HuongDanSuDungLaTeX Talk

8/2/2019 HuongDanSuDungLaTeX Talk

1/81

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
http://find/


2/81

Mc Lc

1 Gii thiu

2 Son tho vn bn LATEXCu trc tp ngun LATEXMi trngTiu chy v mc lc

Trch dn ti liu tham kho3 Son tho cc cng thc ton hc

Mi trng ton v cc cu trc c sMi trng nh lMi trng chng minhTn hmGing cng thc ton

4 a hnh vo ti liu

http://find/http://goback/


3/81

Gii thiu

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 TEX

nhm s dng TEX d dng hn.



4/81

Gii thiu

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 TEX

nhm 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 hi


5/81

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 thi


6/81

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.


Gii thi


7/81

Gii thiu



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.


Gii thiu


8/81

Gii thiu



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


9/81

Gii thiu

V d


Gii thiu


10/81

Gii thiu

V d

\documentclass[12pt,a4paper]{article} % Khai bo lp vn bn% Trn mi dng, ni dung sau k hiu "%" khng c bin dc\usepackage[utf8]{vietnam} % Gi lnh phng ting Vit\usepackage{amsmath,amsthm,amssymb}% Cc gi lnh v mi tr

\usepackage[top=2cm, bottom=2cm, left=2.5cm, right=2cm]{geome

\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


11/81

Son tho vn bn LTEX Cu trc tp ngun LTEX

Cc lp ti liu




12/81

Son tho vn bn LTEX Cu trc tp ngun LTEX

Cc lp ti liu

\documentclass[ty chn]{lpvnbn}

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




13/81

p g

Cc lp ti liu


1 C cc lp: article, book, report, beamer,. . .2 C cc ty chn: 11pt (c font, mc nh 10pt), twoside ( hoc

oneside), landscape, leqno, . . .




14/81

p g

Cc lp ti liu



oneside), landscape, leqno, . . .3 V d nh:

\documentclass[12pt, onside]{book}




15/81

Cc lp ti liu



oneside), landscape, leqno, . . .3 V d nh:

\documentclass[12pt, onside]{book}




16/81

Cc gi




17/81

Cc gi

\usepackage[ty chn]{tn gi}

1 Gi ting Vit vietnam vi ty chn utf8 hoc tcvn


http://find/


18/81

Cc gi


1 Gi ting Vit vietnam vi ty chn utf8 hoc tcvn2 Cc gi k hiu ton hc amsmath, amssymb, ...


http://find/


19/81

Cc gi


1 Gi ting Vit vietnam vi ty chn utf8 hoc tcvn2 Cc gi k hiu ton hc amsmath, amssymb, ...3 Gi cn l geometry vi ty chn top=3cm, bottom=?, left=?,

right=?


http://find/


20/81

Cc gi



right=?4 Gi to lin kt hyperrefvi ty chn unicode


http://find/


21/81

Cc gi



right=?4 Gi to lin kt hyperrefvi ty chn unicode5 Gi a hnh vo graphicx v picinpar



C
http://find/


22/81

Cc gi



right=?4 Gi to lin kt hyperrefvi ty chn unicode5 Gi a hnh vo graphicx v picinpar6 Gi to mi trng lit k enumerate



C i
http://find/


23/81

Cc gi



right=?4 Gi to lin kt hyperrefvi ty chn unicode5 Gi a hnh vo graphicx v picinpar6 Gi to mi trng lit k enumerate7 Gi to header fancyhdr, to bng longtable. . .



K hi bi d
http://find/


24/81

K hiu c bit v du ngoc

K hiu c bit



K hi bi d
http://find/


25/81


K hiu c bit1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~



K hi bi d
http://find/


26/81


K hiu c bit1 Cc k hiu c bit l: # $ % & _ { } \ ^ ~2 Trong cc k t # $ % & _ { } phi nh bng cc

lnh \# \$ \% \& \_ \{ \}



K hi bit d
http://find/


27/81



lnh \# \$ \% \& \_ \{ \}3 Cn cc k t \ ^ ~ phi nh bng cc lnh \char92 \char94

\char126



K hi bit d
http://find/


28/81




\char126

Du ngoc





29/81




\char126

Du ngoc

1 Vi ngoc [ v ) c nh thng thng, iu chnh c ca ngoc

bng cc lnh \big, \bigg, \Big, . . .





30/81




\char126

Du ngoc

1 Vi ngoc [ v ) c nh thng thng, iu chnh c ca ngoc

bng cc lnh \big, \bigg, \Big, . . .2 Mun t ng iu chnh chiu cao ca cc ngoc theo chiu cao

cng thc ta dng lnh \left[ v \right] (chng hn l dngngoc vung).



