[Www.vietMATHS.com] Huong Dan Su Dung Latex Dao Ngoc Minh

HNG DN S DNG LATEX

o Ngc Minh

Khoa Ton - Tin, HSP H Ni

Ngy 17 thng 11 nm 2008

o Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 1 / 18

Mc Lc

1 Gii thiu

2 Son tho vn bn LATEXCu trc tp ngun LATEXMi trngTiu chy v mc lcTrch dn ti liu tham kho

3 Son tho cc cng thc ton hcMi trng ton v cc cu trc c sMi trng nh lMi trng chng minhTn hmGing cng thc ton

4 a hnh vo ti liu

Gii thiu

Hi ton hc Hoa K pht trin TEX thnh AMSTEX, do MichaelSpivak xy dng, thc cht l mt h cc macro vit b sung cho TEXnhm s dng TEX d dng hn.

LaTeX l mt gi cc tp lnh dng cng c nh dng ca TeX lm htnhn c bn phc v cho vic nh dng ti liu. N c s dng rngri trong cc trng i hc v cc nh xut bn bi nhng u im sau:

Gii thiu

Hi ton hc Hoa K pht trin TEX thnh AMSTEX, do MichaelSpivak xy dng, thc cht l mt h cc macro vit b sung cho TEXnhm s dng TEX d dng hn.LaTeX l mt gi cc tp lnh dng cng c nh dng ca TeX lm htnhn c bn phc v cho vic nh dng ti liu. N c s dng rngri trong cc trng i hc v cc nh xut bn bi nhng u im sau:

Gii thiu

u im

1 LATEX h tr ti a vic son tho cc cng thc ton hc v khoahc k thut.

2 Cc chng, mc, nh ngha, nh l, biu thc, bng, hnh nh,. . .c nh s t ng v tham chiu d dng.

3 C cc gi lnh h tr cho vic trnh chiu v trn trc nghim.

4 Tp ngun c bin dch to ra cc tp khc nhau nh .dvi(Device Independent), .pdf (Adobe Portable Document Format) hay.ps (PostScript).

5 TEX l cng c min ph v c th chy trn hu ht cc h thngphn cng v h iu hnh khc nhau.

Gii thiu

Cc chng trnh son tho v bin dch

C nhiu chng trnh son tho v bin dch TEX, trong PCTeX lmt phn mm tch hp c chng trnh bin dch TEX, LATEX, AMSTEXv h son tho theo cc phng TrueType.

MiKTeX l chng trnh bin dch TEX v LATEX m ngun m gm nhiugi lnh v macro cho php bin dch tp ngun ra cc nh dng DVI, PSv PDF mt cch d dng.MiKTeX cn i km vi mt trong cc h son tho nh WinShell,WinEdt, EmEditor, TeXnicCenter, TeXMaker, LaTeXEditor, TeXShell,VieTeX,. . .

Gii thiu

C nhiu chng trnh son tho v bin dch TEX, trong PCTeX lmt phn mm tch hp c chng trnh bin dch TEX, LATEX, AMSTEXv h son tho theo cc phng TrueType.MiKTeX l chng trnh bin dch TEX v LATEX m ngun m gm nhiugi lnh v macro cho php bin dch tp ngun ra cc nh dng DVI, PSv PDF mt cch d dng.

MiKTeX cn i km vi mt trong cc h son tho nh WinShell,WinEdt, EmEditor, TeXnicCenter, TeXMaker, LaTeXEditor, TeXShell,VieTeX,. . .

Gii thiu

C nhiu chng trnh son tho v bin dch TEX, trong PCTeX lmt phn mm tch hp c chng trnh bin dch TEX, LATEX, AMSTEXv h son tho theo cc phng TrueType.MiKTeX l chng trnh bin dch TEX v LATEX m ngun m gm nhiugi lnh v macro cho php bin dch tp ngun ra cc nh dng DVI, PSv PDF mt cch d dng.MiKTeX cn i km vi mt trong cc h son tho nh WinShell,WinEdt, EmEditor, TeXnicCenter, TeXMaker, LaTeXEditor, TeXShell,VieTeX,. . .

