[PDF] LATEX Math for Undergrads - CTAN PDF undergradmath.pdf

30 déc 2020 · LATEX Math for Undergrads Entering gets a mathematical setting Thus, for “ the To have them grow with the enclosed formula, use \left

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18 août 2017 · index/exponent only valid in math mode, e g a2 1 see E 2 B Preamble (before \ begin{document}) B 1 Documentclass (necessary)

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LATEX 2ε Cheat Sheet Document classes latexsym Use LATEX symbol font graphicx Show \begin{equation}[place] Add numbered equation \caption{text}

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LATEX 2ε Cheat Sheet Document latexsym Use LATEX symbol font Use before formula, or just \big for one that acts as an ordinary symbol Every Time

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Comprehensive LATEX Symbols List (Pakin): http://www ctan org/tex-archive/info/ symbols/comprehensive/ 2 Inline math formulas and displayed equations 2 1

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LATEX Mathematical Symbols The more unusual symbols are not defined in base LATEX (NFSS) and require \usepackage{amssymb} F A I A \Theta

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formula, or just \big for one that acts as an ordinary symbol insert whenever displayed math begins The following specify a style for typesetting formulas

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ATEX Math for Undergrads

Rule OneAny mathematics at all, even a single character, gets a mathematical setting. Thus, for "the value ofxis7" enterthe value of $x$ is $7$. TemplateYour document should contain at least this. \documentclass{article} \usepackage{mathtools ,amssymb ,amsthm} % imports amsmath \begin{document} --document body here-- \end{document}

Common constructs

x x i,jx_{i,j}23 ,2/3\frac{2}{3},2/3

Calligraphic lettersUse as in$\mathcal{A}$.

Get script letters, such asPfrom$\mathscr{P}$, by

putting\usepackage{mathrsfs}in the preamble. Greek

ˁϪˁĩˁϪˁ\alpha Ľ İ Ľ \ Ľ İ Ľ , ĝ Đ ĝ \ ĝ Đ ĝ \xi,\Xi

͹ʟ͹¾͹ʟ͹\betaoo

\vartheta,\upsilon,\Upsilon

Ŀ Ħ Ŀ \ Ŀ Ħ Ŀ \nu˔Ќ˔ĸ˔Ќ˔,ʔάʔĘʔάʔ\omega,\Omega

Sets and logic

ĳ ġ ĳ \ ĳ ġ ĳ \in\emptyset | =\models / ĳ ġ ĳ \ ĳ ġ ĳ \notinʵϞʵĩʵϞʵ\aleph\setminus set complementAːЀːİːЀːwithA^{\mathsf{c}}(orAwith

A^{\complement}, orAwith\overline{A}).

Decorations

f f If the decorated letter isiorjthen some decorations need \imathor\jmath, as in\vec{\imath}. Some authors use boldface for vectors:\boldsymbol{x}.Entering\overline{x+y}producesx+y, and \widehat{x+y}givesx+y. Comment on an expression as here (there is also\overbrace{..}). x+y | A | \underbrace{x+y}_{|A|} DotsUse low dots in a list × \ × 0,1,2, ... Ù \ Ù , entered as \{0,1,2,\,\ldots\}. (If you use\ldotsin plain text as withLondon, Paris, \ldots{}\,.then note the thinspace \,before the period.) Use centered dots in a sum or prod- vertical dots\vdotsand diagonal dots\ddots. Roman namesEnter\tan(x), with a backslash, instead oftan(x). These get the same treatment. sin\sinsinh\sinharcsin\arcsin cos\coscosh\cosharccos\arccos tan\tantanh\tanharctan\arctan sec\seccoth\cothmin\min csc\cscdet\detmax\max cot\cotdim\diminf\inf exp\expker\kersup\sup log\logdeg\degliminf\liminf ln\lnarg\arglimsup\limsup lg\lggcd\gcdlim\lim

Other symbols

Usea\mid bfor the divides relation,a | b, and

a\nmid bfor the negation,aΡˋΡÊΡˋΡb. Also use\midto

get set builder notation × \ × a ĳ ġ ĳ \ ĳ ġ ĳ S | ais odd Ù \ Ù , with

\{a\in S\mid\text{$a$ is odd}\}.

