Here are the Code examples of this chapter. You can compile them online right on this web page by pressing the Typeset / Compile button. You can also edit them for testing, and compile again.
For a better view with the online compiler, I sometimes use \documentclass[border=10pt]{standalone} instead of \documentclass{article}. Instead of having a big letter/A4 page, the standalone class crops the paper to see just the visible text without an empty rest of a page.
Any question about a code example? Post it on LaTeX.org, I will answer. As forum admin I read every single question there. (profile link).
Example document
\documentclass[preview,border=10pt]{standalone}\begin{document}\section*{Quadratic equations}The quadratic equation\begin{equation}\label{quad}ax^2 + bx + c = 0,\end{equation}where \( a, b \) and \( c \) are constants and \( a \neq 0 \),has two solutions for the variable \( x \):\begin{equation}\label{root}x_{1,2} = \frac{-b \pm \sqrt{b^2-4ac}}{2a}.\end{equation}If the \emph{discriminant} \( \Delta \) with\[\Delta = b^2 - 4ac\]is zero, then the equation (\ref{quad}) has a double solution:(\ref{root}) becomes\[x = - \frac{b}{2a}.\]\end{document}
Figure 9.1
Subscripts and superscripts
\documentclass[preview,border=10pt]{standalone}\begin{document}\[x_1^2 + x_2^2 = 1, \quad 2^{2^x} = 64\]\end{document}
Figure 9.2
Operators
\documentclass[preview,border=10pt]{standalone}\begin{document}\[\lim_{n=1, 2, \ldots} a_n \qquad \max_{x<X} x\]\end{document}
Figure 9.3
Operators within text
\documentclass[preview,border=10pt]{standalone}\begin{document}Within text, we have \( \lim_{n=1, 2, \ldots} a_n \)and \( \max_{x<X} x \).\end{document}
Figure 9.4
Roots
\documentclass[preview,border=10pt]{standalone}\begin{document}\[\sqrt[64]{x} = \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{x}}}}}}\]\end{document}
Figure 9.5
Fractions
\documentclass[preview,border=10pt]{standalone}\begin{document}\[\frac{n(n+1)}{2} \quad \frac{\frac{\sqrt{x}+1}{2}-x}{y^2}\]\end{document}
Figure 9.6
Greek letters
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{$#1$&\texttt{\string#1}}\setlength{\tabcolsep}{2ex}\begin{document}\begin{tabular}{l@{~}ll@{~}ll@{~}ll@{~}ll@{~}l}\s\alpha & \s\zeta & \s\lambda & \s\pi & \s\phi \\\s\beta & \s\eta & \s\mu & \s\rho &\s\chi \\\s\gamma & \s\theta & \s\nu & \s\sigma &\s\psi\\\s\delta & \s\iota & \s\xi & \s\tau &\s\omega \\\s\epsilon & \s\kappa & \s o & \s\upsilon&\end{tabular}\end{document}
Figure 9.7
Variants of Greek letters
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{$#1$&\texttt{\string#1}}\setlength{\tabcolsep}{2ex}\begin{document}\begin{tabular}{l@{~}ll@{~}ll@{~}l}\s\varepsilon & \s\varpi & \s\varsigma \\\s\vartheta & \s\varrho & \s\varphi\end{tabular}\end{document}
Figure 9.8
Uppercase Greek letters
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{$#1$&\texttt{\string#1}}\setlength{\tabcolsep}{2ex}\begin{document}\begin{tabular}{l@{~}ll@{~}ll@{~}ll@{~}l}\s\Gamma &\s\Lambda &\s\Sigma &\s\Psi \\\s\Delta &\s\Xi &\s\Upsilon &\s\Omega \\\s\Theta &\s\Pi &\s\Phi\end{tabular}\end{document}
Figure 9.9
Upright Greek letters
\documentclass[border=10pt]{standalone}\usepackage{upgreek}\newcommand*\s[1]{$#1$&\texttt{\string#1}}\setlength{\tabcolsep}{2ex}\begin{document}\thispagestyle{empty}\begin{tabular}{l@{~}ll@{~}ll@{~}ll@{~}ll@{~}l}\s\upalpha & \s\upzeta & \s\uplambda & \s\uppi & \s\upphi \\\s\upbeta & \s\upeta & \s\upmu & \s\uprho &\s\upchi \\\s\upgamma & \s\uptheta & \s\upnu & \s\upsigma &\s\uppsi\\\s\updelta & \s\upiota & \s\upxi & \s\uptau &\s\upomega \\\s\upepsilon & \s\upkappa & $\mathrm{o}$&\texttt{\string\mathrm\{o\}} & \s\upupsilon&\end{tabular}\end{document}
Figure 9.11