Gii thiu

V d

\documentclass[12pt,a4paper]{article} % Khai bo lp vn bn% Trn mi dng, ni dung sau k hiu "%" khng c bin dch\usepackage[utf8]{vietnam} % Gi lnh phng ting Vit\usepackage{amsmath,amsthm,amssymb}% Cc gi lnh v mi trng v k hiu\usepackage[top=2cm, bottom=2cm, left=2.5cm, right=2cm]{geometry}% Cn l

\begin{document} % Bt u thn vn bn\pagestyle{empty} % Kiu trang\noindent % Khng tht u dngNi dung vn bn.\end{document} % Kt thc vn bn

Gii thiu

V d

\documentclass[12pt,a4paper]{article} % Khai bo lp vn bn% Trn mi dng, ni dung sau k hiu "%" khng c bin dch\usepackage[utf8]{vietnam} % Gi lnh phng ting Vit\usepackage{amsmath,amsthm,amssymb}% Cc gi lnh v mi trng v k hiu\usepackage[top=2cm, bottom=2cm, left=2.5cm, right=2cm]{geometry}% Cn l

\begin{document} % Bt u thn vn bn\pagestyle{empty} % Kiu trang\noindent % Khng tht u dngNi dung vn bn.\end{document} % Kt thc vn bn

