboT sasurveli paroli. Reenter password: velSi

gavimeoroT paroli da OK RilakiT davafiqsiroT Sesrulebuli moqmedebebi.

Tu gvsurs dokumentis dacvis moxsna, avirCioT Tools → Unprotect Worksheet... brZaneba. Tu dacva gvqonda paroliT, unda avkriboT Sesabamisi sityva, ris Semdeg

dokumentis dacva moixsneba.

8.5 gamoTvlebis reJimebi

winaswari SeTanxmebiT Mathcad_i muSaobs gamoTvlebis avtomatur reJimSi,

rac niSnavs, rom yvelanairi angariSi da gardaqmna sruldeba myisierad, xolo

nebismieri Secvla gamoiwvevs xelaxal gadaangariSebas. xelaxali gadaangariSeba

xdeba mxolod dokumentis xiluli nawilisaTvis, xolo momdevno maTematikuri

gamosaxulebebi dokumentis qveviT gadaadgilebisamebr gamoiTvleba manam mTeli

samuSao furceli ar ganaxldeba. rodesac angariSebis dasamTavreblad programas

dro sWirdeba, Tagvis maCvenebeli Seicvlis formas da furclis qveviT

Setyobinebis striqonSi gamoCndeba sityva “Wait” (daicade). avtomaturi reJimis CarTva_gaTiSva xdeba Tools → Calculate → Automatic

Calculation brZanebiT, romelic arsebiTad alams warmoadgens.

roca avtomaturi reJimi gamorTulia, Mathcad_i muSaobs xeliT gamoTvlebis

reJimSi (Manual Mode) . am dros gamoTvlebi ar sruldeba specialuri brZanebis

miRebamde da momxmarebels ar sWirdeba angariSebis damTavrebis lodini. Tu

xeliT gamoTvlebis reJimSi movaxdineT cvlilebebi, romelnic gamoiwveven

ganaxlebis aucileblobas, Setyobinebis striqonSi wavikiTxavT “Calc”. amiT

Mathcad_i gvaxsenebs, rom saWiroa ekranze gamosaxuli Sedegebis ganaxleba.

Tools → Calculate → Calculate Now brZanebiT (an F9 klaviSiT an Standard panelis

= RilakiT) xdeba gamoTvlebis ganaxleba, magram gadaangariSdeba mxolod

dokumentis xiluli nawili. dokumentis qveviT gadaadgilebiT Setyobinebis

striqonSi isev gamoCndeba “Calc” anu axali gamosaxulebebis gamosaTvlelad isev

saWiro gaxdeba Tools → Calculate → Calculate Now brZaneba. xeliT gamoTvlebis reJimSi sifrTxiliT unda visargebloT beWdvis

brZanebiT, radgan dokumentis nawili SeiZleba iyos ganaxlebuli, nawili ki – ara.

Tu gvsurs movaxdinoT mTeli dokumentis gadaangariSeba, unda visargebloT

Tools → Calculate → Calculate Worksheet (Ctrl + F9) brZanebiT.

gamoTvlebis Sesawyvetad viyenebT Esc klaviSs. gamoCndeba dialoguri

fanjara, sadac OK–ze daWeriT vadasturebT Sewyvetas. maTematikur

gamosaxulebaze davinaxavT saTanado Setyobinebas. gamoTvlebis gasagrZeleblad

davawkapunoT am gamosaxulebaze da davaWiroT F9 klaviSs an Standard panelis =

Rilaks.

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8.6 calkeuli maTematikuri aris gaangariSebis

procesidan gamoricxva

gamoTvlebis dros SesaZlebelia calkeuli maTematikuri aris

gaangariSebis procesidan gamoricxva. amis gansaxorcieleblad arsebobs ramdenime

saSualeba:

davawkapunoT maTematikur areSi, Format → Properties… brZanebiT SevideT Properties dialogSi, romlis Calculation CanarTSi davayenoT Disable Evaluation alami (ix. 7.7);

davawkapunoT maTematikur areSi da mivceT Tools → Disable Evaluation brZaneba, romelic arsebiTad alams warmoadgens;

maTematikuri aris konteqsturi meniudan avirCioT Disable Evaluation punqti.

8.7 gamoTvlebis optimizacia

simboluri da ariTmetikuli gamoTvlebi Mathcad_Si erTmaneTisagan

damoukideblad sruldeba sxvadasxva procesorebis mier. imisaTvis, rom am orma

procesorma erTianad miiRon monawileoba gamoTvlebis procesSi, saWiroa

movaxdinoT gamoTvlebis optimizacia. optimizacia mdgomareobs imaSi, rom jer

simboluri procesori axdens maTematikuri gamosaxulebis gamartivebas, xolo

Semdeg iwyeba miRebuli gamartivebuli gamosaxulebis ricxviTi gamoTvla.

Tools → Optimize brZanebas aqvs sami qvebrZaneba:

Equation _ maTematikuri gamosaxulebis optimizacia;

Worksheet _ samuSao furclis optimizacia;

Show optimization _ optimizaciis Sedegad miRebuli gamartivebuli

gamosaxulebis Cveneba. nax.8.5_ze moyvanilia gamoTvlebis optimizaciis magaliTi.

SeviyvanoT monacemebi. davawkapunoT gamosaxulebaze da mivceT Tools → Optimize → Equation brZaneba an am gamosaxulebis konteqsturi meniudan avirCioT

Optimize punqti. Tu Mathcad_i “moZebnis” gamosaxulebis gamartivebul formas, mis

marjvniv gamoCndeba wiTeli varskvlavi (rogorc naCvenebia nax.8.5_ze moyvanil

magaliTSi), sawyisi gamosaxuleba Seicvleba gamartivebuliT (ara vizualurad,

aramed programis “SigniT”) da gamoiTvleba gamartivebuli gamosaxuleba.

Tu gvsurs gamartivebuli gamosaxulebis daTvaliereba, davawkapunoT masze

Tagvis marjvena RilakiT da avirCioT Show Optimization punqti an davawkapunoT

gamosaxulebaze da mivceT Tools → Optimize → Show Optimization brZaneba. gamoCndeba Optimized Result fanjara, sadac iqneba Cawerili gamartivebuli gamosaxuleba.

swored am gamartivebuli gamosaxulebis gamoTvliT miiReba ricxviTi Sedegi. ra

Tqma unda, igive Sedegs miviRebT optimizaciis gareSec, magram rTuli

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gamosaxulebebis SemTxvevaSi optimizacia sagrZnoblad amcirebs gamoTvlebis

xangrZlivobas.

nax.8.5. gamoTvlebis optimizaciis magaliTi

Tu Mathcad_ma ver SeZlo sawyisi gamosaxulebis gamartiveba, mis marjvniv

gamoCndeba lurji varskvlavi.

Tools → Optimize → Worksheet brZanebiT, romelic arsebiTad alams

warmoadgens, xdeba optimizaciis reJimis dayeneba_moxsna mTeli dokumentisaTvis.

Tu samuSao furclis optimizaciis reJimi dayenebulia, calkeuli gamosaxuleba

SeiZleba gamovricxoT optimizaciis procesidan konteqsturi meniudan Optimize punqtis SerCeviT.

8.8 Secdomis wyaros gamovlineba

Tu Mathcad_i ver agrZelebs gamoTvlebs raRaca Secdomis gamo, is wiTlad

gaaferadebs Sesabamis adgils, xolo gamosaxulebaze dawkapunebiT gamoitaneba

Setyobineba Secdomis tipis mokle aRweriT (nax.8.6).

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nax.8.6. Secdomis wyaros gamovlineba

rogorc vxedavT magaliTidan, Secdoma gamoaSkaravda meoTxe

gamosaxulebaSi, magram is warmoiSva g(x) funqciaSi, sadac moxda 0_ze gayofa. momxmarebels SeuZlia TviTon gamoavlinos Secdomis warmoSobis wyaro an

miandos es procedura Mathcad_s. amisaTvis: 1. davawkapunoT gamosaxulebaze, romelSic gamovlinda Secdoma, da mivceT

Tools → Trace Error brZaneba. gamoCndeba Trace Error fanjara (nax.8.7);

nax.8.7. Trace Error fanjara

2. Trace Error fanjaraSi aris 4 Rilaki, romelTa meSveobiT xdeba SecdomasTan

dakavSirebuli erTi gamosaxulebidan meoreze gadaadgileba. es Rilakebia:

|<<First (pirveli); <Previous (wina); Next> (momdevno); Last>>| (bolo). |<<First

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Rilakis gamoyenebiT xdeba im gamosaxulebaSi gadasvla, romelSic

warmoiSva Secdoma.