Variants of upright Greek letters
\documentclass[border=10pt]{standalone}\usepackage{upgreek}\newcommand*\s[1]{$#1$&\texttt{\string#1}}\setlength{\tabcolsep}{2ex}\begin{document}\begin{tabular}{l@{~}ll@{~}ll@{~}l}\s\upvarepsilon & \s\upvarpi & \s\upvarsigma \\\s\upvartheta & \s\upvarrho & \s\upvarphi\end{tabular}\end{document}
Figure 9.11
Script letters
\documentclass[preview,border=10pt]{standalone}\begin{document}\[\mathcal{A}, \mathcal{B}, \mathcal{C}, \ldots, \mathcal{Z}\]\end{document}
Figure 9.12
Ellipsis
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\begin{document}\centering\begin{tabular}{*3{c@{~}l}}\s\ldots & \s\ddots \\\s\cdots & \s\vdots \\\end{tabular}\end{document}
Figure 9.13
Math font styles
\documentclass[border=10pt]{standalone}\usepackage{booktabs}\usepackage{amsfonts}\usepackage{bbm}\usepackage{dsfont}\usepackage{eufrak}\renewcommand*\c{\textbackslash\ttfamily}\begin{document}\sffamily\begin{tabular}{lll}\toprule\textbf{Command} & \textbf{Used package} & \textbf{Example} \\\midrule\c mathrm\{\ldots\} & & \(\mathrm{roman\ 123}\) \\\c mathit\{\ldots\} & & \(\mathit{italic\ 123}\) \\\c mathsf\{\ldots\} & & \(\mathsf{sans-serif\ 123}\) \\\c mathbb\{\ldots\} & amsfonts & \(\mathbb{ABC}\) \\\c mathbbm\{\ldots\} & bbm & \(\mathbbm{C R Q Z 1}\) \\\c mathds\{\ldots\} & dsfont &\(\mathds{C R Q Z 1}\) \\\c mathfrak\{\ldots\} & eufrak & \(\mathfrak{A B C \ 1 2 3}\) \\\c mathnormal\{\ldots\} & & \(\mathnormal{normal}\) \\\bottomrule\end{tabular}\end{document}
Figure 9.14
Math versus text italic
\documentclass[border=10pt]{standalone}\begin{document}\(Definition\) and \textit{Definition}\end{document}
Figure 9.15
Typesetting multi-line formulas
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\begin{multline}\sum = a + b + c + d + e \\+ f + g + h + i + j \\+ k + l + m + n\end{multline}\begin{gather}x + y + z = 0 \\y - z = 1\end{gather}\begin{align}x + y + z &= 0 \\y - z &= 1\end{align}\end{document}
Figure 9.16
Figure 9.17
Figure 9.18
Customized tagging
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\begin{align}x + y + z &= 0 \tag{$\star$} \\y - z &= 1 \tag{$\star\star$}\end{align}\end{document}
Binary operation symbols
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1ex}\usepackage{booktabs}\usepackage{latexsym}\begin{document}\sffamily\centering\begin{tabular}{*4{c@{~}l}}\toprule\multicolumn{8}{c}{\bfseries Standard \LaTeX} \\\s\amalg & \s\circ & \s\ominus & \s\star \\\s\ast & \s\cup & \s\oplus & \s\times \\\s\bigcirc & \s\dagger & \s\oslash & \s\triangleleft\\\s\bigtriangledown & \s\ddagger & \s\otimes & \s\triangleright \\\s\bigtriangleup & \s\diamond & \s\pm & \s\uplus \\\s\bullet & \s\div & \s\setminus & \s\vee \\\s\cap & \s\mp & \s\sqcap & \s\wedge \\\s\cdot & \s\odot & \s\sqcup & \s\wr \\\midrule\multicolumn{8}{c}{\bfseries latexsym }\\\s\unlhd & \s\unrhd & \s\rhd & \s\lhd \\\bottomrule\end{tabular}\end{document}
Figure 9.19
Binary relation symbols
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\usepackage{booktabs}\usepackage{latexsym}\begin{document}\begin{tabular}{*4{c@{~}l}}\toprule\multicolumn{8}{c}{\bfseries Standard \LaTeX} \\\s\approx & \s\equiv & \s\prec & \s\succ \\\s\asymp & \s\frown & \s\preceq & \s\succeq \\\s\bowtie & \s\mid & \s\propto & \s\vdash \\\s\cong & \s\models & \s\sim & \\\s\dashv & \s\parallel & \s\simeq \\\s\doteq & \s\perp & \s\smile \\\midrule\multicolumn{8}{c}{\bfseries latexsym }\\\multicolumn{8}{c}{\(\Join\) ~ \texttt{\string\Join}} \\\bottomrule\end{tabular}\end{document}
Figure 9.20
Inequality relation symbols
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\usepackage{booktabs}\begin{document}\sffamily\centering\begin{tabular}{*5{c@{~}l}}\toprule\s\geq & \s\gg & \s\leq & \s\ll & \s\neq \\\bottomrule\end{tabular}\end{document}