Son tho vn bn LATEX Cu trc tp ngun LATEX

Cc lp ti liu

\documentclass[ty chn]{lpvnbn}

1 C cc lp: article, book, report, beamer,. . .

2 C cc ty chn: 11pt (c font, mc nh 10pt), twoside ( hoconeside), landscape, leqno, . . .

3 V d nh:

\documentclass[12pt, onside]{book}

Cc lp ti liu

3 V d nh:

Cc lp ti liu

3 V d nh:

Cc lp ti liu

3 V d nh:

Cc lp ti liu

3 V d nh:

Cc gi

\usepackage[ty chn]{tn gi}

1 Gi ting Vit vietnam vi ty chn utf8 hoc tcvn

2 Cc gi k hiu ton hc amsmath, amssymb, . . .

3 Gi cn l geometry vi ty chn top=3cm, bottom=?, left=?,right=?

4 Gi to lin kt hyperref vi ty chn unicode

5 Gi a hnh vo graphicx v picinpar

6 Gi to mi trng lit k enumerate

7 Gi to header fancyhdr, to bng longtable. . .

Cc gi

K hiu c bit v du ngoc

K hiu c bit

1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~

2 Trong cc k t # $ % & _ { } phi nh bng cclnh \# \$ \% \& \_ \{ \}

3 Cn cc k t \ ^ ~ phi nh bng cc lnh \char92 \char94\char126

Du ngoc

1 Vi ngoc [ v ) c nh thng thng, iu chnh c ca ngocbng cc lnh \big, \bigg, \Big,. . .

2 Mun t ng iu chnh chiu cao ca cc ngoc theo chiu caocng thc ta dng lnh \left[ v \right] (chng hn l dngngoc vung).

K hiu c bit

1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~

Du ngoc

K hiu c bit

1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~

Du ngoc

K hiu c bit

1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~

Du ngoc

K hiu c bit

1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~

Du ngoc

K hiu c bit

1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~

Du ngoc

K hiu c bit

1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~

Du ngoc

Xung dng, ngt trang, Khong trng

Xung dng, ngt trang

1 Cc lnh xung dng: \\, \par, \newline. Mun xung dng v tothnh on mi th g Enter v trng mt dng.

2 Xung dng v mun tht u dng dng \indent v ngc lidng lnh \noindent

3 Sang trang mi dng lnh \newpage

Khong trng

1 Khong trng n gin: \, hoc \. hoc \quad hoc \qquad,. . .

2 Khong trng ngang \hspace{2cm} hoc \phantom{123456} cchmt khong ng bng rng ca ch trong {}

3 Khong trng dc \vspace{2cm}

Xung dng, ngt trang

Khong trng

Xung dng, ngt trang

Khong trng

Xung dng, ngt trang

Khong trng

Xung dng, ngt trang

Khong trng

Xung dng, ngt trang

Khong trng

Xung dng, ngt trang

Khong trng

Xung dng, ngt trang

Khong trng

Thay i kiu ch v c ch

1 Ch m {\bf vn bn} vn bn, ch in nghing {\it vn bn}vn bn

2 Thay i c ch ton vn bn. Np thm gi extsizes v thay tychn c font trn bng c fonts mi.

3 Thay i c ch cc bNgoi vic dng cc lnh \large,\small,\tiny,\scriptsize,. . .bn c th dng lnh sau

{\fontsize{17pt}{12pt}\selectfont y l font ch 17}

y l font ch 174 Cch s dng font cc b {\usefont{T5}{put}{b}{n} Vn bn}Vn bn

y l font ch 17

4 Cch s dng font cc b {\usefont{T5}{put}{b}{n} Vn bn}Vn bn

y l font ch 174 Cch s dng font cc b {\usefont{T5}{put}{b}{n} Vn bn}

Vn bn

Son tho vn bn LATEX Mi trng

Cn chnh on vn

CCH DNG MI TRNG

\begin{tn mi trng}[ty chn nu c]Ni dung\end{tn mi trng}

1 Dng mi trng center cn gia, mi trng flushleft cn tri,mi trng flushright cn phi

2 Cc mi trng lit k l itemize, enumerate, description.

\begin{tn mi trng}[ty chn nu c]\item Ni dung th nht\item Ni dung th hai\end{tn mi trng}

Cn chnh on vn

CCH DNG MI TRNG

Cn chnh on vn

CCH DNG MI TRNG

Cn chnh on vn

CCH DNG MI TRNG

Cn chnh on vn

CCH DNG MI TRNG

Gi enumerate v mi trng enumerate

Mi trng enumerate nu dng thm gi enumerate c ty chn l cchnh s [1.] hoc [a,]. . . .

Cho PT $x^2-2(m-1)x+1=0$.\begin{enumerate}[a)]\item Gii PT vi $m=3$.\item Tm $m$ PT c nghim.\end{enumerate}

Cho PT x2 2(m 1)x + 1 = 0.

a) Gii PT vi m = 3.

b) Tm m PT c nghim.

Cho PT $x^2-2(m-1)x+1=0$.\begin{enumerate}[\ding{51}]\item Gii PT vi $m=3$.\item Tm $m$ PT c nghim.\end{enumerate}

Cho PT x2 2(m 1)x + 1 = 0.

3 Gii PT vi m = 3.

3 Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

a) Gii PT vi m = 3.

b) Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

3 Gii PT vi m = 3.

3 Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

a) Gii PT vi m = 3.

b) Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

3 Gii PT vi m = 3.

3 Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

a) Gii PT vi m = 3.

b) Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

3 Gii PT vi m = 3.

3 Tm m PT c nghim.

Cc v d khc v mi trng lit k

Nu khng khai bo gi enumerate th s khng dng c ty chn cchnh s [1.] hoc [a,]. . . . Khi LATEX s nh s cc kt qu lit k tng.

Cho PT $x^2-2(m-1)x+1=0$.\begin{enumerate}\item Gii PT vi $m=3$.\item Tm $m$ PT c nghim.\end{enumerate}

Cho PT x2 2(m 1)x + 1 = 0.

1 Gii PT vi m = 3.

2 Tm m PT c nghim.

Cho PT $x^2-2(m-1)x+1=0$.\begin{itemize}\item Gii PT vi $m=3$.\item Tm $m$ PT c nghim.\end{itemize}

Cho PT x2 2(m 1)x + 1 = 0.