Xung dng ngt trang Khong trng


31/81

Xung dng, ngt trang, Khong trng

Xung dng, ngt trang





32/81


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.





33/81


Xung dng, ngt trang


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





34/81


Xung dng, ngt trang



3 Sang trang mi dng lnh \newpage





35/81


Xung dng, ngt trang




Khong trng





36/81


Xung dng, ngt trang




Khong trng

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





37/81


Xung dng, ngt trang




Khong trng

1 Khong trng n gin: \, hoc \. hoc \quad hoc \qquad, . . .2 Khong trng ngang \hspace{2cm} hoc \phantom{123456} cch

mt khong ng bng rng ca ch trong {}





38/81

u g d g, gt t a g, o g t g

Xung dng, ngt trang




Khong trng

1 Khong trng n gin: \, hoc \. hoc \quad hoc \qquad, . . .2 Khong trng ngang \hspace{2cm} hoc \phantom{123456} cch

mt khong ng bng rng ca ch trong {}3 Khong trng dc \vspace{2cm}



Thay i kiu ch v c ch


39/81

y





40/81

y

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





41/81

y

1 Ch m {\bf vn bn} vn bn, ch in nghing {\it vn bn}vn bn2 Thay i c ch ton vn bn. Np thm gi extsizes v thay ty

chn c font trn bng c fonts mi.





42/81

y


chn 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


Son tho vn bn LATEX Cu trc tp ngun L

ATEX

http://find/


43/81




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

y l font ch 17



ATEX



44/81





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



ATEX



45/81





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


46/81


Son tho vn bn LA

TEX Mi trng

Cn chnh on vn


47/81

CCH DNG MI TRNG


Son tho vn bn LA

TEX Mi trng

Cn chnh on vn
http://find/


48/81

CCH DNG MI TRNG

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


Son tho vn bn LATE

X Mi trng

Cn chnh on vn
http://find/


49/81

CCH DNG MI TRNG


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


Son tho vn bn LATE

X Mi trng

Cn chnh on vn
http://find/


50/81

CCH DNG 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}


Son tho vn bn LATE

X Mi trng

Gi enumerate v mi trng enumerate
http://find/


51/81


Son tho vn bn LATE

X Mi trng



52/81

Mi trng enumerate nu dng thm gi enumerate c ty chn l cch

nh s [1.] hoc [a,]....


Son tho vn bn LATE

X Mi trng



53/81


nh 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.


Son tho vn bn LATE

X Mi trng



54/81


nh 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.

Gii PT vi m = 3.

Tm m PT c nghim.


Son tho vn bn LATE

X Mi trng

Cc v d khc v mi trng lit k


55/81


Son tho vn bn LATE

X Mi trng

http://find/


56/81

Nu khng khai bo gi enumerate th s khng dng c ty chn cchnh s [1.] hoc [a,].... Khi LAT

EX s nh s cc kt qu lit k t

ng.



http://find/


57/81



ng.

Cho PT $x^2-2(m-1)x+1=0$.\begin{enumerate}


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

1

Gii PT vi m = 3.2 Tm m PT c nghim.





58/81



ng.

Cho PT $x^2-2(m-1)x+1=0$.\begin{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.



Tabbing


59/81

Mi trng tabbing to ra bng m mi ct c cn tri. rng ca

mi 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 tnh1 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.


60/81

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

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

01/01 My birthdayNew year14/02 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}|}\hlinepos & Cn v tr ca bng theo chiu dc

pos Cn v tr ca bng theo chiu ddng ngoi bng. Mc nh l gi


61/81

i vi dng ngoi bng. Mc nh l gia bng,{\tt t} l dng u v {\tt b} l dng cui.\\\hlinecols & 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}

dng ngoi bng. Mc nh l gil dng u v b l dng cui.

cols nh dng tng ct theo cc k hi

l Cn tri.r Cn phi.c Cn gia.

p{width} Ct c chiu rngv vn bn c c

@{text} Chn thm text v

trong ct. C thkhong trng bn@\hpace{width}width l di.

