SUAT SEZA GR'nnansna ithaf edilmitir.

I I I

MAKINA MHENDSLE L KTABI

Cilt 1

RETM VE TASARIM

Baskya HazrlayanA. Mnir CERIT

( Makina Yk. Mhendisi)2. Bask

TMMOB MAKNA MHENDSLER ODASI

Ekim 1994

Yayn no: 169

.*!?

tmmobmakina mhendisleri odas

Smer Sokak 36/1-A 06440 Demirtepe / ANKARATel : (0-312) 231 31 59 - 231 80 23 Fax : (0-312) 231 31 65

Yayn no : 169

ISBN : 975-395-124-8 (Tk. No)ISBN : 975-395-125-6 (1. Cilt)

Bu Yaptn yayn hakk Makina Mhendisleri Odas'na aittir. Kitabnhibir blm deitirilemez. MMO'nn izni olmadan kitabn hibirblm elektronik, mekanik vb. yollarla kopya edilip kullanlamaz.

Kaynak gsterilmek kayd ile alnt yaplabilir.

Ekim 1994 - Ankara

Dizgi: Ali Rza Falcolu (Makina Mhendisleri Odas)Bask: MF Ltd. ti. Tel: (0-312) 425 37 68

i t

M:

NDEKLER

Ayrntl iindekiler listesi her blmn banda verilmitir. Alfabetik szck dizini isekitabn sonundadr.

BOLUM - 1

MATEMATIK TABLOLARVE L BIRIMLERI

Matematik Tablolar 1-02l Birimleri 1-31

BLM - 4

KAT CISIMLERIN MEKANII

Kat Cisimlerin Mekanii 4-02Jiroskpik Hareket ve Jiroskop 4-21Srtnme 4-23

BLM - 2

MHENDSLK GERELER

Demir ve elik 2-03Demir D Metaller ve Alamlar 2-43Toz Metalrjisi 2-64Bileik Gereler 2-83Koruyucu Gereler 2-94Seramikler 2-100

BLM - 5

SlZDIRMAZLIK ELEMANLARI

Dner Miller iin SzdrmazlkElemanlar 5-05Satatik S/.drmazlk Elemanlar(Contalar) 5-42Mekanik Keeler 5-60Szdrmazlk F.lemanlarnda KullanlanGereler 5-76

BLM - 3

KOROZYUN (YENIM) VEDENETLENMESI

Buhar Santrallarnda Korozyon Sorunlar 3-11Kimya Fabrikalarnda Korozyon 3-13Korozyonun Denelenmesi 3-18

BOLM - 6

MEKANIK TITREIMLER VEGRLTNN KONTROL

Mekanik Titreimler 6-02Titreimin Snmlenmesi 6-30Ses ve Grltnn Denetlenmesi 6-36

W t ; "

V

BLM - 7

MALZEME LETIMI

Malzeme letim Dzenekleri 4-02Gtrcler 7-41

BLM - 8

YALAMA VE YATAKLAR

Yalama 8-02Yalayanlar ve zellikleri 8-04Yataklar 8-15Yatak Seimi 8-50

BLM - 9

ISTMA, HAVALANDRMA VEKLIMLENDIRME

Istma 9-02Is Pompalar 9-26Havalandrma 9-46Hava artlandrma 9-53

BLM - 10

BASNL HAVA DONANMLAR

Basnl Havann zellikleri 10-03Basnl Hava ebekeleri 10-16Kmpresrlerde Atk IsnnGeri Kazanlmas 10-21Sistemin Koruyucu Bakm 10-23

BLM -11

MHENDSLK EKONOMS

Edeerlik Kavram 11-03Yatrm AlternatiflerininDeerlendirilmesinde Kulanlanltler 11-10Kullanmdan Kaldrma ve YenilemeAnalizi 11-16Vergi Sonras Analiz 11-19

BLM - 12

TESIS PLANLAMAS

Tesis Yerinin Seimi 12-02Tesis Yerleim Dzeni Tasarm 12-04Nicel zmleme Modelleri veTeknikleri 12-14

BLM - 13

EVRE MHENDISLII

evre Bilimleri 13-03evre Mikrobiylojisi 13-06Endstri Giri Suyu Artm 13-12evre Mevzuat 13-14ALFABETK DZN

it

m

SUNU

Makina Mhendislii El Kitab'nn ikinci basksn meslektalarmznve gen mhendis adaylarnn kullanmna sunmaktan kvan duyuyoruz.

Bilim ve teknolojideki hzl gelimeler, yllar nce yaynlamolduumuz 4 ciltlik El Kitab'nn kapsaml bir ekilde gzdengeirilmesini gerekli kld. Bu sorumluluun bilinciyle ikinci bask konukapsam ve her konu ierii itibariyle adeta btnyle yeniden yazld.l itibariyle de daha byk tutulan El Kitab drt cilt halindedzenlendi.

Bylesine geni kapsaml bir bilimsel eserin ortaya konmasnn nekadar youn bir aba ve sreyi gerektireceini takdir edeceinizegveniyoruz. Yine bylesi bir eser, maliyeti itibariyle ancak kazandrtsnden uzak, bilimsel katk endiesinin ar bast bir giriimigerektirmekteydi ve bu onur, retim-aratrma-sanayi kurulularndanseilmi, herbiri kendi arasnda youn kurumsal ve uygulamaluzmanlklar ile bilinen, byk bir zveri ve maddi karlllemeyecek emek katks ile blmlerini hazrlayan yazarlara aittir.

Byle bir almann gsterebilecei gecikme ve olabilecek eksikliklerinanlayla karlanacana inanyoruz.

El Kitabnn hazrlanmasnda emei geen, bata blm yazarlarolmak zere Makina Mhendisleri Odas Kitap Komisyonunun saynyelerine, kitab baskya hazrlayan Sayn A. Mnir CERT'e, ve ElKitab'nn dizgi, dzenleme ve basksnda stn aba gsteren Oda'mzyayn personeline teekkr eder, kitabn meslektalarmza, mhendislikeitimi gren genlerimize ve tm ilgililere yararl olmasn dileriz.

Makina Mhendisleri OdasYnetim Kurulu

BRNC BASKININ NSZ

Odamzn hemen her genel kurulunda, meslektalarmzn belirttikleri balca ortak arzuolan MAKNA MHENDSL EL KTABI'nn ilk cildini yaynlamaktan mutluyuz. El Kitab,yaklak 32 blmden oluacak biimde planlanmtr. Her blm ayr bir meslektamztarafndan yazlmtr. Blmler arasnda dil ve sayfa dzeni bakmndan bir uyum salanmasiin nemli aba harcanmtr. Ancak, bu alma srasnda, blm yazarnn yaz slubu,olabildiince korunmaya allmtr. Teknik yazn (literatr) zengin sanayi lkelerinde bir elkitabndan beklenen hizmet, genellikle, bavurulan konudaki ana ilkelerin, balca formllerinve uygulamada kullanlan ortalama saysal deerlerin hatrlanmasdr. Bir el kitabnn tasarm(design) amacyla kullanlmas, ounlukla, nerilmez. nk buradaki bilgiler, ancak birhesabn kontrol, seilen tasarm verilerinin uygun snrlar iinde bulunup bulunmadkonusunda fikir verirler.

Ancak, lkemizin koullar bizi, yukarda zetlenen bu temel grlerde deiiklik yapmayazorlamaktadr. Teknik yaznmzn zengin olmay nedeniyle, birok konuda olduka genibilgi verilmitir. Bylece, bir el kitabnn erevesinin ald sylenebilir. Yukarda aklanannedenlerle, yazar meslektalarmz bu konuda olduka serbest braktk. Sonu olarak,Trkiye'de ilk defa yaynlamaktan kvan duyduumuz bu teknik el kitab, birok konuda, birbavurma kitab durumuna geldi. Bu durumun, meslektalarmz tarafndan olumlukarlanacan umuyoruz.

4-5 cilt olarak yaynlamay planladmz MAKNA MHENDSL EL KTABI, her cilt,birbiriyle yakndan ilgili olan konular kapsayacak biimde dzenlenmitir. Temel bilimleri,zellikle mhendisler iin gerekli lde ieren bu birinci ciltte,

MATEMATKL BRMLER VE EVRME KATSAYILARIKATI CSMLER VE AKIKANLAR MEKANTTREM VE SESCSMLERN MUKAVEMETTERMODNAMK VE ISI LETM

blmleri kapsanmtr.Yurdumuzda, bu apta yaynlanan ilk yapt olarak elbette birok eksii ve kusuru bulunmas

doal olan bu kitabn, meslektalarmzn ve dier okuyucularn eletiri ve uyarlarylaolgunlaabilecei aktr. Bu bakmdan eletiri ve uyarlarnz bekliyoruz. Sizlere daha iyihizmet istei ile sevgi ve sayglar.

Ankara-Ocak 1976A. Mnir CERT

MAKNA MHENDSL EL KTABI1. CLT

KNC BASKININ NSZ

MAKNA MHENDSL EL KTABI'nn birinci basksnn zerinden ok zaman geti(1.-3. ciltler 1976-1977; 4. cilt 1981).

Bilim ve teknikteki olaanst hzl gelimeler ve yeni uygulamalar bir yeni basky zorunlukld.

Birinci bask, birinci basknn nsznde de belirtildii gibi, bir el kitabndan beklenendendaha geni kapsaml hazrlanmt. Ksa zamanda tkenmi olmas, bu amacn gerekliinikantlamtr.

u anda meslektalarmzn kullanmna sunulan bu ikinci baskda klasik el kitaplarnnsnrlarna ekilmek istedik.

Ancak, yine de blm yazarlarn bir lde serbest braktk. Bu bakmdan, bu ikincibasknn klasik el kitab ile bavuru kitab arasnda bir yer aldn sylemek mmkndr.

Kitabn basm elde olmayan nedenlerle gecikti. Okuyucularmzn bu konuda bizibalayacaklarna inanyorum.

Bu ikinci bask da yine 4 cilt olarak kmaktadr. Ancak, bu kez yle bir i ayrm yaptk:

RETM VE TASARIM 2 CiltENERJ VE G 2 CiltBu ikinci basknn da eletirilecek birok yan olduunu kabul ediyorum. Ancak,

meslektalarma ve gen mhendis adaylarna yararl bir yapt hazrlamak iin ok abaharcadmz sylemek zorundaym.

Bu basknn gereklemesinde, benden daha nce balayan stn aba ve zverilerindendolay blm yazar arkadalarma ve Kitap Komisyonunun eski ve yeni deerli yeleri

Serdar TANProf. Dr. Alp ESNDo. Dr. Kahraman ALBAYRAKBilal BAYRAMNihat ANGIErturul CANKI

dostlarma en iten teekkrlerimi sunmak isterim.Gen meslektalarmn gelecekte daha gzel yaptlar vermesi dileiyle.

Ankara, Ekim 1994A. Mnir CERT

t I

M A M A MHENDSLE L KTABI

Cilt 1

RETM VE TASARIM

Baskya HazrlayanA. Mnir CERIT

( Makina Yk. Mhendisi)2. Bask

TMMOB MAKNA MHENDSLER ODASI

Ekim 1994

Yayn no : 169

tmmobmakina mhendisleri odas

Smer Sokak 36/1-A 06440 Demirlepe / ANKARATel : (0-312) 231 31 59 - 231 80 23 Fax : (0-312) 231 31 65

Yayn no : 169

ISBN : 975-395-124-8 (Tk. No)ISBN : 975-395-125-6 (1. Cilt)

Bu Yaptn yayn hakk Makina Mhendisleri Odas'na aittir. Kitabnhibir blm deitirilemez. MMO'nn izni olmadan kitabn hibirblm elektronik, mekanik vb. yollarla kopya edilip kullanlamaz.

Kaynak gsterilmek kayd ile alnt yaplabilir.

Ekim 1994 - Ankara

Dizgi: Ali Rza Falcolu (Makina Mhendisleri Odas)Bask: MF Ltd. ti. Tel: (0-312) 425 37 68

, T ,

i:?