Gii PT vi m = 3.

Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

1 Gii PT vi m = 3.

2 Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

Gii PT vi m = 3.

Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

1 Gii PT vi m = 3.

2 Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

Gii PT vi m = 3.

Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

1 Gii PT vi m = 3.

2 Tm m PT c nghim.

Cho PT x2 2(m 1)x + 1 = 0.

Gii PT vi m = 3.

Tm m PT c nghim.

Tabbing

Mi trng tabbing to ra bng m mi ct c cn tri. rng cami ct c xc nh dng u tin. Chng hn, nu t\=\bf Mi trng\hspace{1cm} th rng ca ct ny bng chiurng ca cm t Mi trng cng vi 1 cm nh trong v d sau:

\begin{tabbing}\bf STT\quad \=\bf Mi trng\hspace{1cm} \=\bf Thuc tnh\\1\> tabbing\> Cn tri tt c cc ct\\2\> tabular\> Cn ty cho tng ct\end{tabbing}

STT Mi trng Thuc tnh

1 tabbing Cn tri tt c cc ct2 tabular Cn ty cho tng ct

Nu mun dng u tin ch dng cho vic cn khong cch cc ct mkhng hin ra, ta t lnh \=\kill cui dng.

\begin{tabbing}dd/mm\qquad \=Ivents \=\kill01/01\> My birthday\\

\> New year\\14/02\> Valentines Day\end{tabbing}

01/01 My birthdayNew year

14/02 Valentines Day

Mi trng tabular c nhp theo mu nh sau:

\begin{tabular}[pos]{cols}\hline % ng k (c th c hoc khng)dng 1 (cc ct c ngn bi du &)\\ \hline...\end{tabular}

Cc i s bt buc v ty chn bao gmo Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

\begin{tabular}{|l||p{5.9cm}|}

\hline

pos & Cn v tr ca bng theo chiu dc

i vi dng ngoi bng. Mc nh l gia bng,

{\tt t} l dng u v {\tt b} l dng cui.\\

\hline

cols & nh dng tng ct theo cc k hiu:\\

&\begin{tabular}{r p{3.4cm}}

l & Cn tri.\\

r & Cn phi.\\

c & Cn gia.\\

p\{width\} & Ct c chiu rng {\tt width}

v vn bn c cn trn.\\

@\{text\} & Chn thm {\tt text} vo mi

trong ct. C th chn khong trng bng lnh

\verb+@\hpace{width}+ vi {\tt width} l di.\\

*\{n\}\{cols\} & nh dng lp li cho {\tt n} ct.

V d, *\{3\}\{l\} = l l l

\end{tabular}\\ \hline

\end{tabular}

pos Cn v tr ca bng theo chiu dc i vidng ngoi bng. Mc nh l gia bng, tl dng u v b l dng cui.

cols nh dng tng ct theo cc k hiu:l Cn tri.r Cn phi.c Cn gia.

p{width} Ct c chiu rng widthv vn bn c cn trn.

@{text} Chn thm text vo mi trong ct. C th chnkhong trng bng lnh@\hpace{width} viwidth l di.

*{n}{cols} nh dng lp li cho nct. V d, *{3}{l} = l ll

Mun nh trc rng ca bng ta dng mt mi trng tabular*tng t nh tabular nhng c thm mt i s trc i s nh dngo Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

tng ct. Nu khai bo thm gi lnh array th c th dng cc i sm{width} hoc b{width} cho ct c chiu rng width v vn bn ccn gia hoc di.Cc lnh tc ng ln dng ca bng l

& Du ngn cch cc ct.

\\ Kt thc dng.\hline ng k ngang.

\cline{i-j} K ng ngang t ct i ti ct j, c t sau \\.\vline ng k dc "" trn mt dng ca ct.