8.9 samuSao furclis ofciebi

Tools → Worksheet Options… brZanebiT gaixsneba Worksheet Options dialoguri

fanjara (nax.8.8) Semdegi CanarTebiT:

Built-In Variables _ CaSenebuli cvladebi;

Calculation _ gamoTvla;

Display _ displei;

Unit System _ erTeulTa sistema;

Dimensions _ ganzomilebebi.

nax.8.8. Worksheet Options dialoguri fanjara

Built-In Variables CanarTSi xdeba sistemuri cvladebis: ORIGIN (veqtorebis da matricebis sawyisi indeqsi, winaswari SeTanxmebiT udris 0); Convergence Tolerance (TOL) (ricxobrivi gamoTvlebis cdomileba, winaswari SeTanxmebiT udris 0.001);

Constraint Tolerance (CTOL) (SezRudvebze daSveba, winaswari SeTanxmebiT udris 0.001)

da sxv. _ mniSvnelobebis Secvla, ris Semdeg rekomendirebulia mivceT Tools → Calculate → Worksheet brZaneba raTa davrwmundeT, rom dokumentis yvela

maTematikuri gamosaxuleba gamoTvlilia CaSenebuli cvladebis axali

mniSvnelobebisaTvis.

Calculation CanarTSi SeiZleba davayenoT ori alami:

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Recalculate automatically – avtomaturi gadaangariSeba; Optimize expression before calculating – optimizaciis reJimis dayeneba.

Tools → Worksheet Options → Display CanarTSi SesaZlebelia zogi

operatorisaTvis sxva misi aRmniSvneli simbolos daweseba. es operatorebia:

lokaluri da globaluri miniWeba, muqi toloba, gamravleba da gayofa. am

operatorebis simboloebis Secvla calkeuli maTematikuri gamosaxulebisaTvis

SesaZlebelia Sesabamisi simbolos konteqsturi meniudan.

Unit System CanarTSi xdeba erTeulTa sistemis SerCeva ganzomilebis mqone

sidideebisaTvis: SI, MKS, CGS, US customary (aSS_s sistema), None. winaswari

SeTanxmebiT Mathcad_i iyenebs SI sistemas. Dimensions CanarTSi Display Dimensions almiT xdeba masis (Mass), sigrZis

(Length), drois (Time), temperaturis (Temperature), ganaTebulobis (Luminosity), denis (Current) da nivTierebis raodenobis (Substance) ganzomilebebis Cvenebis reJimis

dayeneba_moxsna.

8.10 parametrebis momarTva

Tools → Preferences… brZanebiT xdeba Preferences dialoguri fanjris

gamoZaxeba, romelsac aqvs oTxi CanarTi: General, HTML Options, Script Security da Language (nax.8.9).

nax.8.9. Preferences dialoguri fanjara

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General CanarTis ganyofilebebia:

o Startup Options (sastarto ofciebi), sadac SeiZleba davayenoT alami

Show Mathcad tips at startup _ programis gaSvebisas sasargeblo rCevebis

Cveneba;

o Keyboard Options (klaviaturis ofciebi) 2 almiT: Standard Windows shortcut keys _ standartuli swrafmoqmedebis klaviSebis gamoyeneba da

Context_sensitive equal signs _ konteqstis mimarT mgrZnobiare

Semoklebebis gamoyeneba;

o Default Worksheet Location (winaswari SeTanxmebiT dokumentis Senaxvis

adgili), sadac Browse… RilakiT SesaZlebelia arsebuli Senaxvis

adgilis Secvla;

o Recently Used Files (bolos gamoyenebuli failebi), sadac misaTiTebelia

bolos gamoyenebuli failebis raodenoba, romlebsac vnaxavT File menius CamonaTvalSi;

o Undo History (istoriis gauqmeba), sadac Maximum number of undoable actions per document: velSi xdeba dokumentSi gauqmebul moqmedebaTa

maqsimaluri ricxvis miTiTeba;

HTML Options CanarTSi xdeba Mathcad_is dokumentis .html gafarToebis mqone

failebis ofciebis SerCeva; Script Security CanarTSi SesaZlebelia Script_obieqtebis anu momxmareblis mier

Casmuli komponentebis dacvis ofciis SerCeva; Language CanarTSi xdeba marTlweris leqsikonis dialeqtis SerCeva.

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Tavi IX mTavari menius Window (fanjara) punqti

9.1 mTavari menius Window punqtis Semadgenloba

rogorc yvela programas, romelic muSaobs Windows operaciuli sistemis

garemoSi, Mathcad_sac gaaCnia momxmareblisTvis moxerxebuli mravalfanjriani

interfeisi.

Mathcad_Si SesaZlebelia vimuSaoT erTdroulad ramdenime dokumentTan,

romlebic programis CatvirTvis Semdeg iyvnen gamoyenebulni. maT Soris erT_erTi

aqtiuria. danarCenebis gaaqtiureba nebismier momentSi SesaZlebelia.

fanjrebTan muSaoba xdeba mTavari menius Window punqtis meSveobiT,

romelic Sedgeba Semdegi qvepunqtebisagan:

Cascade – dokumentis fanjrebis kaskaduri ganlageba; Tile Horizontal _ dokumentis fanjrebis horizontaluri ganlageba; Tile Vertical _ dokumentis fanjrebis vertikaluri ganlageba.

am qvepunqtebis garda, Window menius qveda nawilSi moyvanilia programis

CatvirTvis Semdeg gamoyenebuli dokumentebis sia. SesaZlebelia siis nebismieri

dokumentis gaaqtiureba. Window punqtis qvepunqtebis gamoZaxeba xdeba agreTve klaviaturis Alt + W

klaviSebis kombinaciiT.

9.2 fanjrebis kaskaduri ganlageba

(Cascade)

Window → Cascade brZaneba dokumentebis fanjrebs kaskadurad ganalagebs.

kaskaduri ganlagebisas fanjrebi ganTavsdebian Tanmimdevrulad, erTimeoris

nawilobrivi gadafarviT. sxva fanjrebze zemoT ganlagebuli fanjara Cans

mTlianad da aqtiuria. yvela dokumentis saTauris striqoni xilulia (nax.9.1).

aseT mdgomareobaSi SesaZlebelia fanjrebis minimizacia, zomebis Secvla da

daxurva saTauris striqonis marjvena kideSi arsebuli Sesabamisi Rilakebis

gamoyenebiT.

kaskaduri ganlageba moxerxebulia bevr fanjarasTan erTdrouli muSaobis

dros maTi gadarTvisaTvis. GgadarTva da sxva fanjris gaaqtiureba xdeba

saTauris striqonze dawkapunebiT.

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nax.9.1. fanjrebis kaskaduri ganlageba

9.3 fanjrebis horizontaluri da vertikaluri ganlageba

(Tile Horizontal, Tile Vertical)

Window → Tile Horizontal brZaneba dokumentebis fanjrebs horizontalurad

ganalagebs (nax.9.2), xolo Window → Tile Vertical brZaneba dokumentebis fanjrebs

ganalagebs vertikalurad (nax.9.3), amasTan rogorc horizontaluri, ise

vertikaluri ganlagebis dros yvela fanjris zoma erTi da igive iqneba.

rac ufro metia fanjrebis raodenoba ekranze, miT ufro mcirea maTi zoma

da Sesabamisad miT ufro mcirea fanjrebSi moTavsebuli dokumentebis xiluli

nawili. amitom am brZanebebis gamoyeneba mizanSewonilia ori_sami fanjris

SemTxvevaSi.

fanjrebis horizontaluri da vertikaluri ganlagebisas moxerxebulia

erTi Ffanjridan meoreSi obieqtebis kopireba_gadatana rogorc Edit → Copy, Edit → Cut, Edit → Paste brZanebebiT (an konteqsturi menius igive punqtebiT an Standard

129

instrumentTa panelis Sesabamisi RilakebiT), aseve Drag and Drop teqnikiT Tagvis

meSveobiT.

