latex-course/example-document/doc/math.tex

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\section{Math}
\subsection{Equation}
This is an equation
\begin{equation}
% A lonesome ( will have a fixed size
% But a \left( will be scaled to contain whatever it has to
\langle f, g \rangle_{\left[a, b\right]}
=
\int_a^b f(x)\overline{g(x)} dx
% \\ % The equation env ignores \\
% a^2 + b^2 = c^2
\label{eq:inner_product} % You may label equations for referencing later
\end{equation}
\subsection{Gather}
This is the gather environment
\begin{gather*}
E = mc^2
\\
E^2 =
\frac{ % You
mc^2 % May
} % Use
{ % As
\sqrt{ % Many
1 % Lines
- % As
\frac{ % You
v^2 % Want
}
{ % Sometimes
c^2 % It makes
} % Things more
} % Structured
} % ...though not always...
\end{gather*}
\subsection{Align}
This is an \emph{anonymous} align environment
\begin{align*}
24 &= 8 \cdot 3 \\ % Allows aligning glyphs by using &
&= 4 \cdot 6 \\ % The glyph marked with & on each line
&= 2 \cdot 2 \cdot 2 \cdot 3 % Will be aligned
\end{align*}
\subsection{Inlined math}
% Math can be inlined with \( ..my math.. \) or $..also my math..$
% $_$ is the old TeX way and is not advisable to use
% \(_\) is the more modern LaTeX way and is more robust
A \(\sum_n^k\) sum! And a $\frac{1}{n}$.
% The \[\] is a \displaystyle math environment
% There is no real reason to use it over the \begin syntax, but it's there. This env is displayed on its own line and is not a part of the paragraph in the same way $_$ and \(\) are.
You can also: \[\alpha\] do this.
\subsection{Some symbols}
Greek
\begin{gather*}
\psi,\ \Psi % The "\ " thing forces the insert of a space, otherwise whitespace is ignored
\\
\alpha, \beta, \gamma, \delta % Lower case with _small_ letters
\\
\Gamma, \Delta % Upper case with _Capital_ letter
\\
\epsilon, \varepsilon % Variants with _var_
\end{gather*}
Other things
% If you want a glyph, but don't know what it's called
% Either try something (most glyphs have sensible names)
% Or just search it up online, after a while you'll remember
\begin{gather*}
\nabla, \partial
\\
\int, \iint, \oint
\\
\sum_{i = 1}^{n}, \prod_{1 \leq i \leq n}
\\
\frac{a + ib}{c + id}, i = 1, \dots, n
\\
\bar{x}, \vec{x}, x^\circ
\end{gather*}
Matrices (and vectors)
\begin{gather*}
\begin{pmatrix} % Parantheses
1 & 2 & 3 \\ % Columns separated with &
4 & 5 & 6 \\ % Rows separated with \\
7 & 8 & 9
\end{pmatrix}
,
\begin{bmatrix} % Brackets
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
,
\begin{Bmatrix} % _Curly_ brackets
1 & 2 & \\ % You can leave elements empty
4 & \displaystyle\int_0^1x^2 dx & 6 \\ % You can make the elements complicated (and force roomy display with \displaystyle
7 & 8 & 9
\end{Bmatrix}
,
\begin{pmatrix} % Essentially a vector
x_1 \\ x_2 \\ x_3 % Just because \\ causes linebreak, doesn't mean you need a new line in the source
\end{pmatrix}
\end{gather*}
% Defining a new command, don't do it here, do it in the preamble or something similar
% newcommand takes a command name, a number of arguments and the "function body" of the command. The arguments to the new command being defined can be accessed by #<number>
\newcommand{\myvec}[1]{
\begin{pmatrix}
#1
\end{pmatrix}
}
% Works like a charm
\begin{gather*}
\myvec{x_1\\x_2\\x_3} \leftarrow \text{My vector command}
\end{gather*}