BOLUM 1

MATEMATK TABLOLARIVE L BRMLER

Hazrlayan

A. Mnir CERT, Mak. Yk. Mhendisi, Danman

MATEMATK TABLOLARI

izelgeNo.

Bilim ve Mhendislikte KullanlanSimgeler la-lbDayire ve embere likinDeerler 2Dzgn okgenler 3Binom Katsaylar 4Baya Logaritmalar 5Doal (Napierian) Logaritmalar 6stel Fonksiyonlar 7Doal Trigonometrik Fonksiyonlar(Alar Radyan olarak) 8Doal Trigonometrik Fonksiyonlar(Alar derece olarak) 9Hiperbolik Fonksiyonlar 10Bessel Fonksiyonlar 11R=l Dayiresindeki Yay Uzunluklar veDerece Radyan Karlklar 12-16Kalanlarn Standart Dalm 17Olas Hatay Hesaplama Faktrleri 18

L BRMLER

izelgeNo.

Metrik Sistem (SM) 1A.B.D. Sistemi (UScS) 2Uluslararas Sistem (SI) 3SI Teme] Birimleri ve Simgeleri 4Birimlerin Alfabetik Listesi 5Snflandrlm Birimler Listesi 6Basn ve Gerilmeninpsi-kN/m2 (ksi-MN/m2) Karlklar 7Basn ve Gerilmenin Metrik Sistem-SIKarlklar 8Younluk-Baume Derecesi Karlklar 9zgl Arhk-API Derecesi Karlklar 10KAYNAKA 52LGL TSE STANDARTLARI 52

1-01

MATEMATK TABLOLARI

izelge.l- Bilim ve Mhendislikte Kullanlan Simgeler

la. Grek Harflerinin Simgeledii Byklkler :

Harf Okunuu

A , a

B,p

Alfa

Beta

Gamma

A, 5

E, e

Delta

Epsilon

Zeta

Simgeledii Byklkler

A (5,6); absorplama (sourma) faktr (3); asal ivme(1,4,5); hcum (attack) as (1); yaynm katsays (1); sluzama (izgisel) katsays (3,5,6); sl yaynm katsays (3);scaklk katsays direnci (2).

A (5,6); pala (blade) as (1); yan kayma as (1); dalgaboyu sabiti (2); faz sabiti (2); sl genleme katsays (kbik)(3,6); beta parac.A (5,6); aktivite sabiti (mol temelinde) (6); dihedral a(F,l); elektriksel iletkenlik (y,a, 2) ; snma lan oran (1,3);zgl arlk (3,4); kayna birim yer deitirmesi (1,5); yayma(propagasyon) sabiti (8,2); zgl arlk (g

c ile 3); birim hac-

min arl (4,5);

Diferansiyel; asal yer deitirme (1); snr tabaka kalnl(1); snm sabiti veya katsays (2); kirite kme (sehim) (5);kirite maksimum kme (5); kontrol yzeyleri takmnn as(1); bal basn (1); deerler arasndaki fark (A,3,6); toplamuzama (5);

Aa doru ykama as (1); kapasitivite (2); boaltlm me-kann kapasitivitesi (, 2); bal kapasitivite (t); dielektriksabiti (2); yaym (emisivite ve toplam emisivite) (1,3,6); hataiareti (1); geirgenlik (permitivitite) (2); trblans deiimi,trblans katsays (1); sonsuz kk;

Kompleks hz = ^ - u - iv (Burada w akkann komplekesdz

fonksiyonu; u, v akkan hznn yatay dzlemdeki bileen-leridir) (1, 4);

H,

, e

K, K

A, 5

Eta

Teta

lota

Kappa

Lambda

1-02

Verim (1,2,3,4,5,6); geri kazanm faktr (1); dielektrik du-yarll (2);Radyasyon as; scaklk derecesi (3); scaklk oran (1); mut-lak scaklk derecesi (Kelvin) (0 veya T 1,2,3,4,5,6); basit s-caklk derecesi (8 veya t, 1,2,3,4,5,6);

Manyetik duyarllk (2); snma lan oran (K, k,3,6); defor-masyondan dolay kiri eriliindeki deime (5);Ykn hat younluu (2); snm faktr (1); buharlama gizliss(X, hfg, 6); sabit basnta buharlama ss (k, hrg veya Hfg);ortalama serbest yrnge (1); trblansn mikrolei (1);meme (nozzle) yayma as (1); iletkenlik edeeri (A,2); s-prme destei as (A,l); koniklik (1); dalga boyu(l,2,3,5);iinden geme yetisi (relktansn tersi) (p, A,2);

Harf Okunuu

M

MATEMATK TABLOLARI

Simgeledii Byklkler

N, v N

Mach as (1); kayma, srtnme katsays (n,f,5); manyetikgeirgenlik (2); boaltlm mekann geirgenlii (|i

c,2); bal

geirgenlik (|ir,2); Poisson oran (u.,v>,5); Poisson oran (1);

Joule-Thomson katsays (3): mutlak (dinamik) viskozite(1,3,4,6); mutlak viskozite katsays (1,3,4,6); bal (suyagre) mutlak viskozite (u,/u,

w 3.6); kayma srtnmesi katsays

(f,u, 5); akkanlk (l/u, 6);

Ima (radyasyon) enerjisinin frekans; zgl hacim (3,6); ki-nematik viskozite (1,3,4,6); bal (suya gre) kinematik visko-zite (3,6); relktivite (isteksizlik) (2);

Ksi Akkanlar mekaniinde konfonn tasvir (conformal mapping)dnmlerinde kullanlan yardmc dzlem denkleminingerel terimi : = + T|(1,4);

O, o

p,p

, o

Omikron

Pi

Ro

Sigma

T, T Tau

Pi says; Poynting vektr (11.2)

Ykn hacim younluu (2); younluk (1,3,4,5,6); su buhar-nn nem younluu (pM , 3); doyma noktasnda su buharnnyounluu (p

s.3); yanstma faktr (3); elektiriksel diren (re-

zistivite) (2);

Yan ykama as (1); ykn yzey younluu (2); elektirikseliletkenlik (6, 8,2); bal (standart havaya gre) younluk (1);elastivite (2); pervane katl (1); normal (kesite dikey) geril-me (8,\), 5); normal gerilme (1); Stefan-Boltzmann sabiti(3,6); yzey gerilim (3,4,6); kinematik yzey gerilim (5/=w,4);Kesme gerilmesi (1); kesme (kayma) gerilmesi (T, s

s, 5);

zaman (t,t; ayn yazda t basit scaklk derecesini gsteriyorsazaman iin T kullanlmaldr) (1.3.6); zaman sabiti (2); iletimfaktr (3);

Y,\) Upsilon

Fi

Hacim (3, 6);

A (P,, 1); helisin ilerleme as (1); manyetik ak (, 2); fazas (2); faz yer deitirmesi (5): potansiyel fonksiyonu (1);ma (radyasyon) aks (, 3): etkin helis as (1);

Ki

Psi Ak yer deitirmesi (2); akm fonksiyonu (1); etkin helis as(1); elektrostatik ak (2);

1-03

Harf Okunuu

Omega

MATEMATK TABLOLARI

Simgeledii Byklkler

Kat a (3); asal frekans (2); asal hz (1,2,3,4,5); dayireselfrekans (2jf, 5 ); kinematik yzey gerilim (5/p, 4); elektrikseldiren birimi (R, ohm, 2);

1

lb. Latin Harflerinin Simgeledii Byklkler :

Harf

A, a

Simgeledii Byklkler

vme, genel dorusal (3,4,5,6); aktiflik (6); genlik (A, 5); alan (A,1,3,4,5,6): grnm oran (A, AL, 1); atom arl (A); zayflatma(2); birim alan bana iletkenlik (1/RA, 2); Helmolt7. serbest enerji-si (A, 6); i potansiyel vektr A- 2); geciktirilmi potansiyel vek-tr (Ar, 2); birim alan bana sl diren (RA, 3); kaldrma erisi-nin eimi (1); birim hacmin alan (6); iin sl edeeri (A , l/J, 3);

B, b

C,c

D, d

E, e

Pervanede pala genilii (1); en, enlilik, genilik (5,6); etkin filmkalnl (B, 6); manyetik ak younluu (fi, 2); manyetik polari-zasyon (Bi. 2); duyarllk (B, 2); savaklarda kret uzunluu (4); akyata genilii (4); kanal yzeyi genilii (4); menzil (1); manye-tik endktans (B);

Kapasitans, kapasite (C,2); Chzy katsays (c, 4); tel uzunluu(1); mutlak katsay (C, 1); genel katsay (C, 4); bzlme katsays(C

c, 4); boaltma katsays (C, 6); boaltma katsays (Cq, 4); birim

arlk bana enerji katsays ( Ce formlnde); birim arlk2g

bana momentum katsays ( Cm formlnde ); hz katsays

(Cv, 4); younluk (konsantrasyon) (C,c 1,3); hacmsal younluk(6); kritik durum veya kritik deer (indisli) (3); snm katsays(3); sabit basnta snma ss (Cp, 1,3); sabit hacimde snma ss(C, 1,3); snma ss (3,6); sabit hacimde molar snma ss (C,1,3.6); en dtaki lifin tarafsz eksenden uzakl (5); k hz (2,3); dalga abukluunun hz (4); ses hz (c,a,4);ap (D); yaynm (katsays) (D

v. 3); buharn sl yaynm katsay-

s (Dv, 6); elektriksel yer deitirme (D. 2); mutlak srklenme

(drag) katsays (D, 1); kalnlk (d.t. 1.3);

Elektiriksel potansiyel fark (E.e, 2); kuvvetin uygulama noktas-nn merkezkal (eksantrisitesi) (5); F.lastiklik modl (E, 5);kinematik elastiklik (K ^ 4 ); toplam i(E); elektronik ykn mut-

p 'lak deeri (2); enerji (E, 1); kinetik enerji (Ek.T, 5); potansiyelenerji (Ep.V, 5); elektromotor kuvvet (E.e, 2); menzil etkinlii (1);elektrik iddeti (E,& 2); voltaj (E.e, 2);

1-04

MATEMATK TABLOLARI

Harf Simgeledii Byklkler

F, f Srtnme katsays (VVeisbach-Darcy, 4); srtnme katsays (F,f,5); arlk merkezinden yatay kuyruk yzeyinin basn merkezineolan uzaklk (1); kuvvet (E, 2); kuvvet (F, 1,4); frekans (1,2,3,5);kayma srtnmesi katsays (f,X, 5); boruda srtnme kayb katsa-ys (4.6); enerji balansnda srtnme (F, 6); ka (fugacity 3,6);tekil kuvvet veya yk (F,P,Q, 5); ak itmesi (F, 1);

G, g Yerekimi ivmesi (1,3,4,5,6); yerel yerekimi ivmesi (gL, 3); Ulus-lararas Standart Yerekimi vmesi (g

c, 3,6); yerekimi ivmesine

ilikin evirme faktr (gc, 3,6); elektriksel iletkenlik (G, 2);

Gibbs serbest enerjisi (G,6); Gibbs fonksiyonu ve tmel (total) po-tansiyel fonksiyon (G,g, 3,6); ktlesel hz (G, 1,6); kayma elastik-lik modl (G, 5); kesme modl (1); bal arlk (suya veya ha-vaya gre, G, 3); birim kesit alanndan birim zamanda geen ktleakmnn hz, (G, 6);

H, h Asal momentum (II, 1); derinlik, ykseklik (3,5); entalpi (H,h,3); entalpi (II, 6); kuru doymu buharn entalpisi (hg, 3); doymusvnn entalpisi (hf, 3); birim arlk bana entalpi (3); s tutumu(entalpi) (H,h, 3); Planck sabiti (3); Bir snr yzeyi boyunca s a-k hz (1); buharlama gizli ss (hrg, A 6^); sabit basnta buhar-lama ss (Hgf, hgf, X, 3); s transferinde yzey katsays (3,6);ykseklik (3,5); basn ykseklii (atmosferik) (h

a, 4); basn

kayb (uygun indisle kullanlr) (4); potansiyel basn (ykseklik)(hpz, 4); basn ykseklii (hp, 4); hz ykseklii (basnc) (hB, 4);nemlilik (H, 6); nem doygunluunun ksmi basnc (H

r, 3,6); man-

yetik iddet (H, 2), kalnlk (5);