Tu gvaqvs fanjrebis didi raodenoba, Mathcad_i uars ityvis damatebiTi

dokumentebis gaxsnaze da gamoitans sainformacio Setyobinebas amis Taobaze.

muSaobis gasagrZeleblad saWiroa nawili fanjrebis daxurva Sesabamisi

fanjrebis saTauris striqonze mdebare daxurvis RilakiT an saTauris striqonis

konteqsturi menius Close brZanebiT.

nax.9.2. fanjrebis horizontaluri ganlageba

9.4 dokumentebis fanjrebis marTva

garda 9.1_Si moyvanili mTavari menius Window punqtis qvebrZanebebisa,

dokumentebis fanjrebTan muSaoba SesaZlebelia sxva gziTac.

rogorc ukve iTqva, programis CatvirTvis Semdeg momxmareblis mier yvela

gamoyenebuli dokumenti dafiqsirdeba Sesabamisi saTauris saxiT mTavari menius

130

nax.9.3. fanjrebis vertikaluri ganlageba

Window punqtSi, saidanac advilad SesaZlebelia sasurvel momentSi romelime

maTganis gaaqtiureba. aqtiuri dokumentis saxels CarTuli aqvs alami. aqtiuri

dokumentis fanjaraze SesaZlebelia vimoqmedoT menius striqonis marjvena kideSi

arsebuli RilakebiT (minimizaciis, fanjris zomis Secvlis da fanjris daxurvis).

aqtiuri dokumentis daxurva SesaZlebelia agreTve File → Close brZanebiT.

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Tavi X sainformacio resursebi. mTavari

menius Help punqti

10.1 mTavari menius Help (daxmareba) punqtis Semadgenloba

mTavari menius Help punqti gvexmareba Mathcad_is yvela SesaZleblobis

gamoyenebaSi. is Sedgeba Semdegi qvepunqtebisagan:

Mathcad Help F1 _ sacnobaro sistemis gamoZaxeba; What’s This? (ra aris es?) Shift +F1 – daxmareba miTiTebuli Temis

Sesaxeb;

Developer’s Reference – ganmviTareblebTan mimarTva;

Author’s Reference – avtorebTan mimarTva;

Tutorials _ Mathcad_Tan muSaobis TviTmaswavlebeli;

QuickSheets _ Mathcad_is gamoyenebis magaliTebi;

Reference Tables _ maTematikuri formulebis da cxrilebis sruli

cnobari;

E_books _ eleqtronuli wignebi;

User Forum – momxmarebelTa forumi;

Mathcad.com – Web_misamarTze gadasvla;

Mathcad Update – Mathcad_is ganaxleba;

About Mathcad... – mokle informacia Mathcad_is Sesaxeb. aqve aRvniSnoT, rom menius am punqtebTan muSaoba moiTxovs inglisuri enis

sabazo codnas.

10.2 Mathcad_is sacnobaro sistema

sacnobaro sistema warmoadgens did monacemTa bazas, romelic moculobiT

aRemateba eleqtronul wigns. sacnobaro sistemis da eleqtronuli wignebis

daniSnuleba erTmaneTisagan gansxvavebulia. eleqtronuli wigni Mathcad_Si warmoadgens Tematikurad gaerTianebuli dokumentebis erTobliobas, romlebic

exeba sistemis gamoyenebis sxvadasxva sferos da dakavSirebuli arian erTmaneTTan

hiperlinkebiT.

sacnobaro sistema Seicavs sistemasTan muSaobis yvela mniSvnelovani

sakiTxis srul da detalur informacias.

sacnobaro sistemis gamoZaxeba SesaZlebelia:

menius Help → Mathcad Help brZanebiT;

klaviaturidan F1 funqcionaluri klaviSiT;

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Standard instrumentTa panelis RilakiT.

samive SesaZleblobis gamoyenebiT gamodis daxmarebis dialoguri fanjara

(nax.10.1), romelic Sedgeba sami CanarTisagan: Contents (Semadgenloba), Index (sagnobrivi saZiebeli) da Search (Zieba):

nax.10.1. Mathcad Help dialoguri fanjara

Contents CanarTi warmodgenilia wignebis katalogis saxiT. yovel wigns

gaaCnia Tavisi dasaxeleba da is Tavis mxriv Sedgeba qvesaTaurebisagan. mag.,

Tu gvainteresebs Mathcad_Tan muSaobis dawyeba, avirCioT Sesabamisi wigni

(Getting Started), davawkapunoT mis marcxniv arsebul Rilakze da SevarCioT

sasurveli qvesaTauri (nax.10.2). fanjris marjvena areSi ganTavsdeba arCeuli

qvesaTauris Temis aRwera; Index CanarTSi moyvanilia terminebis da funqciebis CamonaTvali.

informaciis mopoveba xdeba sagnobrivi miTiTebiT. Type in the keyword to find: teqstur velSi Caiwereba mosaZebni Temis dasaxeleba an dasaxelebis nawili.

sasurvel Temaze ormagi wkapuniT an misi moniSvniT da Display Rilakze

daWeriT fanjris marjvena areSi gamoitaneba arCeuli Temis aRwera; Search CanarTSi Type in the keyword to find: teqstur velSi mosaZebn

informaciasTan dakavSirebuli sityvis SetaniT gamoitaneba yvela Tavebi,

sadac naxsenebia miTiTebuli sityva. aseTi tipis Zieba gvaZlevs ufro

farTo saSualebebs mivagnoT sasurvel Temas.

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nax.10.2. Mathcad Help dialogi arCeuli qvesaTauris Temis ganxilviT

mTavari menius Help → What’s This? brZanebis gamoyenebisas kursors eZleva

kiTxvis niSnis simbolos forma, ris Semdeg SeiZleba menius brZanebebidan an

instrumentTa panelidan avirCioT sasurveli Tema da davawkapunoT masze. miviRebT

daxmarebas am Temis Sesaxeb. Help → What’s This? brZaneba warmoadgens informaciis mopovebis martiv da moxerxebul formas.

mTavari menius Help → Developer’s Reference da Help → Autor’s Reference brZanebebiT SesaZlebelia eleqtronul biblioTekasTan dinamiuri kavSiris

damyareba, sxva maTematikur sistemebTan mimarTva, gamoqveynebuli eleqtronuli

publikaciebis avtorebTan dakavSireba da a.S.

10.3 sainformacio resursebis gamoyeneba (Resource Center)

sainformacio resurs_centri warmoadgens mZlavr monacemTa bazas, romelic

aerTianebs eleqtronul wignebs, sistemis Seswavlis sawyis sakiTxebs, swraf

magaliTebs, sistemis SemqmnelTa Web_biblioTekasTan kavSirs da a.S.

menius Help → Tutorials (Help → QuickSheets, Help → Reference Tables) brZanebiT

gamoiZaxeba Mathcad_is resursebis fanjara. Home Rilakze daWeriT gamoitaneba

resurs_centrSi Semavali Tematikis CamonaTvali (nax.10.3), romelTa gaaqtiureba

SesaZlebelia maTze dawkapunebiT.

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nax.10.3. resurs_centris fanjara

resurs_centris gamoZaxebisTanave aqtiurdeba Resources instrumentTa

paneli, sadac siis saxiT warmodgenilia yvela masSi Semavali Tematika (nax.10.4).

nax.10.4. Resources instrumentTa paneli

resurs_centris TematikebTan muSaobaSi gvexmareba Mathcad_is resursebis

fanjris instrumentTa paneli, romelSic Sedis Semdegi Rilakebi:

_ sawyis furcelze dabruneba;

_ Web_misamarTze gadasvlis instrumentTa panelis gaaqtiureba;

135

_ aqtiuri dokumentidan erTi nabijiT ukan dabruneba (Back);

_ Back moqmedebis uaryofa (Forward);

_ aqtiuri Tematikidan wina Tematikaze gadasvla;

_ aqtiuri Tematikidan momdevno Tematikaze gadasvla;

_ istoriis anu momxmareblis mier Sesrulebuli yvela moqmedebis

Cveneba;

_ Zebnis fanjris gamoZaxeba, sadac misaTiTebelia saZebni Temis

dasaxeleba;

_ moniSnuli obieqtis kopireba buferSi;

_ moniSnuli obieqtis Senaxva;

_ aqtiuri dokumentis dabeWdva.

resurs_centris Tematikebia:

Tutorials – aq damxmare eleqtronul saxelmZRvaneloSi aRwerilia Mathcad_i da ganxilulia sistemis axali versiis siaxleebi;