*{n}{cols} nh dng lp lict. V d, *{3}{l

l

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 dng



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 c

i h di


62/81

cn 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, \vline ng k dc "" trn mt dng ca c

\multicolumn{n}{cols}{text} Kt hp n ct trong dng v in vcols 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, sepa

\begin{center}\begin{tabular}{|l|r@{-}r@{-}r|l|}\hline\multicolumn{1}{|c|}{Color} &\multicolumn{4}{c|}{Codes}\\ \cl

&\multicolumn{3}{c|}{RGB} &\multicolumn{1}{c|}{Hex} \\ \hlino Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18


Sky Blue &135 &206 &235 &87CEEB \\ \hlineDark Violet &148 &0 &211 &9400D3 \\ \hline\end{tabular}
http://goback/http://find/http://find/http://goback/


63/81

\end{tabular}\end{center}

\caption{Mt v d tng hp.}\end{table}

Color CodesRGB HexSky Blue 135-206-235 87CEEBDark 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 vd sau


Son tho vn bn LATEX Tiu chy v mc lc

\begin{tabular}{| l | l |}\hlinePlanet &Features\\ \hline

Planet FeaturesL lik t


64/81

Planet &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}

MercuryLunar like crustCrustal faulting

Small 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), . . .


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}


65/81

\renewcommand{\footrulewidth}{0.4pt}.LATEX h tr vic chia vn bn thnh cc chng, mc, mc nh,. . . v t

ng 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 c


66/81

- \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:



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


67/81

\end{math}.Mi trng ton trn mt dng ring: Ni dung c nhp vo gia

du \[ v \], 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 \wideha

b\frac{a}{b}

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

an a^{n} n

a \sqrt[n]{a} a \bar{a} AB \overlan a_{n} f(x) f(x) a \vec{a}

AB \overr



\forall \exists \infty \emptyset \angle \triangle \nabla \partial
http://goback/http://find/http://find/http://goback/


68/81

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 mt

k 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}}}, \quad

a_0 +\dfrac{1}{a_1 +\dfrac{1}{a_2 +\dfrac{1}{a_3}}}$

a0 + 1a1+

1a2+

1a3

, a0 +

1

a1 + 1a2 +

1a3

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


69/81

/ \div \diamond \ \setminus \wedge

Cc ton t quan h:

\le, \leq \ge, \geq .= \doteq = \ne, \not \ll \gg \equiv \sim \in \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 ,. 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:



\sum

\bigcup

\bigvee

\prod

\bigcap

\bigwedge
http://goforward/http://find/http://goback/


70/81

\prod

\bigcap

\bigwedge

\coprod \bigsqcup \int

\oint

Cc du mi tn:

\leftarrow, \gets \longleftarrow \leftrightarrow \

\Leftarrow = \Longleftarrow \Leftrightarrow \

\rightarrow, \to \longrightarrow \mapsto \

\Rightarrow = \Longrightarrow \hookleftarrow \

Bng ch ci Hy Lp:



\alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \vartheta \iota \kappa


71/81

pp \lambda \mu \nu \xi

\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 ton

u 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 bn


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


72/81

ba chm dc (.) v cho ( .) th c cho bi \vdots v \ddots. Hyxem 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 = C0n +C1n x+ +

Cnn xn =

n

k=0 Ckn x

k nn

21 (1+x)

n

dx=2

1 (

nk=0 C

k

n xk

)dx.

Do 3n+1 2n+1

n + 1=

nk=0

2k+1

1k+ 1 Ckn .

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 ta


Son tho cc cng thc ton hc Mi trng chng minh

khai bo bng lnh

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


73/81

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 v

secCounter 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 lnh



74/81

Son tho cc cng thc ton hc Ging cng thc ton

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.


75/81

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

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


Son tho cc cng thc ton hc Ging cng thc ton

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


76/81

\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*}

limxx+ sin x

x sin x= lim

x

1+ sin xx

1 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)

2

ab

a + b.

(2)

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

o Ngc Minh (HSP H Ni) Hng dn s dng LATEX Ngy 17 thng 11 nm 2008 15 / 18 a hnh vo ti liu

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

$$\begin{cases}1 & \text{Em} \\

1. Em,


77/81

1. & \text{Em},\\2. & \left[\begin{matrix}\text{Anh},\\

\text{Hn ta}.\end{matrix}\right.\end{cases}$$

2. Anh,

Hn ta.


Cu trc


78/81

a hnh t mt tp no vo ti liu ang son tho ta s dng gi

graphicx 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.


\includegraphics[scale=0.5]{hinh1.png}\hspace{2cm}
http://find/


79/81

\includegraphics[scale=0.4]{hinh2.png}


Ti liu tham kho


80/81

Frank Mittelbach and Michel Goossens, The LATE

X Companion(Second Edition), Addison-Wesley, 2004.

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

Nguyn Hu in, LATE

X vi gi lnh v phn mm cng c, NXB ihc Quc gia H Ni, 2004.

Tobias Oetiker - Hubert Partl - Irene Hyna - Elisabeth Schlegl, TheNot So Short Introduction to LATEX 2 -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).



81/81

Xin trn trng cm n!


Documents

HuongDanSuDungLaTeX Talk