I, i Elektrik akm (1,2); arpma (impuls) (I, 1); eylemsizlik momenti(I. kutupsal, 1,5); eylemsizlik momenti (karteziyen) (I, 1,5,6); ey-lemsizlik arpm (I

x y, 5)

J, j Pervanenin ilerleme oran (J, 1); iin sl edeeri (l/J, 3); eylem-sizlik momenti (kutupsal, 5); snn mekanik edeeri (J, 1,3,6);nm (radyasyon) iddeti (J, 3);

K, k Jirasyon yarap (5); elektrik iddeti (E, J, 2); svlarn ktleselelastiklik modl (K); indirgenmi frekans (titreme, 1); sl diren(-L ,3); snma slar oran (k, X, K, 3,6); yay sabiti (5); gerilme y-

klmas faktr (K, 5); sl iletkenlik (1,3); kavrama katsays (2)

L, 1 Endktans (L, 2); karlkl endktans (Lm, 2); self-endktans (L,U, 2); uzunluk (L, 3, 4,5,6,) ;k iddeti (lambert, L, 2);

M, m Manyetemotor kuvvet (M, F, 2); kuvvetin momenti (M, 5); Machsays (M, 1); molekl arl (M, 3,6); manyetik moment (m, 2);kuvvetin momenti (eilme momenti de iinde, 1,5); manyetik po-tansiyel (M, F); iftin momenti (M,T); przllk katsays(Bazin) (4); ktle (1,3,4,5,6); faz numaras (2); kutup kuvveti (2);

N, n Przllk katsays (Kutter ve Manning) (4); normal kuvvet (N,1); emniyet katsays (N, 5); mol says (mol-pound, mol-kg) (3);genel olarak say (N, 1,3,4,5,6); iletken says ya da evrim (tur)says (N, 2); birim zamanda dnme says (devir) (1,3,5); ykfaktr (1); dnme hz (devir) (2,6);

1-05

MATEMATK TABLOLARI

Harf

P.P

Simgeledii Byklkler

Q.q

Aktif g (P, 2); g (1,3.4,5,6): basn iddeti (birim alana gelenkuvvet (1,3,4,5,6); slak evre (bir kesit alannn slak evresi) (P,4); su buharnn doyma basnc (P

s, 3); titreim sabiti (p, 2); birini

zaman bana enerji (g) (P. 4): tekil yk (P,Q,R, 5); toplam yk(P,W); elektriksel moment (r>. 2); manyetik isteklilik (permeans)(reliiktansn tersi) (P. A, 2); geometrik adm (piteh) (1);

Elektrik yk veya miktar (Q. 2); tekil ykler (F,P,Q); basmamiktar veya akm verdisi (debi) (Q, 4); birim genilik bana akmmiktar (4); elektrik miktar (Q.q, 2); hacmsal verdi (6); tekil ykya da kuvvetler (F.P.Q): dinamik (darbe) basnc (1); s ak hz(3); bir alann verilmi bir eksene gre momenti (statik) (Q, 5); re-aktif g (2); birim ktle ya da arlk bana s miktar (1); birimzaman bana s miktar (1.3.6): bir akkann hacmsal toplamss (Q, 1,3,6); kuvvet iftinin momenti (Q, 1); sl gei (3); birakkann hacmsal hz (q. Q. 3);

R,r

S, s

T, t

U,u

V, v

W, w

1-06

Isl iletkenlik |-L 31; birim alan bana sl iletkenlik;\R ' " / VRA

bant (correlation) katsays (R. 1); gaz sabiti (R, 1,3.6); hidrolikyarap (Rh, 3,6); ortalama hidrolik yarap (R

m, 4); kesit alannn

hidrolik yaralp (R. 4); yelpaze (R.l); isteksizlik (relktans) (R,1); elektriksel diren (R, 2); sl diren (R, 3,6); birim alan banasl diren (RA, 3,6): Reynolds says (R, 1,4); karm zenginlii(yanmada edeerlik oran) (R. 1);Alan (S, 1,3,6); izgisel uzaklk (3,5); elastans (S, 2); karlklelastans (S

m, S

r, 2); z-elastans (S, S,*, 2); grnr g (S,2);

kayma (2); kanal yatann eimi (So, 4); evlerin ve eddelerin

eimi (4); enerji gradyeninin eimi (S, 4); hidrolik gradyenineimi (S

w, 4); kayma gerilmesi (s

s, t, 5); normal gerilme (s, x, 5);

Kinetik enerji (T, F*. 5); mutlak scaklk derecesi (Kelvin) (T,0,1,2,3,4,5,6); basit scaklk derecesi (t, 6,1,2,3,4,5,6); kalnlk(t,d,3); kalnlk (4): pervane itkisi (T, 1); zaman (t, T, 1,3,6); iftinmomenti (tork) (T.M. 5); i (T. 3,5);i enerji (U,u, 1,3,6); s transferi katsays (toplam) (U, 1,3,6);ma (radyan) enerjisi (U, 3); ma iddeti (3); hz bileenleri(u,v,w, 1,4); yerel hz (6); hz bileenlerinin geici ortalamalar(u,v,w, 4);

Is transfer katsays (toplam) (1); kiri kesitindeki kesme kuvveti(V, 5); kuru havann birim arl bana slak hacim (karmhacmi) (VH, 3); izgisel hz (5); elektriksel potansiyel (fark)(elektromotor kuvvet ile elektriksel potansiyel fark arasnda birayrm yapmak istendiinde birinci iin E, e simgeleri, ikinci iinV, v simgeleri kullanlabilir. 2); izgisel hz (V,v,u, 3); hz (V,1,3,4); hz (V,v, 3); ses hz (V

a. 6): ortalama hz (V, 6); Belanger

kritik hz (Ve, 4): ortalama ktle hz (Q/A=V, 4); bal hz (3);hacim (V, 1,4,5,6); mol hacmi (V, Vm, 3); zgl hacm (1,3); top-lam hz (V, VL, 3);Enerji (W, 2); madde miktar (W. 6); ma (radyan) iddeti (3);hzn bileenleri (w.u,v); toplam arlk (W, 1,3,4,5,6); i (W,2,4,5,6); d i (W

e, 6); birim arlk bana i (w,wk); mukavemet

momenti (W, 5);

mi

MATEMATK TABLOLARI

Harf Simgeledii Byklkler

X, x Adyabat faktr (X, 3); yere bal koordinat eksenleri sistemi(x,y,z, 1); boyuna eksen (X, 1); hacmsal kesir (X

v, 6); arlka

kesir (Xw, 6); buhar kalitesi (3); reaktans (X, 2); kapasitif reak

tans (Xc> 2); endktif reaktans (X,. 2); karlkl reaktans (Xm,

Xrc

); z (elf) reaktans (X,XCC);Y, y Kabul (Y, 2); yanal eksen (Y, 1); derinlik (6); kanallarda ak de-

rinlii (4);Z, z Dey (normal) eksen (Z, 1); sktrlabilme faktr (6); referans

dzleminden ykseklik (Z, 4); akm yatandan ykseklik (Zo, 4);savaklarda kret ykseklii (4); Rmpedans (Z, 2); mukavemet mo-menti (Z, 5);

Aklamalar :

1- Parantez iinde gsterilen saylar :(l)IIavachkta (Amerikan Havaclk Bilimleri, ASA. Z10.7)(2)Elektrik Mhendisliinde (Amerikan Elektrik Mhendislii Standartlar Enstits, ASA. Z10.5)(3)Is ve Termodinamikte (Is ve Tennodinamik iin Amerikan Standart Simgeleri, ASA. Z10.4)(4)Hidrolikte (Hidrolik iin Amerikan Standart Simgeleri, ASA, Z10.2)(5)Kat Cisimler Mekaniinde (Kat Cisimler Mekanii iin Amerikan Standart Yazm Simgeleri ASA,

Z10.3)(6) Kimya Mhendislinde (Kimya Mhendislii iin Amerikan Standart Yazm Simgeleri ASA, Z10.12)

2- Kk harflerle gsterilen byklklerde kk harf parantez iinde tekrar yazlmamtr. Byk harfle ya daindisli olarak gsterilenler parantez iine yazlmtr.

1-07

MATEMATK TABLOLARI

lc. Logaritma ve Trigonometriye likin Simgeler :

Logaritmalar

loga = log o

a

n a = logg a

log"1 a = colog a

Trigonometri

(a) nn baya (ondalk) ya da10 tabanna gre logaritmas

(a) nn doal (neperiyen) yada e (2,718) tabanna gre lo-garitmas

Logaritmas (a) olan say

ruj IJV^IJ^VIVI

Ay : y deki art

dy : y nin diferansiyeli

dy : y deki deiiklikb

: a dan b ye kadar i zerinde toplamai = a

itF\MEfrf

lim (y) = b, y b eer x - a isex -* a

I : in entegrali

sin, cos, tg (tan) b

cosec (esc), sec, cotg (etn) Trigonometrik fonksiyon- f . jn belirli entegrali

lardr Ja'

sin"1, cos"1 Bu fonksiyonlarn tersidir.

d. Cebirsel lemler ve Simgeler :

y = f (x): y, x in fonksiyonudur.

y1 = f (x) = Q- = D v y = f ( x) fonksiyonunun x edx gre trevi

y" = f' (x) = = D2X y y = f (x) fonksiyonunun x edx2 gre 2. trevi

u = f (x,y) u, x ve y nin fonsiyonudur.

duu', = f' (x, y) = D

x (u) = u= f (x, y) fonksiyonunun

9x x e gre k'smi trevi

U'xy = f"xy (X, y ) = Dy ( D , u) = -d y d x

u = f (x, y) fonksiyonunun x ve y ye gre 2. trevi

V : dalle ya da nabla (vektrel diferansiyel operatr)

: Laplace ilemi

V2: Laplace operatr

le. Vektr Analizi

i , j , k : Eksenler boyunca birim vektrler(sa el kural)

s . b =(a . b) = S ab : a ile^b nin skaler arpm,iddeti AB cos (A, B)

a x b^.a . bj = V ab : a ile b nin vektrel arpmiddeti AB sin (A, B)

1-08

MATEMATK TABI .OLARI

izelge.2- Dayire ve embere likin Deerler

apevre

Alan

Yay

Kiri

:d = 2r

: = 2Jtr =

: A = 7tr2 =

: PAQ = s

: R Q - 1

7td

d27t =

4SAK de

s = r9 = 2

s I'-1 (Huygens forml 120 ye kadar olan alarda hata oran3 % 0.25 den kktr).

Ok :h

l = 2rsin S.2

e 2 SI,, e.2

1 = V 2 hr- h2 (yaklak forml).

4 h2 + I2

8 h(yaklak forml).

1 12 (6 180 ise art iaret kullanlr).

h = r 11 - cos 2

1-09

P (x,y) noktasnn ordinat:

Dayire diliminin alan (ORQ dilimi):

Dayire kesmesinin alan :(RAQ kesmesi)

MATEMATK TABLOLARI

y = h - r + Vr2 - x2

A= = -~ 2 ~ 2

Dayire halkasnn alan:

Tam halkann alan

MRQN halka parasnn alan

A =-2JL = _b_ (8l'+ 6) (yaklak formller)3 15

A = 7t (rV2) = 7t (r+r1) (r-r')

A = $- (r? - r'2) = 5- (r + r') (r - r')2 2

l/cljje.3- D/.gii okgcnlrr.