Quicksheets – aq moyvanilia yvelaze gavrcelebuli sxvadasxva saxis

sainJinro amocanebi, sadac Tavmoyrilia rogorc martivi, aseve rTuli

magaliTebi, romlebsac praqtikulad iyeneben maTematikur da

samecniero_teqnikur gamoTvlebSi, miTiTebani statistikuri gamoTvlebis

Casatareblad, programebis magaliTebi, miTiTebebi statistikuri analizisa

da monacemTa damuSavebis Casatareblad da a.S.;

Reference Tables – aq Tavmoyrilia yvela fundamenturi teqnikuri mecnierebis

cxrilebi, kanonebi, Teoremebi, mag., mendeleevis periodulobis sistema,

geometriuli sxeulebis moculobis, farTobisa da perimetris

gamosaTvleli formulebi, yvela metalis kuTri winaRoba da a.S.;

Image Processing – videogamosaxulebis Seqmna da damuSaveba, raSic

igulisxmeba Mathcad_Si matricebis saxiT warmodgenili ricxviTi masivebis

grafikul gamosaxulebad warmodgena, videogamosaxulebis warmodena

ricxviTi masivebis saxiT, am procesebTan dakavSirebul funqciaTa aRwera

da a.S.; Signal Processing – aq moyvanilia yvelaze gavrcelebul signalTa

damuSavebasTan dakavSirebuli informacia, aRwerilia Sesabamisi funqciebi,

maTi gamoyenebis semantika da a.S.; Wavelets Extension Pack – aq Tavmoyrilia veivletis analizis (signalebis

modelirebis sinusoidebis kombinaciebiT) funqciebis aRwera da magaliTebi.

sainformacio resurs_centrSi arsebuli nebismieri magaliTis Casma

momxmareblis samuSao furcelSi martivad SesaZlebelia.

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10.4 daxmarebis sxva saSualebebi

mTavari menius Help → User Forum brZanebiT SesaZlebelia internetis

gamoyenebiT daregistrireba rogorc Mathcad_is momxmarebeli da sxva

momxmareblebTan forumSi CarTva, sadac xdeba azrebis mimocvla, gamocdilebis

gaziareba da a.S. (nax.10.5).

nax.10.5. momxmarebelTa forumSi Sesvla

Help → Mathcad.com brZanebiT xdeba Mathcad_is produqtis Semqmneli firmis

Web_misamarTze gadasvla da siaxleebis gacnoba, xolo Help → Mathcad Update brZanebiT _ Mathcad_is ganaxleba.

menius Help → About Mathcad... brZanebiT SesaZlebelia momxmareblis

kompiuterze dayenebuli Mathcad_is versiis Sesaxeb informaciis moZieba.

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Tavi XI funqciebi Mathcad_Si

11.1 momxmareblis mier funqciebis Seqmna

Mathcad_s gaaCnia fundamentur da teqnikur mecnierebebSi arsebuli

maTematikuri funqciebis farTo speqtri. maTi im saxiT gamoyeneba, rogoricaa

Cadebuli sistemaSi Tavisi sintaqsiTa da semantikiT, amartivebs dasaxuli

amocanis gadaWras. funqciis mniSvnelobis gamosaTvlelad Insert → Function… brZanebiT CavsvaT SerCeuli funqciis Sabloni, markerebis adgilas SevitanoT

funqciis argumentebis mniSvnelobebi da gamoviyenoT tolobis niSani an avkriboT

funqciis saxeli, mrgval frCxilebSi mivuTiToT mZimeebiT erTimeorisagan

gamoyofili argumentebis konkretuli mniSvnelobebi da gamoviyenoT tolobis

niSani. saWiroebis SemTxvevaSi momxmarebels SeuZlia Seqmnas sakuTari funqciebic.

funqciis Seqmnisas momxmarebelma unda daicvas moqmedebaTa Semdegi

Tanmimdevroba:

1. akribos funqciis saxeli;

2. mrgval frCxilebSi Casvas funqciis argumenti an argumentebi, romlebic

erTimeorisagan mZimiT gamoiyofa;

3. gamoiyenos klaviaturis : simbolo an Calculator instrumentTa panelis

miniWebis niSani;

4. Seiyvanos formula, romelic gansazRvravs funqcias.

momxmareblis mier Seqmnili funqciisa da CaSenebuli funqciis

SedarebisaTvis ganvixiloT puasonis ganawileba – SevqmnaT sakuTari funqcia da

gamoviyenoT Mathcad_Si arsebuli puasonis ganawilebis funqcia (nax.11.1).

11.2 CaSenebuli funqciebis mimoxilva

Mathcad_Si CaSenebuli funqciebi dayofilia kategoriebad: beselis

funqciebi, kompleqsuri ricxvebis funqciebi, logariTmuli da eqsponencialuri

funqciebi, trigonometriuli funqciebi, SemTxveviTi ricxvebis Ffunqciebi,

finansuri funqciebi, interpolaciis da eqstrapolaciis funqciebi da a.S.

aRvweroT ramdenime funqcia Tematikis mixedviT.

matriculi da veqtoruli funqciebi

arsebobs matricebTan muSaobisaTvis gankuTvnili Semdegi CaSenebuli

funqciebi:

augment(M1,M2,...) _ erT matricaSi aerTianebs M1,M2,... matricebs, romelTac

striqonTa erTnairi raodenoba gaaCniaT;

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nax.11.1. momxmareblis mier Seqmnili puasonis ganawilebis amsaxveli funqciisa da

Mathcad_Si arsebuli puasonis ganawilebis funqciis Sedareba

identity(n) _ qmnis kvadratul erTeulovan n X n zomis matricas; stack(M1,M2,...) _ erT matricaSi aerTianebs M1,M2,... matricebs, romelTac

svetebis erTnairi raodenoba gaaCniaT, amasTan M2 matricis

elementebi M1_is qveS iqnebian ganlagebuli, M3 matricis _

M2_is qveS da a.S.; submatrix(A,ir,jr,ic,jc) _ gamoyofs sawyisi matricidan qvematricas, romlis striqonebi

Sedgeba sawyisi matricis ir_dan jr_mde striqonebis

elementebisagan, xolo svetebi – ic_dan jc_mde svetebis

elementebisagan;

diag(V) _ qmnis matricas, romlis mTavari diagonalis elementebi V veqtoris elementebia;

matrix(m,n,f) _ qmnis matricas, romlis (i, j)_uri elementi udris f(i,j)_s,

sadac i = 0,1..m da j = 0,1..n; length(V) _ gamoTvlis veqtoris sigrZes.

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kompleqsuri ricxvebis funqciebi

Re(z) _ gvaZlevs kompleqsuri ricxvis namdvil nawils. z SeiZleba

iyos rogorc skalari, ise kompleqsuri ricxvebiT Sedgenili

veqtori an matrica;

lm(z) _ gvaZlevs kompleqsuri ricxvis warmosaxviT nawils. z SeiZleba

iyos rogorc skalari, ise kompleqsuri ricxvebiT Sedgenili

veqtori an matrica;

arg(z) _ gvaZlevs kompleqsuri ricxvis X RerZTan daxris kuTxis

mniSvnelobas (radianebSi).

interpolaciis da eqstrapolaciis funqciebi

samecniero_teqnikuri gamoTvlebis Catarebisas xSirad warmoiqmneba

interpolaciis (Caketili intervalis nebismier wertilSi fenqciis mniSvnelobebis

gansazRvra am funqciis mocemuli diskretuli mniSvnelobebis mixedviT, rac

grafikulad niSnavs funqciis warmodgenas sakvanZo (sayrdeni) wertilebis

SeerTebiT ama Tu im saxis wirebis gamoyenebiT) da eqstrapolaciis (funqciis

mniSvnelobebis gansazRvra Caketili intervalis gareT) Catarebis aucilebloba.

interpolaciis amocana amoixsneba mocemul monacemTa aproqsimaciiT martivi

funqciiT Secvlis safuZvelze, amasTan miRebuli funqcia zustad unda gadiodes

sakvanZo wertilebSi. Mathcad sistemaSi SesaZlebelia ori saxis interpolacia:

wrfivi da splainuri.

wrfivi interpolacia grafikulad niSnavs sakvanZo wertilebis SeerTebas

wrfis monakveTebiT, funqciis mniSvnelobebis gamoTvla xdeba wrfivi

damokidebulebis safuZvelze.

linterp(VX, VY, x) _ wrfivi interpolacia mocemuli sakvanZo wertilebis VX da

VY veqtorTa safuZvelze; gamoiTvleba funqciis mniSvneloba

miTiTebul x wertilSi.