Figure 9.21
Subset and superset symbols
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\usepackage{booktabs}\usepackage{latexsym}\begin{document}\sffamily\centering\begin{tabular}{*3{c@{~}l}}\toprule\multicolumn{6}{c}{\bfseries Standard \LaTeX} \\\s\sqsubseteq & \s\subset & \s\supset \\\s\sqsupseteq & \s\subseteq & \s\supseteq \\\midrule\multicolumn{6}{c}{\bfseries latexsym }\\\multicolumn{3}{c}{\(\sqsubset\) ~ \texttt{\string\sqsubset}}& \multicolumn{3}{c}{\(\sqsupset\) ~ \texttt{\string\sqsupset}}\\\bottomrule\end{tabular}\end{document}
Figure 9.22
Arrows
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\usepackage{booktabs}\usepackage{latexsym}\begin{document}\sffamily\centering\begin{tabular}{*3{c@{~}l}}\toprule\multicolumn{6}{c}{\bfseries Standard \LaTeX} \\\s\downarrow & \s\Longleftarrow & \s\Rightarrow \\\s\Downarrow & \s\longleftrightarrow & \s\searrow \\\s\hookleftarrow & \s\Longleftrightarrow & \s\swarrow \\\s\hookrightarrow & \s\longmapsto & \s\uparrow \\\s\leftarrow & \s\longrightarrow & \s\Uparrow \\\s\Leftarrow & \s\Longrightarrow & \s\updownarrow \\\s\leftrightarrow & \s\mapsto & \s\Updownarrow \\\s\Leftrightarrow & \s\nwarrow \\\s\longleftarrow & \s\rightarrow \\\midrule\multicolumn{6}{c}{\bfseries latexsym }\\\multicolumn{6}{c}{\(\leadsto\) ~ \texttt{\string\leadsto}}\\\bottomrule\end{tabular}\end{document}
Figure 9.23
Harpoons
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\usepackage{booktabs}\begin{document}\sffamily\centering\begin{tabular}{*3{c@{~}l}}%\toprule\s\leftharpoondown & \s\rightharpoondown & \s\rightleftharpoons \\\s\leftharpoonup & \s\rightharpoonup \\%\bottomrule\end{tabular}\end{document}
Figure 9.24
Symbols dereived from letters
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\usepackage{booktabs}\usepackage{latexsym}\begin{document}\sffamily\centering\begin{tabular}{*5{c@{~}l}}\toprule\multicolumn{10}{c}{\bfseries Standard \LaTeX} \\\s\bot & \s\forall & \s\imath & \s\ni & \s\top \\\s\ell & \s\hbar & \s\in & \s\partial & \s\wp \\\s\exists & \s\Im & \s\jmath & \s\Re \\\midrule\multicolumn{10}{c}{\bfseries latexsym }\\\multicolumn{10}{c}{\(\mho\) ~ \texttt{\string\mho}}\\\bottomrule\end{tabular}\end{document}
Figure 9.25
Misc symbols
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{\(#1\)&\texttt{\string#1}}\setlength{\tabcolsep}{1.8ex}\usepackage{booktabs}\usepackage{latexsym}\begin{document}\sffamily\centering\begin{tabular}{*4{c@{~}l}}\toprule\multicolumn{8}{c}{\bfseries Standard \LaTeX }\\\s\aleph & \s\emptyset & \s\nabla & \s\sharp \\\s\angle & \s\flat &\s\natural & \s\spadesuit \\\s\clubsuit & \s\heartsuit & \s\neg & \s\surd \\\s\diamondsuit & \s\infty &\s\prime & \s\triangle \\\midrule\multicolumn{8}{c}{\bfseries latexsym}\\\multicolumn{4}{c}{\(\Box\) ~ \texttt{\string\Box}}& \multicolumn{4}{c}{\(\Diamond\) ~ \texttt{\string\Diamond}}\\\bottomrule\end{tabular}\end{document}
Figure 9.26
Variable sized operators
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{$\displaystyle#1$&\texttt{\string#1}}\renewcommand*\arraystretch{1.8}\setlength{\arraycolsep}{3ex}\begin{document}\begin{tabular}{*4{c@{~}l}}\s\bigcap & \s\bigotimes & \s\bigwedge & \s\prod \\\s\bigcup & \s\bigsqcup & \s\coprod & \s\sum \\\s\bigodot & \s\biguplus & \s\int \\\s\bigoplus & \s\bigvee & \s\oint \\\end{tabular}\end{document}
Figure 9.29
Inline text equation
\documentclass[border=10pt]{standalone}\usepackage{amsmath}\begin{document}\(\int_a^b \! f(x) \, dx = \lim_{\Delta x \rightarrow 0}\sum_{i=1}^{n} f(x_i) \,\Delta x_i\)\end{document}
Figure 9.30
Displayed style equation