Dzgn okgenler (Kenarlar birbirine eit. alar birbirine eit)

n = kenar says

Merkez a: 2 a = (radyan)n

Ke as : p = n (radyan)n

evre : = ns

Kenar : s = 2r tg a = 2R sin a

u

W-

i'i

u1-10

iten teet emberin yarap:

Da izilen emberin yarap

Alan :

MATEMATK TABLOLARI

r = cotg a

R = cosec a2

A =-Q5r_ = nr2tg a = Ii-B_ sin 2a2 2

= cotg a = nx AOB alan4

Genel okgenin alan: okgenin blnebildii saydaki gen alanlarnn toplam.Dzgn okgende Deerler

n

3456789101215162024324864

2a

1209072605143454036302422.50181511257505.625

Alans

2

0.4331.0001.7212.5983.6344.8286.1827.69411.20017.64020.11031.57045.58081.230183.100325.700

AlanR2

1.2992.0002.3782.5982.7362.8282.8932.9393.0003.0513.0623.0903.1063.1213.1333.137

Alan2

5.1964.0003.6333.4643.3713.3143.2763.2493.2153.1883.1833.1683.1603.1523.1463.144

Rs

0.5770.7070.8511.0001.1521.3071.4621.6181.9322.4052.5633.1963.8315.1017.64510.190

A l a n

7t

2.0001.4141.2361.1551.1101.0821.0641.0521.0351.0221.0201.0131.0091.0051.0021.001

a/R

1.7321.4141.1761 0000.8680.7650.6840.6180.5180.9160.3900.3130.2610.1960.1310.098

a/r

3.9642.0001.4531.1550.9630.82840.7280.6500.5360.4250.3980.3170.2630.1970.1310.098

r/R

0.5000.7070.8090.8660.9010.9240.9400.9510.9660.9780.9810.9880.9910.9950.9980.997

r/a

0.2890.5000.6880.8661.0381.2071.3741.5391.8662.3522.5143.1573.7985.0777.62910.180

izelge.4- Binom Katsaylarn

1234567

91011121314

(n)o

11111

11

(n)123456789

1011121314

(nh

136

10152128364555667891

(n)j

14

1020355684

120165220286364

(n)4

15

152170

126210330495715

1001

(n)5

16

2156

126252462792

12872002

(n)

17

2884

210462924

17163003

(n>

18

36120330792

17163432

19

45165495

12873003

(11)9

11055

220715

2002

(n)o

11166

2861001

(11)11

1278

364

(n)n

11391

1-11

MATEMATK TABLOLARIAklamalar :

1x2x3

(n)0 = l(n), = n(n))2 = (n-(n)3 = (n-1(n)

r = n(n-l

[ n - ( r - 1)] / 1x2x3 xrDier Gsterimler : n C

r = (n

r) = (n)

r

n = 14 iin katsay: (n) | 4 = 1n = 15 iin katsaylar : (n)14 = 15 ve (n) l 5 = 1

izelge.5- Baya Logaritmalar

w

1.0l.l1.21.31.4

1.51.61.71 81.9

2.02.12.22.32.4

2.52.62.72.82.9

8.03.13.23.33.43.53.63.73.83.9

4.04.14.24.34.4

4.54.64.74.84.9

0

0.00000414079211391461

17612041230425532788

0.30103222342436173802

39794150431444724624

0.47714914505151855315

54415563566257985911

0.60216128623263356435

65326628672168126902

1

00430453082811731492

17902068233025772810

30323243344436363820

39974166433044674639

47864928506551985328

54535575569458095922

60316138624363456444

65426637673068216911

2

00860492086412061523

16182095235526012833

30543263346436553838

40144183434645024654

46004942507952115340

54655587570558215933

60426149625363556454

65516646673968306920

3

01280531089912391553

18472122238026252856

30753284348336743856

40314200436245184669

48144955509252245353

5478559571758325944

60536160626363656464

65616656674968396928

4

01700569093412711584

18752148240526482878

30963304350236923874

40484216437845334683

18294969510552375366

54905611572958435955

60646170627463756474

65716665675868486937

5

02120607096913031614

19032175243026722900

31183324352237113892

40654232439345484698

48434983511952505378

55025t>23574058555966

60756180628463856484

65806675676768576946

02530645100413351644

19312201245526952923

31393345354137293909

40824249440945644713

48574997513252635391

55145635575258665977

60856191.629463956493

65906684677668666955

7

02940682103813671673

19592227248027182945

31603365356037473927

40994265442545794728

48715011514552765403

55275647576358775988

60%620163046405

'6503

65996693678568756964

8

03340719107213991703

19872253250427422967

31813385357937663945

41164281444045944742

48865024515952895416

553956S8577558885999

61076212631464156513

66096702679468846972

9

03740755110614301732

20142279252927652969

32013404359837843962

41334298445646094757

49005038517253025428

55515670578658996010

61176222632564256522

66186712680368936981

2120191817

1716161515

1414131313

121212IIIIII10101010

10109Q9

log T 0 4971log t - 0 4343

lop T'2 = 0.1901 log Tlog (0.43!.')! - 0 M7,

MATEMATK TABLOLARI

izelge.5- Baya logaritmalar (devam)

Say

l3.05.15.25.35.45.55.65.75.85.96.06.16.26.36.4

6.56.66.76.86.97.07.17.27.37.47.57.67.77.87.98.08.18.28.36.48.58.68.78.88.9

9.09.19.29.39.4

9.59.69.79.89.9

0

0.69907076716072437324

74047482755976347709

0.77827853792479938062

81298195826183258388

0.84518513857386338692

87518808886589218976

0.90319085913891919243

92949345939594459494

0.95429590963896859731

97779823986899129956

1

69987084716872517332

74127490756676427716

77897860793180008069

81368202826783318395

84578519857986398698

87568814887189278982

90369090914391969248

92999350940094509499

95479595964396899736

97829827987299179961

2

70077093717772597340

74197497757476497723

77967868793880078075

81428209827483388401

84638525858586458704

87628820887689328987

904290%914992019253

93049355940594559504

95529600964796949741

97869832987799219965

3

70167101718572677348

74277505758276577731

78037875794580148082

81498215828083448407

84708531859186518710

87688825888289388993

90479101915492069258

93099360941094609509

95579605

965296999745

979198369881-99269969

4

70247110719372757356

74357513758976647738

78107882795280218089

81568222828783518414

84768537859786578716

87748831888789438998

90539106915992129263

93159365941594659513

95629609965797039750

97959841988699309974

S

70337118720272847364

74437520759776727745

78187889795980288096

81628228829383578420

84828543860386638722

87798837889389499004

90589112916592179269

93209370942094699518

95669614966197089754

98009845989099349978

6

70427126721072927372

74517528760476797752

782578%796680358102

81698235829983638426

84888549860986698727

87858842889989549009

90639117917092229274

93259375942594749523

9571%I9966697139759

98059850989499399983

7

70507135721873007380

74597536761276867760

78327903797380418109

81768241830683708432

84948555861586758733

87918848890489609015

90699122917592279279

93309380943094799528

95769624967197179763

98099854989999439987

8

70597143722673087388

74667543761976947767

78397910798080488116

81828248831283768439

.85008561862186818739

87978854891089659020

90749128918092329284

93359385943594849533

95819628%7597229768

98149859990399489991

9

706771527235731673%74747551762777017774

78467917798780558122

81898254831983828445

85068567862786868745

88028859891589719025

90799133918692389289

93409390944094899538

95869633968097279773

981898639908995299%

Ort

. 1

fark

1

98888

88877

77777

77666

6666666665555555555555555

54444

Bu iki sayfa 1 ile 10 arasndaki saylarn 4 basamakl baya (10 tabanl) logaritmalarn verir. Sayda ondalkbasama saa (ya da sola) a ev yrtmek, logaritmaya a (ya da -n) eklemek demektir. Yani ]o 0.017453 =0.2419-2 deeri, 2,2419 ya da8.2419-10 biiminde de yazlabilir. Negatif saylarn logaritmas yoktur.

1-13

MATEMATK TABLOLARI

izelge.6- Doal (Ncperiycn) Logaritmalar

A1.0.1.2.3.4.5.6.7.8.9

2.02.12.22.32.42.52.62.72.82.9it.O3.13.23.33.4

3.53.63.73.83.94.04.14.24.34.44.54.64.74.84.9

0

0.00000953182326243365

0.40554700530658786419

0.69317419788583298755

0.91639555

0.99331.02960647

1.09861314163219392238

1.25282809308333503610

1.38634110435145864816

1.50415261547656865892

1

01001044190627003436

41214762536559336471

698174677930837287%92039594996903320682

10191346166319692267

25562837311033763635

38884134437546094839

50635282549757075913

2

01981133198927763507

41874824542359886523

70317514797584168838

92439632

000603670716

10531378169420002296

25852865313734033661

39134159439846334861

50855304551857285933

3

02961222207028523577

42534886548160436575

70807561802084598879

92829670004304030750

10861410172520302326

26132892316434293686

39384183442246564884

51075326553957485953

4

03921310215129273646

43184947553960986627

71297608806585028920

93229708008004380784

11191442175620602355

26412920319134553712

39624207444646794907

51295347556057695974

6

04881398223130013716

4383500855%61526678

71787655810985448961

93619746011604730818

11511474178720902384

26692947321834813737

39874231446947024929

51515369558157905994

6

05831484231130753784

44475068565362066729

72277701815485879002

94009783015205080852

1184"1506181721192413

26982975324435073762

40124255449347254951

51735390560258106014

7

06771570239031483853

45115128571062596780

72757747819886*99042

94399821018805430886

12171537184821492442

27263002327135333788

40364279451647484974

51955412562358316034

8

07701655246932213920

45745188576663136831

73247793824286719083

94789858022505780919

12491569187821792470

27543029329735583813

40614303454047704996

52175433564458516054

9

08621740254632933988

46375247582263666881

73727839828687139123

95179895026006130953

12821600190922082499

27823056332435843838

40854327456347935019

52395454566558726074

S*0,295878074696561575451494744434139383635343332313029

282727262525242323222221212020

n x = (2.3026) log10 x

Burada 2.3026 = n 10 ve 0.4343 = log 0 e

log 0 x = (0.4343) n x

Bu iki sayfa, 1 ile 10 arasndaki saylarn, virglden sonraki 4 eve kadar doru doal logaritmalarn (ln) verir.

Saynn kesir virgln saa (ya da sola) doru n ev yrtmek, saynn logaritmasna 2.3026 x n eklemek (ya dan x 3.6974 karmak) anlamna gelir.

1-14

MATEMATK TABLOLARI

izclge.6- Doal Logaritmalar (Devam)

Say

5.05.152535.45.55.65.75.85.9606.16.26.36.46.56.66.76.86.9

7.07.17.27.37.47.57.67.77.87.98.08.18.28.38.48.58.68.78.88.9

9.09.19.29.39.49.59.69.79.89910.0

0

1.60946292648766776864

1.70477228740575797750

1.79188083824584058563

1.87188871902191699315

1.945996019741

1.98792.0015

2.01490281041205410669

2.07940919104111631282

2.14011518163317481861

2.19722083219223002407

2.25132618272128242925

2.3026

1

61146312650666966882

70667246742275967766

79348099826284218579

87338886903691849330

94739615975598920023

01620295042505540681

08070931105411751294

14121529164517591872

19832094220323112418

25232628273228342935

2

61346332652567156901

70847263744076137783

79518116827884378594

87498901905919993*4

94889629976999060042

01760308043805670694

08190943106611871306

14241541165617701883

19942105221423222428

25342638274228442946

3

61546351654467346919

71027281745776307800

79678132829484538610

87648916906692139359

95029643978299200055

01890321045105800707

08320956107811991318

14361552166817821894

20062116222523322439

25442649275228542956

4

61746371656367526938

71207299747576477817

79848148831084698625

87798931908192289373

95169657979699330069

02020334046405920719

08440968109012111330

14481564167917931905

20172127223523432450

25552659276228652966

S

61946390658267716956

71387317749276647834

80018165832684858641

87958946909592429387

95309671981099470082

02150347047706050732

08570980110212231342

14591576169118041917

20282138224623542460

25652670277328752976

6

62146409660167906974

71567334750976817851

80178131834285008656

88108961911092579402

95449685982499610096

02290360049006180744

08690992111412351353

14711587170218151928

20392148225723642471

25762680278328852986

7

62336429662068086993

71747352752776997867

80348197835885168672

88258976912592729416

95599699983899740109

02420373050306310757

08821005112612471365

14831599171318271939

20502159226823752481

258626902793289529%

8

62536448663968277011

71927370754477167884

80508213837485328687

88408991914092869430

95739713985199880122

02550386051606430769

08941017113812581377

14941610172518381950

20612170227923862492

25972701280329053006

9

62736467665868457029

72107387756177337901

80668229839085478703

88569006915593019445

95879727986500010136

02680399052806560782

09061029115012701389

15061622173618491961

20722181228923962502

26072711281429153016

Ort

.

fark

1

2019191818

1818171717

1616161615

1515151514

1414141313

13131313121212121217.1212IIIIII

IIIIIIIIII

1010101010

Saynn kesir virgln saa (ya da sola) doru n ev yrtmek, saynn logaritmasna 2.3026 x n eklemek (ya dar. * 1.6974 karmak) anlamna gelir.

