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LaTeX

https://en.wikibooks.org/wiki/LaTeX/Mathematics

Symbols

• $ + - \cdot \times \div = ! / ( ) [ ] < >

  ’ : * \leftarrow \Rightarrow $

• $\forall x \in X, \quad \exists y \leq \epsilon$

Greek letters

• $\alpha, \Alpha, \beta, \Beta, \gamma, \Gamma, \pi, \Pi, \phi, \varphi, \mu, \Phi$

Operators

• $\cos (2\theta) = \cos^2 \theta - \sin^2 \theta$
• $\lim\limits_{x \to \infty} \exp(-x) = 0$
• $a \bmod b$
• $x \equiv a \pmod b$
• $\cfrac {dy} {dx}$ vs $\cfrac {\mathrm d y} {\mathrm d x}$ vs $\cfrac {\operatorname d y} {\operatorname d x}$ vs $\cfrac {\operatorname d \operatorname y} {\operatorname d \operatorname x}$

Powers and indices

• $k_{n+1} = n^2 + k_n^2 - k_{n-1}$

• $f(n) = n^5 + 4n^2 +2

  _{n=17}$

• $\cfrac{n!}{k!(n-k)} = \displaystyle\binom{n}{k}$
• $\cfrac {\frac{1}{x} + \frac{1}{y}} {y-z}$
• $^3/_7$
• $ 3 \times \frac{1}{2} = 1^1/_2$
• $x^ {\frac {1} {2}}$

Continued fractions

• $x = a_0 + \cfrac {1} {a_1 + \cfrac {1} {a_2 + \cfrac {1} {a_3 + \cfrac {1} {a_4}}}} $

Multiplication of two numbers

• $\cfrac { \begin{array} {r} (x_1x_2)
  \times (x’_1x’_2) \end{array} } { (y_1y_2y_3y_4) } $

Roots

• $\sqrt{\cfrac{a}{b}}$
• $\sqrt[n]{1+x+x^2+x^3+\dots+x^n}$

Sums, products and integrals

• $\sum_{i=1}^{10} t_i$ vs $\displaystyle\sum_{i=1}^{10} t_i$ vs $\sum\limits_{i=1}^{10} t_i$
• $\displaystyle\int_0^\infty \mathrm{e}^{-x}\, \mathrm{d}x$
• $\displaystyle\sum_{\substack{ 0<i<m
  0<j<n }} P(i, j) $
• $\int_a^b$ vs $\int\limits_a^b$ vs $\displaystyle\int_a^b$
• $\displaystyle \prod _{x_m} ^{x_n} = {x_m} $

Brackets, braces and delimiters

• $( a ), [ b ], { c }, | d |, | e |, \langle f \rangle, \lfloor g \rfloor, \lceil h \rceil, \ulcorner i \urcorner, / j \backslash$

Automatic sizing

• $\left(\cfrac{x^2}{y^3}\right)$

• $P\left(A=2\middle

  \frac{A^2}{B}>4\right)$

• $\left{\cfrac{x^2}{y^3}\right}$

• $\cfrac{x^3}{3}

  _0^1$ vs $\left.\cfrac{x^3}{3}\right

  _0^1$

Manual sizing

• $( \big( \Big( \bigg( \Bigg($
• $\cfrac{\mathrm d}{\mathrm d x} \left( k g(x) \right)$ vs $\cfrac{\mathrm d}{\mathrm d x} \Bigg( k g(x) \Bigg)$

Matrices and array

• $\left[ \begin{matrix} a & b & c
  d & e & f
  g & h & i \end{matrix} \right]$
• $\begin{matrix} -1 & 3
  2 & -4 \end{matrix} $
• $A_{m, n} = \begin{pmatrix} a_{1, 1} & a_{1, 2} & \cdots & a_{1, n}
  a_{2, 1} & a_{2, 2} & \cdots & a_{2, n}
  \vdots & \vdots & \ddots & \vdots
  a_{m, 1} & a_{m, 2} & \cdots & a_{m, n} \end{pmatrix}$
• $\begin{array}{c|c} 1 & 2 \ \hline 3 & 4 \end{array}$
• $M = \begin{bmatrix} \frac{5}{6} & \frac{1}{6} & 0 \[0.5em] \frac{5}{6} & 0 & \frac{1}{6} \[0.5em] 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix}$

Adding text to equations

• $ 50 apples \times 100 apples = lots of apples^2$
• $ 50 \text{apples} \times 100 \text{apples} = \text{lots of apples}^2$
• $ 50 \text{ apples} \times 100 \text{ apples} = \text{lots of apples}^2$

Formatted text

• $ 50 \textrm{ apples} \times 100 \textbf{ apples} = \textit{lots of apples}^2$
  • \textrm: roman font family
  • \textbf: bold
  • \textit: italic shape
  • …

Accents

• $a’ a’’ a’’’ a’’’$
• $\bar{a} \quad \acute{a} \quad \check{a} \quad \grave{a}$
• $\vec {a}$ $\overrightarrow {AB}$ $\overleftarrow {AB}$

Color

• $k = {\color{red}x} \mathbin{\color{yellow}-} 2$

Plus and minus signs

• \pm $\pm$
• \mp $\mp$

Controlling horizontal spacing

• $f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ > 0}
  5 & \quad \text{if } n \text{ = 0}
  -(n+1)/2 & \quad \text{if } n \text{ < 0} \end{cases} $

Dots

• $ \dot A$
• $A \cdot B$
• $A \dots B$
• $A \ldots B$
• $A \cdots B$
• $A \dotsm B$
• $A \vdots B$
• $A \ddots B$

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Excecises

• $E=mc^2$
• $x = \frac {-b \pm \sqrt {\Delta}} {2a} \quad\quad (\Delta = b^2 - 4ac)$
• $a^2 + b^2 = c^2$
• $d_{circle} = 2\pi r$
• $S_{circle} = \pi r^2$
• $V_{sphere} = \frac{4}{3} \pi r^3$

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