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[\int_a^b \! f(x) \, dx = \lim_{\Delta x \rightarrow 0}\sum_{i=1}^{n} f(x_i) \,\Delta x_i\]\end{document}
Figure 9.31
Variable sized delimiters
\documentclass[border=10pt]{standalone}\newcommand*\s[1]{$\displaystyle\Big#1$&\texttt{\string#1}}\renewcommand*\arraystretch{1.8}\setlength{\tabcolsep}{2ex}\usepackage{booktabs}\begin{document}\begin{tabular}{*3{c@{\quad}l}}\toprule\multicolumn{6}{c}{\bfseries Pairs of braces, brackets and parentheses} \\\(\Big(\ \Big)\) & \verb|( )| & \(\Big\{\ \Big\}\) & \verb|\{ \}| & \(\Big\lceil\ \Big\rceil\) & \verb|\lceil \rceil|\\\({\Big[\ \Big]}\) & \verb|[ ]| & \(\Big\langle\ \Big\rangle\) & \verb|\langle \rangle|& \(\Big\lfloor\ \Big\rfloor\) & \verb|\lfloor \rfloor| \\\midrule\multicolumn{6}{c}{\bfseries Delimiting symbols and arrows}\\\s/ & \s\downarrow & \s\updownarrow \\\s\backslash & \s\Downarrow & \s\Updownarrow\\\s| & \s\uparrow \\\s\| & \s\Uparrow \\%\s\unlhd & \s\unrhd & \s\rhd & \s\lhd \\\bottomrule\end{tabular}\end{document}
Figure 9.32
Arrays
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[A = \left(\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22}\end{array}\right)\]\end{document}
Figure 9.33
Typesetting matrices
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[A = \begin{pmatrix}a_{11} & a_{12} \\a_{21} & a_{22}\end{pmatrix}\]\end{document}
Figure 9.34
Writing binomial coefficients
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[\binom{n}{k} = \frac{n!}{k!(n-k)!}\]\end{document}
Figure 9.35
Underlining and overlining
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[\overline{\Omega}\]\end{document}
Figure 9.36
An underbrace below an expression
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[N = \underbrace{1 + 1 + \cdots + 1}_n\]\end{document}
Figure 9.37
Accents
\documentclass[border=10pt]{standalone}\setlength{\tabcolsep}{1.8ex}\usepackage{array}\usepackage{booktabs}\begin{document}\sffamily\centering\begin{tabular}{*4{>{$}c<{$}@{~}l}}\toprule\acute{a} & \verb|\acute{a}| &\check{a} & \verb|\check{a}| &\grave{a} & \verb|\grave{a}| &\tilde{a} & \verb|\tilde{a}| \\\bar{a} & \verb|\bar{a}| & \ddot{a} & \verb|\ddot{a}| & \hat{a} & \verb|\hat{a}| & \vec{a} & \verb|\vec{a}| \\\breve{a} & \verb|\breve{a}| & \dot{a} & \verb|\dot{a}| & \mathring{a} & \verb|\mathring{a}| \\\midrule\multicolumn{8}{c}{\textbf{Extensible}} \\\multicolumn{4}{c}{$\widehat{abc}$\,\ \texttt{\string\widehat\{abc\}}} & \multicolumn{4}{c}{$\widetilde{abc}$\,\ \texttt{\string\widetilde\{abc\}}}\\\bottomrule\end{tabular}\end{document}
Figure 9.38
Putting a symbol above or below another one
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[\underset{\circ}{\cap} \neq \overset{\circ}{\cup}\]\end{document}
Figure 9.39
Text above a relation symbol
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\begin{document}\[X \stackrel{\text{def}}{=} 0\]\end{document}
Figure 9.40
Writing theorems and definitions
\documentclass[preview,border=10pt]{standalone}\usepackage{amsmath}\newtheorem{thm}{Theorem}\newtheorem{dfn}[thm]{Definition}\begin{document}\begin{dfn}A quadratic equation is an equation of the form\begin{equation}\label{quad}ax^2 + bx + c = 0,\end{equation}where \( a, b \) and \( c \) are constants and \( a \neq 0 \).\end{dfn}\begin{thm}A quadratic equation (\ref{quad}) has two solutions for theVariable \( x \):\begin{equation}\label{root}x_{1,2} = \frac{-b \pm \sqrt{b^2-4ac}}{2a}.\end{equation}\end{thm}\end{document}
Figure 9.41
This code is available on Github. It is licensed under the MIT License, a short and simple permissive license with conditions only requiring preservation of copyright and license notices.
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