splainuri interpolaciis dros wertilebis SeerTeba xdeba garkveuli

xarisxis mravalwevrebis gamoyenebiT, amasTan polinomis koeficientebi, rogorc

wesi, gamoiTvleba ise, rom miRebuli funqcia splainebis SeerTebis wertilebSic

iyos uwyveti. splainuri interpolacia Mathcad_Si 2 etapad tardeba: jer

cspline(VX,VY), pspline(VX,VY) an lspline(VX,VY) funqciebis meSveobiT gamoiTvleba

kuburi splainis koeficientebis VS veqtori, xolo Semdeg interp (VS, VX, VY, x) meSveobiT gamoiTvleba funqciis mniSvneloba mocemul wertilSi.

interp (VS,VX,VY,x) _ gamoTvlis funqciis interpolirebul mniSvnelobas x wertilSi, romelic miiReba kuburi splainebis meSveobiT VX, VY veqtorebis mniSvnelobebis safuZvelze.

cspline(VX,VY) _ gamoTvlis VS kuburi splainis koeficientebis veqtors.

gamoTvlebisas gaTvaliswinebulia mrudis sayrden wertilebTan

miaxloebisas kuburi damokidebuleba.

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pspline(VX,VY) _ gamoTvlis VS kuburi splainis koeficientebis veqtors.

gamoTvlebisas gaTvaliswinebulia mrudis sayrden wertilebTan

miaxloebisas paraboluri damokidebuleba.

lspline(VX,VY) _ gamoTvlis VS kuburi splainis koeficientebis veqtors.

gamoTvlebisas gaTvaliswinebulia mrudis sayrden wertilebTan

miaxloebisas wrfivi damokidebuleba.

predict(V,k,n) _ axdens eqstrapolacias, V _ monacemTa veqtori, k _ regresiis

polinomis xarisxi, n _ wertilTa raodenoba.

statistikuri funqciebi

Mathcad sistemis meSveobiT SesaZlebelia statistikuri gamoTvlebis

warmoeba. statistikuri funqciebia:

corr(VX,VY) _ gamoTvlis VX da VY erTnairganzomilebiani masivebis elementebis

korelaciis koeficients;

cvar(VX,VY) _ gamoTvlis VX da VY erTnairganzomilebiani masivebis elementebis

kovariaciis koeficients;

mean(A,B,C,...) _ gamoTvlis A,B,C,... elementebis saSualo ariTmetikul

mniSvnelobas, sadac A,B,C,... masivebia an skalarebi;

var(A,B,C,...) _ gamoTvlis A,B,C,... elementebis dispersias (variacias), sadac A,B,C,... masivebia an skalarebi;

stdev(A,B,C,...) _ gamoTvlis A,B,C,… elementebis standartul gadaxras, sadac

A,B,C,... masivebia an skalarebi;

hist(int, V) _ gamoTvlis V monacemebis int intervalebSi moxvedris sixSiris

veqtors. am funqcias iyeneben histogramebis asagebad;

cnorm(x) _ komuliatiuri normaluri funqcia (Sedis Probability Distribution kategoriaSi);

erf(x) _ cdomilebis funqcia anu albaTobis integrali (Sedis Special kategoriaSi);

erfc(x) _ cdomilebaTa funqcia kompleqsuri argumentisaTvis (Sedis Special kategoriaSi);

rnd(x) _ SemTxveviTi ricxvebis generaciis funqcia (Sedis Random Numbers kategoriaSi).

nax.11.2_ze moyvanilia statistikuri funqciebis (rnd, mean, var, min, max, stdev, hist) gamoyenebis magaliTebi.

SemTxveviTi (stoqastikuri) ricxvebis funqciebi

SemTxveviT (stoqastikur) ricxvebTan muSaobisaTvis gamosayenebeli

funqciebi iyofa oTx klasad:

Tu funqciis saxeli “d“–Ti iwyeba, miiReba ganawilebis albaTobis

simkvrivis mniSvneloba;

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nax.11.2. statistikuri funqciebis (rnd, mean, var, min, max, stdev, hist) gamoyenebis magaliTebi

Tu funqciis saxeli “p“–Ti iwyeba, miiReba albaTobis ganawileba anu imis

albaToba, rom SemTxveviTi ricxvis mniSvneloba iqneba konkretul

miTiTebul mniSvnelobaze naklebi an toli;

Tu funqciis saxeli “q“–Ti iwyeba, miiReba albaTobis ganawilebis Sebruneba

anu mocemuli albaTobis mixedviT gamoiTvleba ricxvis iseTi mniSvneloba,

romlis albaToba albaTobis miTiTebul konkretul mniSvnelobaze tolia

an naklebi;

Tu funqciis saxeli “r“–iT iwyeba, Seiqmneba veqtorebi garkveuli

kanonzomierebiT ganawilebuli elementebiT.

qvemoT moyvanilia ganawilebis albaTobis simkvrivis gamoTvlis funqciebi,

romelTa saxelebi “d“ –Ti iwyeba (“p“, “q“ da “r“–iT dawyebuli Sesabamisi funqciebi

moyvanili ar aris):

dbeta(x, s1, s2) _ β ganawileba (formebis parametrebi s1>0, s2>0 da 0< x<1);

dbinom(k,n,p) _ binomialuri ganawileba (gamoiTvleba P(x=k) albaTobis

mniSvneloba, sadac n da k mTeli ricxvebia, 0≤ k≤ n , 0≤ p≤ 1); dcauchy(x,l,s) _ koSis ganawileba (l – daSlis parametri, s>0 – masStabis parametri);

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dchisq(x, d) _ x_kvadrat ganawileba (x>0, Tavisuflebis xarisxi d>0);

dexp(x,r) _ eqsponencialuri ganawileba (r>0, x>0); dF(x,d1,d2) _ fiSeris ganawileba (Tavisuflebis xarisxebi d1>0, d2>0 da x>0);

dgamma(x,s) _ gama_ganawileba (formis parametri s>0, x≥0);

dgeom(k,p) _ geometriuli ganawileba (calkeuli cdis Sedegebis warmatebis

albaToba, 0<p≤1, k _ mTeli arauaryofiTi ricxvi);

dlnorm(x,μ,σ) _ lognormaluri ganawileba (μ _ saSualo mniSvnelobis naturaluri

logariTmi, σ>0 , sadac σ _ saSualo kvadratuli gadaxris

naturaluri logariTmi, x>0);

dlogis(x,l,s) _ logistikuri ganawileba (l – daSlis parametri, s>0 – masStabis

parametri); dnbinom(k,n,p) _ uaryofiTi binomialuri ganawileba (n da k – mTeli dadebiTi

ricxvebi, 0≤p≤1); dnorm(x,μ,σ) _ normaluri ganawileba (μ –saSualo mniSvneloba, σ>0 _ saSualo

kvadratuli gadaxra);

dpois(k,λ) _ puasonis ganawileba (λ>0, k – mTeli dadebiTi ricxvi);

dt(x,d) _ stiudentis ganawileba (d>0 – Tavisuflebis xarisxis maCvenebeli, x _ namdvili ricxvi);

dunif(x,a,b) _ Tanabari ganawileba (a da b – intervalis zRvruli wertilebi,

amasTan a<b da a≤x≤b); dweibull(x,s) _ veibulis ganawileba (s>0 – formis parametri, x>0).

monacemTa gagluvebis funqciebi

eqsperimentTa monacemebi umetesad Seicaven SemTxveviT cdomilebebs. amitom

xSirad wamoiWreba monacemTa statistikuri gagluvebis aucilebloba. Mathcad_s gaaCnia gagluvebis Semdegi funqciebi:

medsmooth(VY, n) _ axdens mcocavi medianis meTodiT monacemTa gagluvebas.

Sedegad miiReba gagluvebuli monacemebis m_ganzomilebiani

VY veqtori. n parametriT moicema gagluvebis CarCos sigane,

amasTan n unda iyos m_ze naklebi kenti ricxvi;

ksmooth(VX, VY, b) _ axdens gagluvebas gausis ganawilebis safuZvelze. Sedegad

miiReba gagluvebuli monacemebis n_ganzomilebiani VY veqtori.