1-15

MATEMATK TABLOLARI

izclge.7- stel Fonksiyonlar (cn ve e")

n

0.00.01.02.03.04

0.05.06.07.08.09

0.10.11.12.13.14

0.15.16.17.18.19

0.202\222

0257.6777829

0.3031323334

03536373839

0.40.41.42.43.44

0.45.46.47.48.49

0.50

- fa

1.000 n

1.010 "1.020 21.030 ?1.041 J o1.051 ,,1.0621.073 11.083 ?1.094 j j1.105 .,1.1161.127 i1.139 21.150 121.162 , ,1.174 21.185 i1.197 \17.09 \\17.21 U34 \i1.246 \1.259 S1771 J|1.284 . ,1.297 \l1.310 \i1.323 \\1336 fi1350 1363 i1377 T1391 i1.405 j j1.419 ,41.433 1.448 1.462 \i1.477 j |1.492 , ,1307 21322 ?1.537 \l1353 ' I1368 ,,1384 51.600 ?1.616 \l1.632 J1.649

n

o.so31323334

0.553637.58.59

0.60,.61.62.63.64

0.65.66.67.68.69

0.7071727374

0.75767 77879

0.80.812.83.84

0.85.86XI.88.89

0.90.91.92.93.94

0.95.96.97.98.99

1.00

- 11.649 .,1.665 S1.682 i1.699 71716 I ;1733 , .1751 51.768 i1.786 \l

\m \l1.822 ,o1.840 51.859 it1.878 [t.1.896 Jg1.916 ,1.935 A1.954 J21.974X 221.994* g2.014 , n2.034 222.054 2?2.075 22.096 |[2.117 ,,2.138 i\2.160 f2.181 2703 2j2776 2.248 S2770 5?2793 2316 g2340 2363 ft2387 52.411 il2.435 g2.460 , 42.484 l\2309 2335 %2360 5^2386 ,,2.612 ,22.638 ,52.664 S2.691 #2.718

n

1.0.1.23.4

1.5.6.7.8.9

2.0.1.23.4

23.67.8.9

3.0.173.4

33.67.8.9

4.0.1

3.4

43

5.06.07.08.09.0

10.0

2T /2 T / 24T/25T/25T/2

5T/2

e

2.718'3.0043.3203.6694.0554.4824.9535.4746.0506.6867.3898.1669.0259.97411.0212.1813.4614.8816.4418.1720.0922.2024.5327.1129.9633.1236.6040.4544.7049.4054.6060.3466.6973.7081.4590.02

148.4403.41097.2981.8103.

22026.4.810

-23.141113535.52576.

12392.59610.

286751.

n

0.00.01.02.03.04

0.05.06.07.08.09

0.10.11.12.13.14

0.15.16.17.18.19

0.2071727374

07576777879

0.3031323334

0353 637383 9

0.40.41.42.43.44

0.45.46.47.48.49

0.50

fa

1.000 .0.990-2

.980 ~ S

.970-'W> I o.951 . 9 4 2 - . 2.932 ~ ' 2.923 I.914 ~ .905

Q.896 ~ I.887 ~ A.878 ~ I869 Z l.861

q.852 ~ I.844-5.835 1.827 Z 8.819 .811 5.803" 5795 ~ 2787 I |779 ..771 2.763 ~ 2.756 Z 8748 Z 7.741 .7 3 3 " S726 " i719 ~ 1

705 1

.698 ~ i

.691 i

.684" i677 1 7670 _

6. 6 6 4 " S

6 5 7 I 6

;651 ,644 1 6.638

7.631 " i. 6 2 5 - 5-

6 1 9 I 6

613 I 60.607

n

0.5031323334

0.55.56373839

0.60.61.62.63.64

0.65.66.67.68.69

0.7071.727374

0.75.76.77.7879

0.80.81.82.83.84

0.85.86.87.88.89

0.90.91.92.93.94

0.95.96.97.98.99

1.00

e"

.607

.600395389383.577371366360354.549343338.533327322.517312.507.502.497.492.487.482.477.472.468.463.458.454.449.445.440.436.432.427.423.419.415.411.407.403399395391387.383379375372368

n

1.0.123.4

13.67.8.9

2.0.173.4

23.67.8.9

3.0.173.4

33.6.7.8.9

4.0.173.4

43

5.06.07.08.09.0

10.0T / 2

2T/23r/24T/25T/26T/27T/2Sr/2

-

368333301773747723202.183.165.150.135.122.111.100.0907.0821.0743.0672.0608.0550.0498.0450.0408.0369.0334.0302.0273.0247.0224.0202.0183.0166.0150.0136.0123.0111

.00674

.00248

.000912

.000335

.000123

.000045708.0432.00898.00187.000388.000081.000017.000003

Notlarr* Bu stunda i kestirim (enterpolasyon) yapmaynz, e = 2.71823 l/e = 0.367879 lofi,

n e = 04343

1/0.4343 = 2.3026 log10 (0.4343) = .6378 log 0 (e") = n (0.4343)

1-16

MATEMATK TABLOLARI

l/.el{;i!.8- Doal Trigonometrik Fonksiyonlar(Aclar radyan olarak)

Rnd.

.00o.02.03.04

.05

.oo

.07

.08

.09

.10.11.12.13.14

.15

.16

.17

.18

.19

.20.21.22.23.24

.25

.20

.27

.2820

.30.31.32.33.34

.35

.36

.37

.38

.39

.40.41.42.43.44

.45

.40

.47

.48An.50

Pa.l.

sin

OOOOO0100002000.03000.03099

.04908

. 05996

.00994

.07991

.08988

.00983

.10978

.11971

.12963

.13954

.14944

.15932

.16018

.17903

.18880

.19807

.20840

.21823

.22798

.23770

.2474025708.26673.27636.28595

.2955230506.31457.32404.33349

.34290

.35227

.30162

.37092

.38019

.38042

.39861

.40776

.41687

.42504

.43497

.44305

.45289

.40178

.47003

.47043

sin

tg

.00000

.01000O20O003001.01002

05004.0600707011.08017.09024

.10033

.11045

.12058

.13074

.14092

.15114

.16138

.17106

.18197

.10232

.2027121314.2230223414.24472

.25534

.20002

.27676

.28755

.29841

30034.32033.33130.34252.35374

.3050337040.3S7S.30041.41105

.42270

.43403

.44057

.45862

.47078

.18300

.4054550707.5200).53330

.54030

MATEMATK TABLOLARI

izclge.8- Doal Trigonometrik Fonksiyonlar (Devam)(Alar radyan olarak)

Rad.

1.001.011.021.031.04

1.051.061.071.081.09

1.101.111.121.131.14

1.161.161.171.181.19

1.201.211.221.231.24

1.251.261.271.281.29

1.301.311.321.331.34

1.351.361.371.381.39

1.401.411.421.431.44

1.451.461.471.481.49

.soRad.

sin84147.84683.85211.85730.86240

.86742

.87236

.87720

.88196

.88663

.89121

.89670

.90010

.90441

.90863

.91276

.91680

.92075

.02461

.02837

.93204

.93562

.93910

.94249

.94578

.94898

.95209

.95510

.06802

.96084

.06366

.96618

.06872

.97115

.97348

.97572

.97788

.97991

.98185

.98370

.98545

.98710

.98866

.99010

.99146

.99271

.99387

.00492

.99588

.99674

.99740

sin

tg

1.65741.60221.62811.66521.7036

1.74331.78441.82701.87121.9171

1.96482.01432.06602.11982.1759

2.23452.29582.36002.42732.4979

2.67222.65032.73282.81982.9119

3.00963.11333.22383.34133.4672

3.00213.74713.00334.07234.2556

4.45524.67344.91315.17746.4707

8.70796.16546.58117.05557.8018

8.23818.98869.887410.08312.350

14.101

ctg

.64200

.62806

.61420

.60051

.68609

.67362

.56040

.64734

.53441

.62162

.60897

.49644

.48404

.47175

.46959

.44753

.43558

.42373

.41199

.40034

.38878

.37731

.36593

.35463

.34341

.33227

.32121

.31021

.20028

.28842

.27762

.26687

.25019

.24556

.23498

.22446

.21398

.20354

.19315

.18279

.17248'.16220.16195.14173.13155

.12139

.11126

.10114

.09105

.08007

.07001

ctg

cos

'.54030.53186.62337.51482.60622

.49757

.48887,.48012.47133.46249

.45360

.44466

.43568

.42666

.41759

.40849

.39934

.39015

.38092

.37166

.36236

.35302

.34365

.33424

.32480

.31532

.30582

.20628

.28672

.27712

.26750

.25785

.24818

.23848

.22875

.21901

.20924

.10945

.18064

. 17081

.16997

.16010

.15023

.14033

.13042

.12060

. 11057

.10063

.09067

.08071

.07074

COS

Rad.I.SO1.611.521.531.54

1.551.561.571.581.59

1.601.611.621.631.64

1651.661.671.681.69

1.701.711.721.731.74

1.751.781.771.781.79

1.801.811.821.831.84

1.851.861.871.881.89

1.901.911.921.931.94

1.951.981.971.981.99

2.00Rad.