\multicolumn{n}{cols}{text} Kt hp n ct trong dng v in vo text c cn bicols l l, r hay c.

Ta cng c th gn nhn cho mi bng nh trong v d sau:

\begin{table}[htbp] % th t u tin: here, top, bottom, separate page\begin{center}\begin{tabular}{|l|r@{-}r@{-}r|l|}\hline\multicolumn{1}{|c|}{Color} &\multicolumn{4}{c|}{Codes}\\ \cline{2-5}&\multicolumn{3}{c|}{RGB} &\multicolumn{1}{c|}{Hex} \\ \hline

Sky Blue &135 &206 &235 &87CEEB \\ \hlineDark Violet &148 &0 &211 &9400D3 \\ \hline\end{tabular}\end{center}\caption{Mt v d tng hp.}\end{table}

Color CodesRGB Hex

Sky Blue 135-206-235 87CEEB

Dark Violet 148- 0-211 9400D3

Bng: Mt v d tng hp.

Nu khai bo thm gi lnh multirow th c th kt hp cc dng trongct nh lnh \multirow{n}{width}{text}. Hy xem v d sauo Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

Son tho vn bn LATEX Tiu chy v mc lc

\begin{tabular}{| l | l |}\hlinePlanet &Features\\ \hline\multirow{3}{*}{Mercury} &Lunar like crust\\&Crustal faulting\\&Small magnetic fiels\\ \hline\multirow{3}{*}{Earth} &Oceans of water\\&Magnetic field\\ \hline\end{tabular}

Planet Features

MercuryLunar like crustCrustal faultingSmall magnetic fiels

EarthOceans of waterMagnetic field

To tiu chy vi gi fancyhdr nh sau:- Khai bo gi fancyhdr: \usepackage{fancyhdr}.- Chn kiu trang (thng sau \begin{document}):\pagestyle{fancy}.- Tiu chy trn v di c to bi cc lnh\fancyhead[options]{headers name} hoc\fancyfoot[options]{footers name} vi cc ty chn l l, r, c (tri,phi, gia) v tiu chy c th trng (\empty) hoc s trang(\thepage), . . .o Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

Son tho vn bn LATEX Tiu chy v mc lc

- Dng k ca tiu chy c th nh ngha li bng nhng lnh nh\renewcommand{\headrulewidth}{0pt} hoc\renewcommand{\footrulewidth}{0.4pt}.LATEX h tr vic chia vn bn thnh cc chng, mc, mc nh,. . . v tng nh s chng theo cc lnh nh sau:\part{partname} % Phn\chapter{chaptername} % Chng\section{secname} % on\subsection{subsecname} % on con\subsubsection{subsubsecname} % on nh\paragraph{parname} % Phn on\subparagraph{secname} % Phn on con

Bng mc lc c to ra bng cch trch ly phn ta ca cc mc vv tr trang ca chng thng qua lnh \tableofcontents. V tr t lnhny ph thuc vo v tr t mc lc trong ti liu cn son tho. Nichung, nhng lnh to ra chng, mc, . . . thng mt trong ba dng:- \section{name}: name l tn mc, c t trn tiu chy va vo bng mc lc (nu s dng cc cu trc ny).

Son tho cc cng thc ton hc Mi trng ton v cc cu trc c s

- \section[shortname]{name}: name l tn mc nhng shortnamec t trn tiu chy v a vo bng mc lc.- \section*{name}: Khng nh s trc tiu v name khng ct trn tiu chy, cng khng c a vo bng mc lc.C th thm mt mc no vo mc lc bng nhng lnh nh\addcontentsline{toc}{section}{{\bf M u }}. Lnh ny sthm mc M u vo trong mc lc v t cng cp vi section. LATEXcung cp mt mi trng nh dng th hin cc ti liu tham kho nhsau:

\begin{thebibliography}{}\bibitem{} ......\end{thebibliography}

di cc k t trong c ly lm khong tht u dngsau dng th nht ca mi \bibitem. Sau mi\bibitem{} l tntc gi, tn sch, bi bo, nh xut bn, nm xut bn, . . .Mt ti liuc tham chiu thng qua lnh \cite{}. LATEX cung cp haidng mi trng ton son tho cc k hiu v cng thc ton hc:o Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

Mi trng ton trn cng dng ang son tho: Ni dung cnhp vo gia du $ v $, hoc $ v $, hoc \begin{math} v\end{math}.