VX da VY – n_ganzomilebiani namdvil ricxvTa veqtorebi, b parametriT (gatarebis zoli) moicema gagluvebis CarCos sigane

(b ramdenimejer unda aRematebodes X RerZis wertilebs Soris

intervals);

supsmooth(VX, VY) _ axdens gagluvebas wrfivi gagluvebis proceduris

safuZvelze umcires kvadratTa meTodiT (k uaxloesi

mezoblebis wesis Tanaxmad k_s adapturi SerCeviT). miiReba

n_ganzomilebiani gagluvebuli VY veqtori. n_ganzomilebiani

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VX veqtoris elementebi zrdadobis mixedviT unda iyos

dalagebuli. monacemTa gagluveba supsmooth funqciiT ilustrirebulia nax.11.3_ze.

nax.11.3. monacemTa gagluveba supsmooth funqciiT

Ggantolebebis da gantolebaTa sistemebis amoxsnis funqciebi

bevr algebrul gantolebas da maT sistemebs ar gaaCniaT analizuri

amonaxsni. maTi amoxsna SesaZlebelia ricxviTi meTodebiT dadgenili

cdomilebebis farglebSi.

root(f(x),x) _ gamoTvlis martivi arawrfivi erTcvladiani gantolebis (f(x)=0) fesvs. fesvis povna xdeba iteraciuli meTodiT, romlis dros saWiroa

cvladisaTvis sawyisi mniSvnelobis miniWeba.

Polyroots(V) _ gamoTvlis Cveulebrivi polinomis fesvebs. am funqciis gamoyeneba

mizanSewonilia rodesac polinomis xarisxi 6_s ar aRematema.

Lsolve(A,B) _ wrfiv gantolebaTa sistemis (A.X=B) amoxsna, A _ koeficientebis

matrica, B _ Tavisufal wevrTa veqtori.

arawrfivi gantolebis an gantolebaTa sistemis amosaxsnelad iyeneben

find(v1,v2,...,vn) da minerr(v1,v2,...,vn) funqciebs. gamoTvliTi bloki iwyeba given direqtiviT, ris Semdeg Caiwereba gantoleba (gantolebebi) da SezRudvebi

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cvladebze. gamoTvliTi bloki mTavrdeba find(v1,v2,...,vn) an minerr(v1,v2,...,vn) funqciiT.

nax.11.4. arawrfivi erTcvladiani gantolebis amoxsna root da given _ minerr funqciebis gamoyenebiT

find(v1,v2,...) _ gamoTvlis cvladis an cvladebis zust mniSvnelobebs,

romlebic akmayofileben mocemul gantolebas (gantolebebs) da

SezRudvebs.

minerr(v1, v2,...) _ gamoTvlis cvladis an cvladebis miaxloebiT mniSvnelobebs.

nax.11.4_ze moyvanilia arawrfivi erTcvladiani gantolebis amoxsna root da given _minerr funqciebis gamoyenebiT, xolo nax.11.5_ze _ arawrfiv gantolebaTa

sistemis amoxsna given _ find funqciebis gamoyenebiT.

Mathcad_Si CaSenebulia agreTve Cveulebrivi diferencialuri gantolebebis

amosaxsneli funqciebi:

rkadapt(Y,x1,x2,acc,n,F,k,s) _ miiReba matrica, romelic Seicavs koSis amocanis

amonaxsnebs. Ddiferencialuri gantolebebis sistemis amoxsna xdeba

runge_kutas meTodiT cvladi bijiT, Y _ sawyisi pirobebis veqtori x1_dan x2_mde intervalSi. gantolebaTa sistemis marjvena nawilebi Cawerilia F simbolur veqtorSi, n – bijTa raodenoba, k – amoxsnis Sualeduri

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wertilebis maqsimaluri raodenoba, s – wertilebs Soris minimaluri

dasaSvebi intervali, acc _ amoxsnis cdomileba;

nax.11.5. arawrfiv gantolebaTa sistemis amoxsna given _ find funqciebis gamoyenebiT

Rkadapt(Y,x1,x2,n,F) _ miiReba matrica, romelic Seicavs Cveulebriv

diferencialur gantolebaTa sistemis amonaxsnebs. diferencialuri

gantolebebis sistemis amoxsna xdeba runge_kutas meTodiT adaptiuri

bijiT, Y _ sawyisi pirobebis veqtori x1_dan x2_mde intervalSi.

sistemis marjvena nawilebi Cawerilia F simbolur veqtorSi, n _ bijTa

raodenoba;

rkfixed(Y,x1,x2,n,F) _ miiReba matrica, romelic Seicavs x1_dan x2_mde intervalSi Cveulebriv diferencialur gantolebaTa sistemis amonaxsnebs.

diferencialuri gantolebebis sistemis amoxsna xdeba runge_kutas

meTodiT fiqsirebuli bijiT da Y veqtoris sawyisi mniSvnelobebiT.

sistemis marjvena nawilebi Cawerilia F simbolur veqtorSi, n _ bijTa

raodenoba. Rkadapt funqcia gvaZlevs ufro zust Sedegebs rkfixed funqciasTan SedarebiT, magram misi gamoTvlis siCqare, rogorc wesi, ufro

dabalia.

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puasonis diferencialuri gantolebis (meore rigis kerZo warmoebulebSi)

da laplasis gantolebis amosaxsnelad Mathcad_s aqvs Semdegi funqciebi: bvalfit(V1,V2,x1,x2,xi,F,L1,L2,score) _ miiReba sasazRvro amocanis sawyisi pirobebi

mocemuli F, V1 da V2 veqtorebisaTvis x1_dan x2_mde intervalSi, amoxsna

cnobilia garkveul Sualedur wertilSi xi; relax(M1,M2,M3,M4,M5,A,U,r) _ miiReba puasonis gantolebis amoxsnis kvadratuli

matrica r speqtraluri radiusisaTvis;

multigrid(M,n) _ miiReba puasonis gantolebis amoxsnis matrica (rodesac

sazRvrebze amonaxsni 0_is tolia);

sbval(Y,x1,x2,F,L,score) _ miiReba F simbolur veqtorSi gansazRvruli sasazRvro

amocanis sawyisi pirobebi. sawyisi pirobebi Caiwereba Y veqtorSi x1_dan x2_mde intervalSi.

furies pirdapiri da Sebrunebuli gardaqmna

maTematikis fundamentur debulebas miekuTvneba periodul funqciaTa

warmodgenis SesaZlebloba furies mwkriviT _ harmoniuli mdgenelebis jamis

saxiT. amiT SeiZleba visargebloT mraval SemTxvevaSi. sakmarisia aRiniSnos, rom

is udevs safuZvlad kavSirgabmulobis arxebisa da gadacemuli signalebis

analizs. furies pirdapiri da Sebrunebuli gardaqmna saSualebas gvaZlevs

signalis droiTi warmodgenidan gadavideT mis sixSirul warmodgenaze da

piriqiT. Ffuries pirdapiri da Sebrunebuli gardaqmnis funqciebia:

fft(V) _ furies pirdapiri swrafi gardaqmna. sawyisi monacemebis V veqtori

Sedgenilia namdvili ricxvebisagan. amasTan V veqtors unda hqondes 2n mdgeneli, sadac n – mTeli ricxvia. am funqciis Semotana ganpirobebulia

imiT, rom namdvili elementebisagan Sedgenili veqtorisaTvis furies

gardaqmna xorcieldeba ufro swrafi algoriTmiT da angariSs sWirdeba

naklebi dro;

cfft(A) _ furies pirdapiri gardaqmna. sawyisi A veqtori kompleqsur ricxvebs

Seicavs. Tu A matricaa, cfft funqcia axdens furies organzomilebian

pirdapir gardaqmnas;

ifft(V) _ furies Sebrunebuli gardaqmna, Seesabameba fft pirdapir gardaqmnas.

sawyisi V veqtori kompleqsur ricxvebs Seicavs. ifft funqciiT miiReba

namdvili ricxvebisagan Sedgenili veqtori;

cifft(A) _ furies Sebrunebuli gardaqmna sruli algoriTmiT, Seesabameba cfft pirdapir gardaqmnas. rogorc sawyisi, aseve miRebuli veqtorebi an

matricebi Seicaven kompleqsur ricxvebs. Tu A matricaa, cifft funqcia

axdens furies organzomilebian Sebrunebul gardaqmnas.

nax.11.6_ze moyvanilia furies pirdapiri da Sebrunebuli gardaqmna fft da ifft funqciebis gamoyenebiT.