sin.00749.99815.90871.99917.99953

.99978

.999941.00000.99996.99082

.99957

.99023

.09879

.09825

.99781

.99687

.99602

.99508

.00404

.99290

.99166

.90033

.98889

.98735

.88572

.98399

.08216

.08022

.07820

.97607

.97385

.97153

.06911

.06050

.96398

.96128

.95847

.95557

.95258

.94949

94630.94302.93965.93618.93262

.92896

.92521

.92137

.91744

.91341

.00630

sin

tg

14.10118.42819.67024.40832.461

48.07892.6211255.8

-108 65-52.067

-34.233-25.495-20 307-16.871-14.427

-12.699-11.181-10.047- 9.1208- 8.3102

- 7.6066- 7.137:1- 6.6524- 6.2281- 5.8535

- 5.5204- 5 2221- 4.0534- 4.7101- 4.4887

- 4.2863- 4.1005- 3.9294- 3.7712- 3.6245

- 3.4881- 3.3008- 3.2410- 3.1304- 3.0257

- 2.9271- 2.8341- 2.7463- 2.6632- 2.6843

- 2.5005- 2.4383- 2.3705- 2.3058- 2.2441

- 2.1850

tg

ctg

.07091

.06087

.05084

.04082

.03081

.02080

.01080

.00080-.00920-.01921

-.02921-.03922-.04924-.05927-.06931

-.07937-.08944-.09953-.10064-.11977

-.12993-.14011-.15032-.16056-.17084

-.18115-.19149-.20188-.21231-.22278

-.23330-.24387-.25449-.26517-.27500

-.28669-.29755-.30848-.31945-.33051

-.34164-.35284-.36413-.37549-.38096

-.39849-.41012-.42185-.43308-.44562

-.45768

ctg

COS

.07074

.06076

.05077

.04079

.03079

.02070

.01080

.00080-.00920-.01920

-.02920-.03919-.04918-.05917-.06916

-.07912-.08900-.09904-.10899-.11892

-.12884-.13875-.14865-.16863-.16840

-.17825-.18808-.19789-.20768-.21745

-.22720-.23603-.24863-.25631-.26506

-.27559-.28519-.20476-.30430-.3138i

-.32329-.33274-.34215-.35153-.36087

-.37018-.37045-.38868-.39788-.40703

-.41616

COS

1-18

:/: rr x - - -Z t> M X C. UO tO 4- O O

Cn OtOt Cn Ot OIOWW*.dCi 'C C: O< O N-

'SiSg)-OM(!l*

n C c c T c 00 OD 00 00 00w o w 5i to -

ya?"??-.;COO3C

"I O C C- O --1 4- > 00O3CO 4* 4- 4*

O CJ t n O OS CS

O Ot 4* ifa 4 COGS -> 00 t O

4. n C- 00 ' t-1CO CS '-O tO OS I-1

CO CC CO (OtOtOC W O *! ^ ^W ^ C QC C

O ^ - t - . - tOtO-Mrf-OOMi

C". C M *! M 0

M -*1 'I -1 -7 00fcO rf*. O M O t-1

rocw(

C CO h - 00 O ;OOOH

OC 00 00 CO tC CDCtf O -1 O tOOO OS -^1 O rffc

s

4- O O O Ot O00 t - 4- - I '-CtO

8co co cc S 00-^ o w o -^to W CO 4- *-

O O O O -^ - C: C

O OO OOO0c oo --1 si - O:*- 00 O' IO ^to 4- t C: ^100

4- - I CC - 4 C

oooo0 - I ^1 --1 CS00 O tO '4*. 00 O tOCS OS "-I CO ' ^ - co t o t ooooo o

iiPiSO H- to CO rf*. O

sssssscctceO O - I - I 00 0

KS5SSSS

o o >- "- - >-

t ^ c o

> $

& d

4- 5 - t CC O - J S

to to to hs to to4- O O O* O

SSS858

CO COO COCO OO CJ & 4 - 4* i -Ot tO O -~l *- MM tO tO O 00 O

c co cO co co ^O

O OS ^J ^ 1 ^1 ^

O -I COO *! 4-O tO > OS CO O

tototototoo

CD

MATEMATK TABLOLARI

izelge.9- Doal Trigonometrik Fonksiyonlar (Devam)(Alar derece olarak)

22" OC1020304050

23 OC1020304050

24 00'1020304050

26 OC1020304050

26 00'1020304050

27 OC1020304050

28 OC10

34050

29 OC1020304050

30 00'1020304050

31 00'1020304050

32 00'1020304050

33 00'

sin.3746.3773.3800.3827.3854.3881.3907.3934.3901.3987.4014.4041.4067.4094.4120.4147.4173.4200.4226.4253.4279.4305.4331.4358.4384.4410.4436.4462.4488.4514.4540.4566.4592.4617.4643.4669.4095.4720.4746.4772.4797.4823.4848.4874.4899.4924.4950.4975

.5000

.5025

.5050

.5075

.5100

.5125

.5150

.5175

.5200

.5225

.5250

.5275

.5299

.5324

.5348

.5373

.5398

.5422

.5446

COS

cos

.9272

.9261

.9250

.9239

.9228

.9216

.9205

.9194

.9182

.9171

.9159

.9147

.9135

.9124

.9112

.9100

.9088

.9075

".9063.9051.9038.9026.9013.9001.8988.8975.8962.8949.8936.8923.8910.8897.8884.8870.8857.8843.8829.8816.8802.8788.8774.8760'.8746.8732.8718.8704.8689.8675

.8660

.8646

.8631

.8616

.8601

.8587

.8572

.8557

.8542

.8526

.8511

.8496

:8480.8465.8450.8434.8418.8403

.8387

sin

tg!.4040.4074.4108.4142.4176.4210.4245.4279.4314.4348.4383.4417.4452.4487.4522.4557.4592.4628

.4063

.4699

.4734

.4770

.4806

.4841

.4877

.4913

.4950

.4986

.5022

.5059

.5095

.5132

.5169

.5206

.5243

.5280

.5317

.5354

.5392

.5430

.5467

.5505

.5543

.5581

.5619

.5658

.5696

.5735

.5774

.5812

.5851

.5890

.5930

.5969

.6009

.6048

.6088

.6128

.6168

.6208

.6249

.6289

.6330

.6371

.6412

.6453

.6494

ctg2.4752.4552.4342.4142.3942.3752.3562.3372.31823Q02.2822.2642.2462.2292.2112.1942.1772.161

2.1452.1282.1122.0972.0812.0662.0502.0352.0202.0061.9911.9771.9631.9491.9351.9211.9071.8941.8811.8681.8551.8421.8291.8161.8041.7921.7801.7671.7561.744

1.7321.7201.7091.6981.6861.675

1.6641.6531.6431.6321.6211.611

1.6001.5901.5801.5701.5601.550

1.540

tg

68 00'5010302010

67 00'5040302010

66 00'5040302010

66 OC5040302010

64 00'5040302010

63 00'5040302010

62 OC5040302010

61 OC5040302010

60 OC5040302010

69 00'5040302010.

68 00'5040302010

67 00'

33 00'1020304050

34 00'1020304050

36 00'1020304050

36 00*1020304050

37 W1020304050

38 0C1020304050

39 00'1020304050

40 00'1020304050

41 00'1020304050

42 00'1020304050

43 00"1020304050

44 00'1020304050

46 00"

sin.5446.5471.5495.5519.5544.5568.5592.5616.5640.5064.5088.5712.5736.5760.5783.5807.5831.5854.5878.5901.5925.5948.5972.5995.6018.6041.6065.6088.6111.6134.6157.6180.6202.6225.6248.6271.6293.6316.6338.6361.6383.6406.6428.6450.6472.6494.6517.6539.6561.6583.6604.6626.6648.6670.6691.6713.6734.6756.6777.6799.6820.6841.6862.6884.6905.6926.6947.6967.6988.7009.7030.7050.7071COS

cos.8387.8371.8355.8339.8323,8307.8290.8274.8258.8241.8225.8208.8192.8175.8158.8141.8124.8107.8090.8073.8056.8039.8021.8004.7986.7969.7951.7934-.7916.7898.7880.7862.7844.7826.7808.7790.7771.7753.7735.7716.7698.7679.7660.7642.7623.7604.7585.7566.7547.7528.7509.7490.7470.7451.7431.7412.7392.7373.7353.7333.7314.7294.7274.7254.7234.7214.7193.7173.7153.7133.7112.7092.7071

sin

.6494

.6536

.6577

.6619

.6661

.6703

.6745

.6787

.6830

.6873

.6916

.6959

.7002

.7046

.7089

.7133

.7177

.7221

.7265

.7310

.7355

.7400

.7445

.7490

.7536

.7581

.7627

.7673

.7720

.7766

.7813

.7860

.7907

.7954

.8002

.8050

.8098

.8146

.8195

.8243

.8292

.8342

.8391

.8441

.8491

.8541

.8591

.8642

.8U3

.8744

.8706

.8847

.8899

.8952

.9004

.90579U0.9163.9217.9271.9325.9380.9435. 9490.9545.9601.9657.9713.9770.9827.9884.9942

1.0000

MATEMATK TABLOLARI

lzelge.10- Hiperbolik Fonksiyonlar

zleyen izelgeler, (x) in 0.00 dan 3.00 deerine kadar 0.01 lik aralklarla e1, e"\ shx, chx ve tgh x deerleriniverirler.

(x) in (3) den byk deerleri iin (ex)

e* = loge1 (x logo e) = log,' 0.43429 x

bantsndan hesaplanabilir. e"x sfra yaklarken sh x ve eh x yaklak olarak bire eit olurlar.Daha duyarl bir hesap yapmak istenirse aadaki bantlardan yararlanlabilir :

1 = 0,36787e = 2.71828

M = log e = 0.43429

e* = log1 Mx

sh x

chx =

sech x =

21

eh x

-- = loge 10 = 2.30258M

e " = log1 (-Mx)

tgh x = > * ce"+e*

ctgh x tgh x

I8

1a

3

2

1

n

Tl' "TU '

i |t ' 11

1

V1\\\ I I L

wI

1

1

I

|

:\y\ V ' \ \ Cos\ V >

\ \

\ s /

|

M

jif

NIIr

~7|///

/:/ i~ t/f

i i

/ /' /

/ /'/ / i

/ / i xT/

S' /

1

irih *( ' i

/ i l i

I v ^y \ ^ * ~

r '

|

I

h

h

X

y

Sech. ; 1 ! '

1

T1

' 1

1

1|

iI

' I 1 11

' i : 1

i

i 1

1 i 1

t i 1 ' ',1 ' ]

i !

1 . ' . 1

h !

X

i |

l i

t

1

iI

1

1 ! \

1 :

t

! I

I

1

|

1

i , ' T '

i 1 : ,

i > i ' ! :

; L 1! 1 !

: ; :

J :- -

!; ; j

~ ' i_1

2 3 4Hiperbolik Radyanlar (x)

Hiperbolik Fonksiyonlarn Grafii

1-21

MATEMATK TABLOLARI

izelge. 10- Hiperbolik Fonksiyonlar (Devam)

X

0.00

0.010.020.030.040.050.060.070.080.09

0.10

0.110.120.130.140.150.16

0.170.180.19

o.ao

0.210.220.230.240.250.260.270.280.29

0.300.310.320.33

0.340.350.36

0.370.380.390.43

0.410.420.43

0.440.450.46

0.470.480.490.500.510.520.53

0.540.550.56

0.570.580.59

0.C0

Doal Deerleri

.oooo1.01011.02021.03051.04081.05131.0618

1.07251.08331.0942

1.1082

i.11631.12751.1388

1.15031.16181.1735

1.18531.1972i. 20921.2S141.23371.2461

^1.25861.27121.20401.2969

1.31001.32311.3364

1.34991.36341.37711.3910

1.40491.41911.43331.44771.46231.4770

1.4918

1.50681.52201.5373

1.55271.56331.5841

1.60001.61611.6323

1.64871.66531.63201.6989

1.71601.73331.75071.76831.78601.8040

1.8221

e'"