Mi trng ton trn mt dng ring: Ni dung c nhp vo giadu \[ v \], hoc $$ v $$, hoc \begin{displaymath} v\end{displaymath}.

Kch c cho cc k t trong mi trng ton c iu khin nh cc lnh:

\displaystyle C cho cng thc ring dng.\textstyle C cho cng thc cng dng.

\scriptstyle C cho ch s trn v di ln u.

\scriptscriptstyle C cho ch s trn v di ln hai.

Sau y l mt s k hiu v ton t c bn:

a/b a/b amn a_{n}^{m} A \hat{A} ABC \widehat{ABC}ab \frac{a}{b}

a \sqrt{a} A \tilde{A} ABC \widetilde{ABC}

an a^{n} na \sqrt[n]{a} a \bar{a} AB \overline{AB}

an a_{n} f (x) f(x) ~a \vec{a}AB \overrightarrow{AB}

\forall \exists \infty \emptyset \angle 4 \triangle \nabla \partial

Trong gi amssymb c thm k hiu tp rng l ($\varnothing$). Giamsmath cung cp thm phng n th hin phn s bng\tfrac{numerator}{denominator} v\dfrac{numerator}{denominator}. Ch rng nu i s ch c mtk t th ta c th b cc du { v }. Chng hn,

$a_0 +\frac{1}{a_1 +\frac{1}{a_2 +\frac{1}{a_3}}}, \quada_0 +\dfrac{1}{a_1 +\dfrac{1}{a_2 +\dfrac{1}{a_3}}}$

a0 +1

a1+1

a2+1a3

, a0 +

1

a1 +1

a2 +1

a3

Cc ton t nh phn c th hin trong bng sau:o Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

\pm \cdot \ast \cup \mp \circ ? \star \cap \times \bullet / / \vee \div \diamond \ \setminus \wedge

Cc ton t quan h:

\le, \leq \ge, \geq .= \doteq 6= \ne, \not= \ll \gg \equiv \sim \in 3 \ni | \mid ' \simeq \subset \supset \parallel \approx \subseteq \supseteq \perp = \cong

Mun th hin khng c mi quan h, ta dng lnh \not trc k hiu thm du / ln n nh $\not\in, \not\subset$ cho ta 6, 6. Nhngch \not\in v \notin cho kt qu khc nhau. c cc k hiu phnh p ta nn dng gi lnh amssymb.Nhng ton t sau y c kch c khc nhau ty thuc vo chng trongmi trng ton cng dng hay ring dng:o Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

Son tho cc cng thc ton hc Mi trng ton v cc cu trc c s \sum

\bigcup

\bigvee

\bigoplus

\prod

\bigcap

\bigwedge

\bigotimes \coprod

\bigsqcup

\bigodot

\int

\oint

\biguplus

Cc du mi tn:

\leftarrow, \gets \longleftarrow \leftrightarrow \longleftrightarrow \Leftarrow = \Longleftarrow \Leftrightarrow \Longleftrightarrow \rightarrow, \to \longrightarrow 7 \mapsto 7 \longmapsto \Rightarrow = \Longrightarrow \hookleftarrow \hookrightarrow

Bng ch ci Hy Lp:

\alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \vartheta \iota \kappa \lambda \mu \nu \xipi \pi $ \varpi \rho % \varrho \sigma \varsigma \tau \upsilon \phi \varphi \chi \psi \omega \Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega