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nax.11.6. furies pirdapiri da Sebrunebuli gardaqmna

fft da ifft funqciebis gamoyenebiT

11.3 momxmareblis mier operatoris Seqmna

funqciebs da operatorebs bevri saerTo gaaCniaT. isini gansxvavdebian

erTmaneTisagan ara Sinaarsobrivad, aramed gamosaxvis formiT. magaliTad, funqcia

f(x,y) SegviZlia gamovsaxoT xfy operatoris saxiT, x+y Canaweri SevcvaloT +(x,y)_iT

da a.S. funqciebis msgavsad, momxmarebels SeuZlia Seqmnas sakuTari operatorebic.

ganvixiloT momxmareblis mier operatoris Seqmna magaliTze (SevqmnaT

gaerTianebis operatori):

1. CavsvaT samuSao furcelSi gaerTianebis simbolo

Help → QuickSheets → Extra Math Symbols CamonaTvalidan;

2. avkriboT klaviaturidan (x,y);

3. gamoviyenoT miniWebis operatori;

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4. markerSi SevitanoT operatoris gansazRvra (Cven

magaliTSi gamoyenebulia gaerTianebis funqcia stack). SemdgomSi dokumentSi stack funqciis nacvlad SesaZlebelia operatoris

gamoyeneba.

momxmareblis mier Seqmnili operatorebis gamosayeneblad vsargeblobT

Evaluation instrumentTa panelis (nax. 11.2) bolo oTxi RilakiT:

nax.11.7. Evaluation instrumentTa paneli

Cvens mier Seqmnili operatoris gamosayeneblad:

1. SeviyvanoT operandebi;

2. gamoviyenoT Evaluation instrumentTa panelis

Rilaki;

3. Sua markerSi SevitanoT operatoris simbolo;

4. marcxena da marjvena markerebSi SevitanoT operandebi;

5. gamoviyenoT tolobis niSani.

oroperandiani operatoris gamoyeneba SesaZlebelia agreTve Evaluation

instrumentTa panelis RilakiT.

erToperandiani operatoris gamoyeneba SesaZlebelia Evaluation instrumentTa

panelis da RilakebiT.

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Tavi XII daprogrameba Mathcad_Si

12.1 Programming instrumentTa panelis operatorebis aRwera

cvladebi da funqciebi Mathcad_Si SeiZleba ganvsazRvroT rogorc

Cveulebrivi gamosaxulebebis meSveobiT, aseve programis saxiT.

Mathcad_is programa warmoadgens daprogramebis operatorebis meSveobiT

Seqmnil brZanebaTa erTobliobas. arsebiTad programa warmoadgens gamosaxulebis

specifikur nairsaxeobas da sxva gamosaxulebebis msgavsad, ricxviTi an

simboluri gamoTvlebisas miRebuli iqneba misi mniSvneloba. programis

mniSvneloba Mathcad_Si SeiZleba iyos ricxvi, ricxviTi masivi, masivi masivSi

(Nested Arrays) an striqoni (String). brZanebebis raodenoba programaSi ar aris

SezRuduli. programis Sesaqmnelad gamoviZaxoT Programming instrumentTa paneli

mTavari menius View → Toolbars CamonaTvalidan an maTematikuri panelis

RilakiT (nax.12.1).

nax.12.1. Programming instrumentTa paneli

daprogramebis operatorebia (frCxilebSi miTiTebulia klaviaturis

klaviSebi an klaviSebis kombinacia, romelTa meSveobiT SesaZlebelia Sesabamisi

operatoris Casma programaSi):

(] ) _ xazis Casmis operatori. am operatoris gamoyenebiT iwyeba

programis Cawera. gamodis vertikaluri xazi ori markeriT.

programaSi SesaZlebelia nebismieri markeris gamoyofa da Add Line operatoris xelmeore gamoyeneba, ris Sedegad vertikaluri xazis

sigrZe izrdeba da Sesabamisad matulobs markerTa ricxvic;

({ ) _ miniWebis operatori;

(} ) _ if (Tu) pirobiTi gadasvlis operatori. misi gamoyenebisas

marjvena markerSi Caiwereba piroba (logikuri gamosaxuleba), xolo

150

f x y( ) logx y2 y

marcxenaSi _ brZaneba an gamosaxuleba, romelic gamoiTvleba pirobis

Sesrulebis SemTxvevaSi;

(Ctrl + Shift) _ otherwise (sxva SemTxvevaSi) operatoris Casma, romelic

gamoiyeneba if logikur operatorTan erTad. markerSi Caiwereba

brZaneba an gamosaxuleba, romelic gamoiTvleba pirobis

Seusruleblobis SemTxvevaSi;

(Ctrl + Shift + “) _ ciklis operatori. for cikli gamoiyeneba rodesac

ciklSi Sesasrulebeli brZanebebis gameorebis ricxvi winaswar anu

ciklSi Sesvlamde gansazRvrulia. for operatoris marcxena markerSi Sesatania ciklis parametris identifikatori, marjvena markerSi am

parametris mniSvnelobaTa Secvlis diapazoni, xolo qvedaSi _ ciklSi

Sesasrulebeli brZaneba;

(Ctrl + ]) _ ciklis operatori. while (manam ... sanam) cikli gamoiyeneba

rodesac ciklSi Sesasrulebeli brZanebebis gameorebis ricxvi

winaswar ar aris gansazRvruli. while operatoris marjvena markerSi

Sesatania piroba, xolo QqvedaSi _ ciklSi Sesasrulebeli brZaneba.

pirobis Seusruleblobisas xdeba ciklidan gamosvla;

(Ctrl + Shift + {) _ ciklis Sesrulebis Sewyvetis operatori;

(Ctrl + [) _ continue operatori, gamoiyeneba ciklis morig iteraciaze

gadasasvlelad;

(Ctrl + Shift + |) _ return operatori, gamoiyeneba programis Sesrulebis

Sesawyvetad. Mmis markerSi Sesatania programidan dokumentSi misawodi

informacia;

(Ctrl + ‘) _ on error (Secdomis SemTxvevaSi) operatori. am operatoriT

jer gamoiTvleba marjvena argumenti, xolo Secdomis SemTxvevaSi _

marcxena.

unda aRiniSnos, rom operatorebis dasaxelebebis klaviaturidan akreba

dauSvebelia.

12.2 miniWebisa da striqonis Casmis operatorebi

rogorc ukve iyo aRniSnuli, miniWebis operatori gamoiyeneba

cvladebisaTvis an funqciebisaTvis mniSvnelobis misaniWeblad, xolo Add Line operatori Casvams programaSi axal xazs.

ganvixiloT programis Seqmnis procesi. vTqvaT, gvinda ganvsazRvroT

funqcia programis meSveobiT. amisaTvis:

151

1. avkriboT klaviaturidan da : miniWebis niSnis

Sesatanad;

2. gamoviyenoT Programming panelis Add Line operatori;

3. davawkapunoT zeda markerze, avkriboT k da

gamoviyenoT Programming panelis operatori;

4. miniWebis marjvniv myof markerSi SevitanoT ;

5. qveda markerze gadasaadgileblad davaWiroT Tab klaviSs da avkriboT log(k).

aRvniSnoT, rom programis SigniT akrZalulia miniWebis niSnis (:=)

gamoyeneba. is cvladebi, romlebic gansazRvrulia programis SigniT

operatoriT (rogorc wina magaliTSi k cvladi), warmoadgenen programis lokalur

cvladebs da ar arian gansazRvrulebi samuSao furclis sxva adgilas.