.oooo

.99005

.90020

.97045

.96079

.95123

.94176

.93239

.92312

.91393

.90484

.89583

.88692

.87810

.86936

.86071

.85214

.84366

.83527

.82696

.81873

.81058

.80252

.79453

.78663

.77800

.77105

.76338

.75578

.74826

.74082

.73345

.72615

.71892

.71177

.70469

.69768

. 69073

.68386

.67706

.7032

.66365

.65705

.65051

.64404

.63763

.63128

.62500

.61878

.61263

.60653

.60050

.59452

.58860

.58275

.57695

.57121

.56553

.55990

.55433

.64881

Sinhz

0.00000.01000.02300.03000.04000.05000.0600

0.07010.08010.0901

0.1002

0.11020.12030.1304

0.14050.15060.16070.17080.16100.19110.2013

0.21150.22180.2320

0.24230.25260.26290.27330.20370.29410.30450.31500.32550.3360

0.34660.35720.3678

0.37850.38920.4000

0.4108

0.42160.43250.4434

0.45430.46530.4/640.48750.49860.5098

0.5211

0.53240.54380.5552

0.56660.57820.58970.60140.61310.6248

0.6367

Cosh*

1.0000

.oooI.0J021.00051.00081.00131.0018

1.00251.00321.0041

1.0050

1.00611.00721.00851.00981.01131.0128

1.01451.01621.0181

1.02011.02211.02431.0266

1.02891.03141.03401.03671.03951.0423

1.04631.04841.05161.0549

1.05841.06191.0655

1.06921.07311.0770

1.0811

1.08521.00951.09391.09841.10301.1077

1.11251.11741.1225

1.12761.13291.13331.14381.14941.15511.1609

1.1669, 1.1730

1.1792

1.1855

Tanhi

.00000.01000.02000.02999.03998.04996.05993

.06989

.07983

.08976

.09967

.10956

.11943

.12927

.13909

.14889

.15865

.16838

.17008

.18775

.19738

.20697

.21652

.22603

.23550

.24492

.25430

.26362

.27291

.28213

.29131

.30044

.30951

.31852

.32748

.33638

.34521

.35399

.36271

.37136

.37995

.38847

.39693

.40532

.41364

.42190

.43008

.43820

.44624

.45422

.46212

.46995

.47770

.48538

.49299

.50052

.50798

.51536

.52267

.52990

.53705

C^uumofl Logaiithnu

0.00000.00434.00869.01303

.01737

.02171

.02606

.03040

.03474

.03909

0.04343

.04777

.05212

.05646

.06080

.06514

. 06949

.07383

.07817

.082520.08686

.09120

.09554

.09989

.10423

.10357

.11292

.11726

.12160

.12593

0.13029

.13463

.13897

.14332

.14766

.15200

.15635

.16069

.16503

.16937

0.17372

.17806

.18240

. 18675

.19109

.19543

.19978

.20412

.23346

.21280

0.21715.22149.22533.23018

.23452

.23386

.24320

.24755

.25189

.25623

0.26058

Sulh z

S.00001.30106.4/719.60218.69915.77841

.84545

.90355

.95483

I.00072

.04227

. 08022

.11517

.14755

.17772

.20597

.23254

.25762

.28136

1.30392.32541.34592.36555

.38437

.40245

.41986

.43663

.45282

.46847

1.48362

.49830

.51254

.52637

.53981

.55290

.56564

.57807

.59019

.60202

1.61358

.62488

.63594

.64677

.65738

.66777

.67797

.68797

.69779

.70744

1.71692.72624.73540.74442

.75330

.76204

.77065

.77914

.78751

.795/61.80390

Coshl

0.00000.00002.00009. 00020.00035.00054.00078.00106.00139.00176

0.00217

.00262

.00312

.00366

.00424

.00487

.00554

.00625

.00700

.00779

0.0O863.00951.01043.01139

.01239

.01343

.01452

.01564

.01681

.01801

0.01926.02054.02107.02323

.02463

. 02607

. 02755

.02907

.03063

.03222

0.03385

.03552

.03723

.03897

.04075

.04256

.04441

.04630

.04822

.05018

0.05217.05419.05625.05834.06046.06262.06481

.06703

.06929

.07157

0.07389

T a n h i

3.99999i.30097

.47699

.60183

.69861

.77763

.84439

.90216

.95307

2.99856

.03965.07710.11151

.14330

.17285

.20044

.22629

.25062

.27357

1.29529

.31590

.33549

.35416

.37198

.38902

.40534

.42099

.43601

.45046

I.4643S.47775.49067.50314

.51518

.52682

.53809

.54899

.55956

.56980

1.57973

.58936

.59871

.60780

.61663

.62521

.63355

.64167

.64957

.65726

1.66475.67205.67916.68608.69284.69942.70584.71211.71822.72419

. 73001

1-22

MATEMATK TABLOLARI

izelge.10- Hiperbolik Fonksiyonlar (Devam)

X

0.600.610.620.630.640.650.660.670.680.690.T0

0.710.720.730.740.750.760.770.780.79O.SO0.810.820.830.840.850.860.870.880.89

0.90

0.910.920.93

0.940.950.96

0.970.960.991.00

]

.01

.02

.03

.04

.05

.06

1.07.08.09

L.10

.11

.12

.131.14

.151.16

1.171.181.19

l . M

Doal Deerleri

1.8H1.8404.8589.8776

.8965

.9155

.9348

.9542

.9739

.9937

.oss2.03402.05442.07512.09592.11702.13832.15982.18152.2034 M M2.24792.27052.29332.31642.33962.36322.38692.41092.4351I.1IH2.48432.50932.5345

2.56002.58572.61172.63792.66452.69121.718S2.74562.77322.80112.82922.85772.8864

2.91542.94472.9743

3. 00413.03443.06493.09573.12683.15823.18993.22203.25443.2871s.no

-*

.MM1

.54335

.53794

.53259

.52729

.52205

.51685

.51171

.50662

.50158

.4MW

.49164

.48675

.48191

.47711

.47237

.46767

.46301

.45841

.45384

.44933

.44486

.44043

.43605

.43171

.42741

.42316

.41895

.41478

.41066

.40667

.40252

.39852

.39455

.39063

.38674

.38289

.37908

.37531

.37158

.36788

.36422

.36059

.35701

.35345

.34994

.34646

.34301

.33960

.33622

.33287

.32956,32628.32303

.31982

.31664

.31349

.31037

.30728

.30422

.3011

Sinhio.ucr0.64850.66050.67250.68460.69670.70900.72130.73360.74610.7580.77120.78380.79660.80940.82230.83530.84840.86150.8748

0.8881

0.90150.91500.9286

0.94230.95610.9700

0.98400.99811.0122

1.0M5

1.04091.05541.0700

1.08471.09951.1144

1.12941.14461.1598

1.17(11.19071.20631.2220

1.23791.25391.2700

1.28621.30251.3190

1.3SM1.35241.36931.3863

1.40351.42081.4382

1.45581.47351.4914

1.60M

Coahz1.18H

1

.1919

.1984

.2051

.2119

.2188

.2258

.2330

.2402

.2476

L . K U

.2628

.2706

.2785

.2865

.2947

.3030

.3114

.3199

.3286

1.1374.3464.3555.3647

.3740

.3835

.3932

.4029

.4128

.4229

1.4331

.4434

.4539

.4645

.4753

.4862

.4973

.5085

.5199

.53141.6431

.5549

.5669

.5790

.5913

.6038

.6164

.6292

.6421

.6552

l.MSf.6820.6956.7093

1.72331.73741.7517

1.76621.78081.7957

1.8107

Tuhz.1370

.54413

.55113

.55805

.56490

.57167

.57836

.58498

.59152

.59798

.80437

.61068

.61691

.62307

.62915

.63515

.64108

.64693

.65271

.65841

.88404

.66959

.67507

.68048

.68581

.69107

.69626

.70137

.70642

.71139

.71630

.72113

.72590

.73059

.73522

.73978

.74428

.74870

.75307

.75736

.76169

.76576

.76987

.77391

.77789

.78181

.78566

.78946

.79320

.79688

.80060

.80406

.80757

.81102

.81441

.81775

.82104

.82427

.82745

.83058

.83366

Baya Logaritmalar

0.S606B.26492.26926.27361

.27795

.28229

.28663

.29098

.29532

.299660.30401

.30835

.31269

.31704

.32138

.32572

.33006

.33441

.33875

.34309

0.34744.35178.35612.36046.36481.36915.37349

.37784

.38218

.38652

0.89087.39521.39955.40389.40824.41258.41692

.42127

.42561

.429950.43429

.43864

.44298

.44732

.45167

.45601

.46035

.46470

.46904

.47338

0.47771.48207.48641.49075

.49510

.49944

.50378

.50812

.51247

.51681

0.61116

Sinhi1.80890

.81194

.81987

.82770

.83543

.84308

.85063

.85809

.86548

.872781.88000

.88715

.89423

.90123

.90817

.91504

.92185

.92859

.93527

.94190

I.4846.95498.96144.96784

.97420

.93051

.98677

.99299

.999160.00528

0.01137.01741.02341.02937.03530.04119.04704

.05286

.05864

.064390.07011

.07580

.08146

.08708

.09268

.09825

.10379

.10930

.11479

.12025

0.116C.13111.13649.14186.14720.15253.15783

.16311

.16836

.17360

0.17881

Coahz

0.0738

.07624

.07861

.08102

.08346

.08593

.08843

.09095

.09351

.09609

0.09870.10134.10401.10670

.10942

.11216

.11493

.11773

.12055

.12340

0.11617.12917.13209.13503

.13800

.14099

.14400

.14704

.15009

.15317

0.16617.15939. 16254.16570

.16888

.17238

.17531

.17855

.18181

.185090.18839

.19171

.19504

.19839

.20176

.20515

.20855

.21197

.21541

.21886

O.lttSS.22582.22931.23283

.23636

.23990

.24346

.24703

.25062

.25422

0.16784

Tanhi

1.78001

.73570

.74125

.74667

.75197

.75715

.76220

.76714

.77197

.77669

. 78130.78581.79022.79453

.79875

.80288

.80691

.81086

.81472

.81850

1.81111

.82581

.82935

.83281

.83620

.83952

.84277

.84595

. 84906

.85211

.86609

.85801

.86088

. 86368

. 86642

.86910

.87173

.87431

.87683

.879301.88171

.88409

.88642

.88869

.89092

.89310

.89524

.89733

.89938

.90139

1.80336.90529.90718.90903

.91085

.91262

.91436

.91607

.91774

.9193

1.9109*

1-23

1-24

MATEMATK TABLOLARI

izclgc.10- Hiperbolik Fonksiyonlar (Devam)

.o.21.22.23

:li.26.27.28.29

.30

.31

.32

.33

.34

.35

.36

.37

.38

.39

.40

.41

.42

.43

.44

.45

.46

.47

.48

.49

1.50.51.52.53.54.55.56.57.58.59

t. 60

.61

.62

.63

.64

.65

.661.67

.681.69L.TO

1.71.72

1.73.74.75

1.761.77

':3.