Trong mi trng ton, nhng k t trng b b qua cn nhng dngtrng th khng c chp nhn. LATEX t thm vo cc khng trng xungquanh cc ton t nh +,,=, . . . Vn bn t trong mi trng tonu thnh ch in nghing v khng c khong trng gia cc t. Munnhng mi trng vn bn vo mi trng ton ta dng\mbox{} hoc vi lnh \text{} ca gi amsmath,vn bn a vo co dn mt cch thch hp.Du ba chm trong mi trng ton c th c nhp trc tip t bno Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

Son tho cc cng thc ton hc Mi trng nh l

phm hoc p hn ta dng \ldots hoc \dots cho du ba chm chn dng (. . . ) v \cdots cho du ba chm gia dng ( ). Cc duba chm dc (

...) v cho (. . .) th c cho bi \vdots v \ddots. Hy

xem v d sau:

Ta c $(1+x)^n = C^0_n+C^1_nx+\cdots+C^n_nx^n= \sum_{k=0}^n C^k_n x^k$ nn$$\int_1^2(1+x)^n dx =\int_1^2(\sum_{k=0}^n C^k_n x^k)dx.$$Do $\dfrac{3^{n+1}-2^{n+1}}{n+1}=\sum\limits_{k=0}^n\dfrac{2^{k+1}-1}{k+1}C^k_n$.

Ta c (1+x)n = C 0n +C1n x+ +

Cnn xn =

nk=0 C

kn x

k nn 21

(1+x)ndx =

21

(n

k=0

C kn xk)dx .

Do 3n+1 2n+1

n + 1=

nk=0

2k+1 1k + 1

C kn .

Trong LATEX c mt mi trng dnh cho vic son tho v nh s ccnh ngha, b , mnh , nh l,. . . nhn c mi trng ny tao Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

Son tho cc cng thc ton hc Mi trng chng minh

khai bo bng lnh

\newtheorem{envname}[procCounter]{name}[secCounter]

y hai thng s tu chn loi tr nhau v

envname l tn mi trng dng trong thn vn bn, c th chn tu nhng nn trnh tn mi trng v tn lnh c.

procCounter l tn mi trng m ta mun nh s lin tip mitrng v mi trng mi ny.

name l tn c gi v in ra cng vi s m nh nh ngha 1,nh l 2.

secCounter l thng s la chn nh s cnh name theo s mchng mc tng ng. Chng hn, nu name l nh l vsecCounter l section th trong mc 1 s c nh l 1.1, nh l 1.2,... nh s ny c th trong subsection, sections hoc chapters.

Sau khi mi trng nh l c khai bo th thn vn bn ta dngn nh mt mi trng bnh thng v vic nh s c thc hin tng. Nu mun mi trng no nh s bt u t n ta dng lnho Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

Son tho cc cng thc ton hc Ging cng thc ton

\setcounter{envname}{n-1}. Trong gi amsthm c nh ngha mitrng chng minh. Mi trng ny bt u bng nhn proof v kt thcl k hiu (\qedsymbol). Ta c th thay i nh sau:

\begin{proof}[Hng dn]Thay k hiu kt thc bng hnh vung en.\renewcommand{\qedsymbol}{$\blacksquare$}\end{proof}

Hng dn.

Thay k hiu kt thc bnghnh vung en.

Nhng k t trong mi trng ton l nhng ch nghing. in ra nhngtn hm ton hc khng nghing, LATEX cung cp nhng tn hm thngdng nh sin, cos, tan, cot, ln, log, lg, deg, dim, det,max,min, sup, inf, . . . to ra mt tn hm mi, trong amsmath s dng lnh

\DeclareMathOperator{\command}{name}

vi \command l lnh gi hm v name l tn hm cn in ra. Lu rngkhng c hm tg v cotg ca Vit Nam nn mun dng ta phi nh ngha\DeclareMathOperator {\tg}{tg} phn khai bo. Khi $\tg x$o Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18

s cho ra tg x .Mi trng array cho ta xp dng v ct cc cng thc ton. Mi trngny c cu trc hon ton tng t nh mi trng tabular.

$$\mathbf{X}=\left( \begin{array}{ccc}x_{11} & x_{12} & \ldots \\x_{21} & x_{22} & \ldots \\\vdots & \vdots & \ddots\end{array} \right)$$

X =

x11 x12 . . .x21 x22 . . ....