12.3 pirobiTi gadasvlis iperatori

programis operatorebi sruldeba mimdevrobiT, zemodan qvemoT. xSirad

saWiroeba moiTxovs am Tanmimdevrobis Secvlas, rac SesaZlebelia if pirobiTi

gadasvlis operatoriT. if operatori gamoiyeneba algoriTmis ganStoebuli

struqturis aRsawerad.

vTqvaT, gvinda ganvsazRvroT Semdegi funqcia:

. iSemTxvevaS sxva

Tu ,

225

50)(

x

xxw

amisaTvis:

1. avkriboT w(x): da gamoviyenoT Programming

panelis Add Line operatori; 2. gamovyoT zeda markeri da gamoviyenoT Programming

panelis if operatori; 3. if sityva_gasaRebis marjvniv mdgom markerSi

SevitanoT x >5 logikuri gamosaxuleba

Boolean panelis gamoyenebiT. marcxena markerSi

w x( )

w x( ) if

f x y( )

f x y( ) kx y2 y

f x y( ) kx y

2 y

log k( )

x y2 y

w x( ) 0 x 5if

f x y( ) k

f x y( )

f x y( )

152

SevitanoT 0, romlis mniSvneloba mieniWeba )(xw funqcias, roca

marjvena markerSi Setanili logikuri gamosaxulebis mniSvnelobaa

“WeSmariti” (true); 4. gamovyoT qveda markeri da gamoviyenoT Programming panelis otherwise

operatori da mis marcxniv mdgom markerSi SevitanoT 225 x ,

romlis mniSvneloba mieniWeba

)(xw funqcias, roca programis

logikuri pirobis mniSvnelobaa

“mcdari” (false). nax.12.2–ze moyvanilia if pirobiTi gadasvlis operatoris gamoyenebis

magaliTi.

nax.12.2. if logikuri operatoris gamoyenebis magaliTi

if operatoris piroba logikur gamosaxulebas warmoadgens, romlis

Sesatanad vsargeblobT Boolean instrumentTa panelis operatorebiT (nax.12.3).

Boolean instrumentTa panelSi Tavmoyrilia Sedarebis operatorebi (Equal to (Ctrl+ =) _ tolia, Less Than (<) _ naklebia, Greater Than (>) _ metia, Less Than or Equal to

w x( ) 0 x 5if

25 x2 otherwise

153

(Ctrl+ ( ) _ naklebia an toli, Greater Than or Equal to (Ctrl+ ) ) _ metia an toli,

Not Equal to (Ctrl+ 3) _ ar udris) da logikuri operatorebi (Not (Ctrl+Shift+5) _ logikuri uaryofa, And (Ctrl+Shift+7) _ koniunqcia anu logikuri “da”, Or (Ctrl+Shift+6) _ dizunqcia anu logikuri “an”, Exclusive or (xor) (Ctrl+Shift+1) _

dizunqciis uaryofa).

nax.12.3. Boolean instrumentTa paneli

Sedarebis operatorebis operandebia ricxviTi an striqonuli tipis

monacemebi (orive operandi unda iyos erTi da igive tipisa), xolo logikuri

operatorebis operandebi logikuri gamosaxulebebia. striqonebis Sedareba

warmoebs simboloebis mixedviT marcxnidan marjvniv. Tu striqonebis raime wyvili

ar emTxveva erTmaneTs, ufro metis mniSvnelobis mqoned iTvleba is simbolo,

romlis Sesabamisi kodi (koduri cxrilidan) ufro metia. Sedarebisa da logikuri

operaciebis Sedegad miiReba 1 (“WeSmariti”) an 0 (“mcdari”).

12.4 ciklis operatorebi

gameorebadi anu cikluri procesi gamoTvliTi procesebis metad

gavrcelebul tips warmoadgens. ciklis operatorebi gankuTvnilia algoriTmis

cikluri struqturis aRsawerad.

Mathcad_s aqvs ori ciklis operatori: for da while. rogorc ukve iyo aRniSnuli, for cikli gamoiyeneba rodesac ciklSi

Sesasrulebeli brZanebebis gameorebis ricxvi winaswar anu ciklSi Sesvlamde

gansazRvrulia. for ciklis Sesaqmnelad:

1. davawkapunoT Programming panelis for operatorze;

2. “”_is marcxniv mdebare markerSi SevitanoT ciklis cvladis saxeli,

marjvniv mdebare markerSi _ ciklis cvladis sawyisi da bolo

mniSvnelobebi da agreTve misi mniSvnelobis Secvlis

biji (Tu es biji 1_sagan gansxvavebulia);

3. qveda markerSi SevitanoT ciklSi Sesasrulebeli brZaneba. Tu ciklSi

sruldeba ramdenime brZaneba, gamovyoT qveda markeri

da Add Line operatoriT jer CavsvaT axali striqonebi,

xolo Semdeg markerebSi SevitanoT ciklis brZanebebi.

i 1 nfor

for

s s i

i 1 nfor

154

while (manam ... sanam) tipis cikls viyenebT rodesac ciklis gameorebis

raodenoba ar aris winaswar cnobili da is dasruldeba mxolod miTiTebuli

pirobis Seusruleblobisas. while ciklis Sesaqmnelad:

1. davawkapunoT Programming panelis while operatorze; 2. zeda markerSi SevitanoT gameorebis pirobis

Sesabamisi logikuri gamosaxuleba, xolo qveda

markerSi SevitanoT ciklSi Sesasrulebeli

brZaneba. Tu ciklSi sruldeba ramdenime brZaneba,

gamovyoT qveda markeri da Add Line operatoriT jer

CavsvaT axali striqonebi, Semdeg ki markerebSi

SevitanoT ciklis brZanebebi.

nax.12.4_ze moyvanilia for da while operatorebis gamoyenebis magaliTebi.

nax.12.4. for da while operatorebis gamoyenebis magaliTebi

while

j j 1

v j twhile

155

12.5 Break, Continue da Return operatorebi

break operatori gamoiyeneba ciklis Sesawyvetad anu raime pirobis

Sesrulebisas ciklidan gamosasvlelad.

Tu saWiroa pirobis Sesrulebisas SevwyvitoT ciklis morigi iteracia da

gavagrZeloT ciklis Sesruleba Semdegi iteraciebisaTvis, vsargeblobT continue operatoriT.

break da continue operatorebis Sesatanad vsargeblobT Programming

panelis Sesabamisad da punqtebiT.

break da continue operatorebi, rogorc wesi, gvxdebian if operatorSi da ciklis operatorebSi.

return operatoris meSveobiT SesaZlebelia programis Sesrulebis Sewyveta.

am dros cvlads an funqcias mieniWeba ara bolo, aramed mimdinare brZanebiT

gamoTvlili mniSvneloba (skalari, veqtori, masivi an striqoni). return operatori, break da continue operatorebis msgavsad, ZiriTadad gvxdeba if operatorSi.

return operatoris Sesatanad:

1. davawkapunoT Programming panelis operatorze;

2. operatoris marcxena markerSi CavsvaT Programming panelis

operatori;

3. return sityva_gasaRebis marjvniv mdgom markerSi avkriboT gamosaxuleba.

Tu gamosaxuleba striqonuli tipis konstantaa, klaviaturidan

SevitanoT “ simbolo da Sesabamisi teqsti;

4. if operatoris marjvniv mdebare markerSi davbeWdoT logikuri

gamosaxuleba.

12.6 operatori on error

am operatoris programaSi CarTva saSualebas gvaZlevs gamoTvlebSi

SesaZlo Secdomebis SemTxvevaSi movaxdinoT Secdomis damuSaveba raTa Mathcad_ma ar Sewyvitos programis Sesruleba da gaagrZelos gamoTvlebi. on error operatori arsebiTad SecdomebisaTvis “xafangs” warmoadgens.

on error operatoris Sesaqmnelad gamoviyenoT Programming panelis

punqti. marjvena markerSi Caiwereba ZiriTadi gamosaTvleli gamosaxuleba, xolo

marcxenaSi _ is gamosaxuleba, romelic Sesruldeba Secdomis SemTxvevaSi.

nax.12.5_Si moyvanilia on error operatoris da error funqciis, romelic

gamoiyeneba Secdomis Sesaxeb teqsturi Setyobinebis gamosatanad, gamoyenebis

magaliTebi.

156

nax.12.5. on error operatorisa da error funqciis gamoyeneba

157

gamoyenebuli literatura

1. Brent Maxfield, “ENGINEERING with MATHCAD”. Using Mathcad to Create and Organize your Engineering Calculations. B/H, 2007.

2. Е. Макаров, «Инженерные расчеты в Маthcad». Учебный курс. Издательство «Питер», 2007, 486 стр.

3. В.П. Дьяконов, «Энциклопедия Mathcad 2001 и Mathcad 11». Солон-Пресс, 2004, 832 стр. 4. Mathcad 11. User’s Guide. Mathsoft Engineering &Education, Inc, 2001, p. 473. 5. Е.М.Кудрявцев, «Mathcad 8». Издательство ДМК. Москва, 2000, 318 стр. 6. В.П.Дьяконов, “MathCAD Plus 7.0 PRO”. Справочник по MathCAD Plus 7.0 PRO.

Издательство « СК ПРЕСС», Москва, 1998, 345 стр. 7. www. mathsoft.com .

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