Arrows

M M \longrightarrow\leftarrow

\Rightarrow\leftrightarrow \nRightarrow\downarrow =\Longrightarrow\uparrow \leadsto\updownarrow The right arrows in the first column have matching left arrows, such as\nleftarrow, and there are some other matches for down arrows, etc. j=0j2 x=0x2dx \int_{x=0}^3 x^2\,dxexpand when displayed. 3 j=0j 3 x=0x2dx

These do the same.

Fences

Fix the size with\big,\Big,\bigg, or\Bigg.

k=0e k2ɷ;ɷćɷ;ɷ \Big[\sum_{k=0}^n e^{k^2}\Big] To have them grow with the enclosed formula, use\left and\right(although sometimes\big, etc., are necessary). i,22i \left\langle i,2^{2^i}\right\rangle

Every\leftmust match a\rightand they must end on

the same line in the output. For a one-sided fence, put a \left.or\right.on the other side. dfdx

0\left.\frac{df}{dx}\right|_{x_0}

Arrays, MatricesMake an array of mathematical text as you make a table of plain text. 00 11 24
......\begin{array}{rcl}

0 &\leftrightarrow &0 \\

1 &\leftrightarrow &1 \\

2 &\leftrightarrow &4 \\

\vdots & &\vdots \end{array}

Definition by cases is an array with two columns.

f n= aifn= 0 \begin{cases} a &\text{if $n=0$} \\ r\cdot f_{n-1} &\text{else} \end{cases} A matrix is an array with fences. With apmatrixenviron- ment, you need not specify column alignments. a b \begin{pmatrix} a &b \\ c &d \end{pmatrix} For the determinant use|A|inline andvmatrixin display. thin space, as in\sqrt{2}\,x. Slightly wider are\:and \;(the three are in ratio3 : 4 : 5). Get the improvement of n/logninstead ofn/lognby using a negative thin space, as inn/\!\log n. Bigger spaces are:\quadfor , and \qquadfor , which are useful between parts of a display. Get arbitrary space as in\hspace*{0.5cm}.Displayed equationsTheequation*environment puts an equation on a separate line.

S=k\cdot\lg W

\end{equation*}

You can break into multiple lines.

sin(x) =x M M x33! x55! \sin (x)=x-\frac{x^3}{3!} \\ +\frac{x^5}{5!}-\cdots \end{multline*}

Align equations usingalign*

\nabla\cdot\boldsymbol{D} &= \rho \\ \nabla\cdot\boldsymbol{B} &= 0 \end{align*} (the left or right side of an alignment can be empty). For each environment, get a numbered version by dropping the asterisk from the name. Calculus examplesThe last three here are display style.

9.8m/s29.8~\text{m}/\text{s}^2

h0f(x+h) M M f(x)h \lim_{h\to 0}\frac{f(x+h)-f(x)}{h} x

2dx=x3/3 +C\int x^2\,dx=x^3/3+C

Discrete mathematics examplesThere are four

a\equiv b\pod m. For combinations the binomial symbolʷϞʷħʷϞʷn kʷϞʷħʷϞʷis from \binom{n}{k}. This resizes to be bigger in a display (to require the display version use\dbinom{n}{k}and require the inline version with\tbinom{n}{k}).

For permutations usenrfromn^{\underline{r}}(some

authors useP(n,r), ornPrfrom{}_nP_r).

Statistics examples

(xi M M ľ ĥ ľ \ ľ ĥ ľ )2/N\sigma^2=\sqrt{\,\sum (x_i-\mu)^2/N} The probability density of the normal distribution comes from this. \frac{1}{sqrt{2\sigma^2\pi}} \,e^{-\frac{(x-\mu)^2}{2\sigma^2}}!. For moreSee also the Comprehensive LATEX Symbols List

DeTEXify atdetexify.kirelabs.org/classify.html.Jim Hefferon, Saint Michael"s College, VT USA 2020-Dec-30

quotesdbs_dbs8.pdfusesText_14

[PDF] [PDF] LATEX Math for Undergrads - CTAN