Doal Deerleri

3.32013.35353.38723.42123.45563.49033.5254

3.56093.59663.6328

S.6933.70623.74343.7810

3.81903.85743.89623.93543.97494.0149

1.05824.09604.13714.1787

4.22074.26314.30604.3492.4.39294.4371

4.48174.52674.57224.61824.66464.71154.7588

4.80664.85504.9037

4.9530

5.00285.05315.1039

5.15525.20705.2593

5.31225.36565.4195

5.4739

5.52905.58455.6407

5.69735.75465.8124

5.87095.92995.9895

e.ous

.-*

.30119

.29820

.29523

.29229

.28938

.28650

.28365

.28083

.27804

.27527

.27353

.26982

.26714

.26448

.26185

.25924

.25666

.25411

.25158

.24908

.24660

.24414

.24171

.23931

.23693

.23457

.23224

.22993

.22764

.22537

.22313

.22091

.21871

.21654

.21438

.21225

.21014

.20805

.20598

.20393

.20190

.19989

.19790

.19593

.19398

.19205

.19014

.18825

.18637

.18452

.18268

.18087

.17907

.17728

.17552

.17377

.17204

.17033

.16864

.16696

.16(30

Sinh x

1.5095

1

1

.5276

.5460

.5645

.5831

.6019

.6209

.6400

.6593

.6788

L.69S4.7182.7381.7583

.7786

.7991

.8198

.8406

.8617

.8829

L.9043.9259.9477.9697

1.99192.01432.03692.05972.08272.1059

2.12932.15292.17682.2008

2.22512. 24962.2743

2.29932.32452.34992.3756

2.40152.42762.4540

2.48062.50752.5346

2.56202.58962.6175

2.6456

2.67402.70272.7317

2.76092.79042.8202

2.85032.88062.9112

2.M22

Coahi

1.810T

.8258

.8412

.8568

.8725

.8884

.9045

.9208

.9373

.9540

1.9709

1.98802.00532.02282.04042.05832.0764

2.09472.11322.1320

2.15092.17002.18942.2090

2.22882.24882.26912.28962.31032.3312

2.3524

2.37382.39552.4174

2.43952.46192.4845

2.50732.53052.5538

2.6776

2.60132.62552.6499

2.67462.69952.7247

2.75022.77602.8020

2.8283

2.85492.88182.90902.93642.96422.9922

3.02063.04923.0782

3.1075

Tanbi

.83365

.83668

.83965

.84258

.84546

. 84828

.85106

.85380.85648.85913

.86172

.86428.86678.86925

.87167

.87405

.87639

.87869

.88095

.88317

.88636

.88749

.88960

.89167

.89370

.89569

.89765

.89958

.90147

.90332

.90515

.90694

.90870

.91042

.91212

.91379

.91542

.91703

.91860

.92015

.92167

.92316

.92462

.92606

.92747

.92886

.93022

.93155

.93286

.93415

.93541

.93665

.93786

.93906

.94023

.94138

.94250

.94361

.94470

.94576

.94681

Baya Logaritmalart*

0.52115

.52550

.52984

.53418

.53853

.54287

.54721

.55155

.55590

. 56024

0.56468

.56893

.57327

.57761

.58195

.58630

.59064

.59498

.59933

.60367

0.60801.61236.61670.62104

.62538

.62973

.63407

.63841

.64276

.64710

0.65144

.65578

.66013

. 66447

.66881

.67316

. 67750

.68184

.68619

.69053

0.69487.69921.70356.70790

.71224

.71659

.72093

.72527

.72961.73396

0.73830

.74264

.74699

.75I3

.75567

.76002

.76436

.76870

.77304

.77739

0.78173

Sinhi

0.17882.18402.18920.19437

.19951

.20464

.20975

.21485

.21993

.22499

0.23004

.23507

.24009

.24509

.25008

.25505

.26002

.26496

.26990

.27482

0.27974.28464.28952. 29440

. 29926

.30412

.30896

.3137

.31862

.32343

0.32823.33303.33781.34258

.34735

.35211

.35686

.36160

.36633

.37105

0.37577.38048.38518.38987

.39456

.39923

.40391

.40857

.41323

.41788

0.42253

.42717

.43180

.43643

.44105

.44567

.45028

.45488

.45948

.46408

0.46867

C o s h i

0.25784.26146.26510.26876

.27242

.27610

.27979

.28349

.28721

.29093

0.29467

.29842

.30217

.30594

.30972

.31352

.31732

.32113

.32495

.32878

0.33262.33647.34033.34420

.34807

.35196

.35585

.35976

.36367

.36759

0.37151.37545.37939.38334

.38730

.39126

.39524

.39921

.40320

.40719

0.41119

.41520

.41921

.42323

.42725

.43129

.43532

.43937

.44341

.44747

0.45153.45559.45966.46374

.46782

.47191

.47600

.48009

.48419

.48830

0.49241

Tanh z

1.92099

.92256

.92410

.92561

.92709

.92854

.92996

.93135

.93272

.93406

1.93637

.93665

.93791

.93914

.94035

.94154

.94270.94384.94495.94604

.94713

.94817

.94919

. 95020

.95119

.95216

.95311

.95404

.95495

.95584

. 6673.95758.95842.95924

.96005

.96084

.96162

.96238

.96313

.96386

1.96457

.96528

.96597

.96664

.96730

.96795

.96858

.96921

.96982

.97042

1.97100.97158.97214.97269.97323.97376.97428

.97479

.97529

.97578

I.9761

MATEMATK TABLOLARI

izclge.10- Hiperbolik Fonksiyonlar (Devam)

X

1.80

.81

.82

.83

.84

.85

.86

.87

.88

.89L.90

.91

.921.931.941.951.96

1.971.981.99

S.002.012.022.032.042.052.06

2.072.082.09

S. 102.112.122.13

2.142.152.16

2.172.182.19

2.202.212.222.23

2.242.252.26

2.272.282.29

S.302.312.322.332.342.352.362.372.382.391.40

Doal Deerlerie*

6.M966.11046.17196.2339

6.29656.35986.4237

6.48836.55356.6194

6.6859

6.75316.82106.8895

6.95887.02877.0993

7.17077.24277.31557.3891

7.46337.53837.6141

7.69067.76797.8460

7.92488.00458.0849

8.1662

8.24828.33118.4149

8.49948.58498.67118.75838.84638.93529.02509.11579.20739.2999

9.39339.48779.5831

9.67949.77679.8749

9.9742

10.07410.17610.27810.38110.48610.59110.69710.SOS10.91311.023

.16530

.16365

.16203

.16041

.15882

.15724

.15567

.15412

.15259

.15107

.11957

.14808

.14661

.14515

.14370

.14227

.14086

.13946

.13807

.13670

.1353i

.13399

.13266

.13134

.13003

.12873

.12745

.12619

.12493

.12369

.12216

.12124

.12003

.11684

.11765

.11648

.P533

.11418

.11304

.11192

.11080

.10970

.10861

.10753

.10646

.10540

.10435

.10331

.10228

.10127

.10026

.09926

.09827

.09730

.09633

.09537

.09442

.09348

.09255

.09163

.oton

Sinh x2.9122

2.97343.00493.0367

3.06893.10133.1340

3.16713.20053.2341

3.2682

3.30253.33723.3722

3.40753.44323.4792

3.51563.55233.5894

3.6269

3.66473.70283.7414

3.78033.81963.8593

3.89933.93983.9806

4.0219

4.06354.10564.1480

4.19094.23424.2779

4.32214.36664.41164.4571

4.50304.54944.59624.64344.69124.7394

4.78804.83724.8868

4.9370

4.98765.03875.09035.14255.19515.24835.30205.35625.41096.4662

Coshi

3.1075

3.13713.16693.1972

3.22773.25853.2897

3.32123.35303.38523.4177

3.45063.48383.5173

3.55123.58553.6201

3.65513.69043.7261

3.7622

3.79873.83553.87273.91033.94833.9867

4.02554.06474.1043

4.1413

4.18474.22564.2669

4.30854.35074.3932

4.43624.47974.52364.66794.61274.65804.70374.74994.79664.8437

4.89144.93954.9881

S. 03725.08685.13705.18765.23885.29055.34275.39545.44875.5026S.55C

Tanhi [.91681

.94783

.94884

.94983

.95080

.95175

.95268

.95359

.95449

.95537

.95624

.95709

.95792

.95873

.95953

.96032

.96109

.96185

.96259

.96331

.96403

.96473

.96541

.96609

.96675

.96740

.96803

.96865

.96926

.96986

.97045

.97103

.97159

.97215

.97269

.97323

.97375

.97426

.97477

.97526

.97574

.97622

.97668

.97714

.97759

.97803

.97846

.97888

.97929

.97970

.98010

.98049

.98087

.98124

.98161

.98197

.98233

.98267

.98301

.98335

.8387

Baya Logaritmalare 1

0.78173

.78607

.79042

.79476

.79910

.80344

.80779

.81213

.81647

.82082

0.82516

.82950

.83385

.83819

.84253

.84687

.85122

.85556

.85990

.86425

0.86859

.87293

.87727

.88162

.88596

.89030

.89465

.89899

.90333

.90768

0.91202

.91636

.92070

.92505

.92939

.93373

.93808

.94242

.94676

.951100.96646

.95979

.96413

.96848

.97282

.97716

.98151

.99585

.99019

.994530.99888

1.00322.00756.01191.01625.02059.02493

.02928

.03362

.03796

1.04231

Snhi0.46867

.47325

.47783

.48241

.48698

.49154

.49610

.50066

.50521

.509760.51430

.51884

.52338

.52791

.53244

.53696

.54148

.54600

.55051

.55502

0.65963

.56403

.56853

.57303

.57753

.58202

.58650

. 59099

.59547

.59995

0.60443

.60890

.61337

.61784

.62231

.62677

.63123

.63569

.64015

.644600.64906

.65350

.65795

.66240

. 66684

.67128

.67572

.68016

.68459

.689030.6*346

.69789

.70232

.70675

.71117

.71559

.72002

.72444

.72885

.73327

0.7*769

Coshi0.49241

.49652

.50064

.50476

.50889

.51302

.51716

.52130

.52544

.52959

0.53374

.53789

.54205

.54621

.55038

.55455

.55872

. 56290

.56707

.57126

0.67511

.57963

.58382

.58802

.59221

.59641

.60061

.60482

.60903

.61324

0.61745

.62167

.62589

.63011

.63433

.63856

.64278

.64701

.65125

.65548

0.65972.66396.66820.67244

. 67668

. 68093

.68518

.68943

.69368

. 69794

0.7O219.70645.71071.71497.71923.72349.72776

.73203

.73630

.74056

0.74181

Tanhi

.97626

.97673

.97719

.97764

.97809

.97852

.97895

.97936

.97977

.98017

I.98067

.98095

.98133

.98170

.98206

.98242

.98272

.98311

.98344

.98377

.98409

.98440

.98471

.98502

.98531

.98560

.98589

.98617

.98644

.98671

.98697.98723.98748.98773

.98798

.98021

.98845

.98868

.98890

.98912I.98934

.98955

.98975

.98996

.99016

.99035

.99054

.99073

.99091

.99109

I.99127.99144.99161.9917.99194.99210.99226

.99241

.99256

.99271

.9MS

1-25

MATEMATK TABLOLARI

izelge.10- Hiperbolik Fonksiyonlar (Devam)

1-26

X

1.402.412.422.432.442.452.46

2.472.482.49

1.502.512.522.53

2.542.552.562.572.582.59

1.602.612.622.63

2.642.652.66

2.672.682.69

1.702.712.722.73

2.742.752.762.772.782.79

1.802.812.822.83

2.842.852.862.872.882.89

2.902.912.922.93

2.942.952.96

2.972.982.99

.00

11.02311.13411.24611.359

11.473II.58811.705

11.82211.94112.061

12.18212.30512.42912.554

12.6802.80712.93613.06613.19713.33013.46413.59913.73613.874

14.01314.15414.296

14.44014.58514.732

14.88015.02915.18015.333

15.48715.64315.80015.95916.11916.281

16.44816.61016.77716.94517.11617.28817.462

17.63717.81417.993

18.17418.35718.54118.728

18.91619.10619.298

19.49219.68819.886

o:os(

Doal Deerleri-*

.09072

.08982

.08892

.08804

.08716

.08629

.08543

.08458

.08374

.08291

.08208

.08127

.08046

.07966

.07887

.07808

.07730

.07654

.07577

.07502

.07427

.07353

.07280

.07208

.07136

.07065

.06995

.06925

.06856

.06788

.06721

.06654

.06587

.06522

.06457

.06393

.06329

.06266

.06204

.06142

.06081

.06020

.05961

.05901

.05843

.05784

.05727

.05670

.05613

.05558

.0M02

.05448

.05393

.05340

.05287

.05234

.05182

.05130

.05079

.05029

.0497*

Sinhi

t.46625.52215.57855.6354

5.69295.75105.8097

5.86895.92885.9892

6.05026.11186.17416.2369

6.30046.36456.4293

6.49466.56076.6274

8.69476.76286.83156.9008

6.97097.04177.1132

7.18547.25837.3319

7.4063

7.48147.55727.633S

7.71127.78947.8683

7.94808.02858.1098

8.19198.27498.35868.4432

8.52878.61508.7021

8.79028.87918.9689

9.01969.15129.24379.3371

9.43159.52689.6231

9.72039.81859.9177

10.018

Coahz

S. 65695.61195.66745.72355.78015.83735.89515.95356.01256.0721

6.13236.19316.25456.3166

6.37936.44266.50666.57126.63656.7024

6.76906.83636.90436.9729

7.04237.11237.1831

7.25467.32687.3998

7.4735

7.54797.62317.6991

7.77587.85337.93168.01068.09058.1712

8.2S278.33518.41828.5022

8.58718.67288.7594

8.84698.93529.0244

9.11469.20569.29769.39059.48449.57919.67499.77169.86939.9680

10.068

jTanhz

.98367

.98400

.98431

.98462

.98492

.98522

.98551

.98579

. 98607

.98635

.98661

.98688

.98714

.98739

.98764

.98788

.98812

.98835

.98858

.98881

.98903

.98924

.98946

.98966

.98987

.99007

.99026

.99045

.99064

.99083

.99101

.99118

.99136

.99153

.99170

.99186

.99202

.99218

.99233

.99248

.99263

.99278

.99292

.99306

.99320

.99333

.99346

.99359

.99372

.99384

.99396

.99408

.99420

.99431

.99443

.99454

.99464

.99475

.99485

.99496

.99506

Baya Logaritmalare*

1.04231.04665.05099.05534.05968.06402.06836.07271.07705.08139

1.C8574.09008.09442.09877

.10311

.10745

.11179

.11614

.12048

.12482

1.13917.13351.13785.14219

.14654

.15088

.15522

.15957

.16391

.16825

1.17260.17694.18128.18562

.18997

.19431

.19865

.20300

.20734

.21168

1.21601.22037.22471.22905

.23340

.23774

.24208

.24643

.25077

.25511

1.25945

.26380

.26814

.27248

.27683

.28117

.28551

.28985

.29420

.29854

1.30288

Siohz

0.73769.74210.74652.75093.75534.75975.76415

.76856

.77296

.77737

0.78177.78617.79057.79497

.79937