.... . .

$$\left[\begin{array}{l}x=1,\\x=2.\end{array}\right.$$

[x = 1,x = 2.

Mi trng eqarray tng t nh array nhng c nh s cng thc. Nukhng mun nh s ta thm du * vo mi trng nh eqarray*.Mi trng multline v multline* dng ngt nhng cng thc qu di

thnh mt s dng: dng u tin y v pha tri, dng cui cng y vpha phi v nhng dng gia c quy tm.

\begin{multline*}\lim\limits_{x\to \infty}\dfrac{x+\sin x}{x-\sin x}\\=\lim\limits_{x\to \infty}\dfrac{1+\frac{\sin x}x}{1-\frac{\sin x}x} =1.\end{multline*}

limx

x + sin x

x sin x= lim

x1 + sin xx1 sin xx

= 1.

Mi trng align v align* dng ging cng thc nhiu dng theo ct.

\begin{align}(1)&\Leftrightarrow (\sqrt a +\sqrt b)^2\le 2(a+b)\notag\\&\Leftrightarrow 2\sqrt{ab}\le a+b.\tag{2}

\end{align}

(1) (a +b)2 2(a + b)

2ab a + b.

(2)

Cn c nhiu mi trng ging cng thc khc nh matrix, pmatrix,bmatrix, vmatrix, Vmatrix, gather, gathered, aligned, flalign, alignat,

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split,. . . V d sau a ra cch son tho h cha php hi v php tuyn.

$$\begin{cases}1. & \text{Em},\\2. & \left[\begin{matrix}\text{Anh},\\\text{Hn ta}.\end{matrix}\right.\end{cases}$$

1. Em,

2.

[Anh,

Hn ta.

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Cu trc

a hnh t mt tp no vo ti liu ang son tho ta s dng gigraphicx vi lnh \includegraphics[options]{filename}. Cc tychn l

bb=a b c d ch a ra mt phn ca hnh nh vi (a, b) l ta gcdi tri v (c, d) l ta gc trn phi. Tham s ny phii lin vi tham s clip=true hin phn hnh nh .

width=s, height=s, totalheight=s a ra rng, chiu cao hoc tng rng v chiu cao ca nh.

scale=s l phng ca hnh

keepaspectratio=true gi hnh cn i khi ta chn c chiu di v chiurng.

angle=s o l gc quay.

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\includegraphics[scale=0.5]{hinh1.png}\hspace{2cm}\includegraphics[scale=0.4]{hinh2.png}

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Ti liu tham kho

Frank Mittelbach and Michel Goossens, The LATEX Companion(Second Edition), Addison-Wesley, 2004.

Michael Doob, A Gentle Introduction to TEX, A Manual for Self-study,2002.

Nguyn Hu in, LATEX vi gi lnh v phn mm cng c, NXB i

hc Quc gia H Ni, 2004.

Tobias Oetiker - Hubert Partl - Irene Hyna - Elisabeth Schlegl, TheNot So Short Introduction to LATEX2 -http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf (bndch ting Vit ca Nguyn Tn Khoa -http://prdownloads.sourceforge.net/vntex/lshort-vn.pdf?download).

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Xin trn trng cm n!

Gii thiuSon tho vn bn LaTeXCu trc tp ngun LaTeXMi trngTiu chy v mc lcTrch dn ti liu tham kho

Son tho cc cng thc ton hcMi trng ton v cc cu trc c sMi trng nh lMi trng chng minhTn hmGing cng thc ton

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