Large operators: inline vs display
+ +Inline: $\sum_{k=1}^{n} k$ and $\int_0^1 x^2\,dx$ and $\prod_{k=1}^{n} k$
+ +Display: +$$\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$$ +$$\int_0^\infty e^{-x}\,dx = 1 \qquad \int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}$$ +$$\prod_{p\;\text{prime}} \frac{1}{1-p^{-s}} = \sum_{n=1}^{\infty} \frac{1}{n^s}$$ +
+ +Algebra
+ +Quadratic formula: +$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
+ +Pythagorean theorem: $a^2 + b^2 = c^2$
+ +Binomial theorem: +$$\sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k} = (x + y)^n$$
+ +Calculus
+ +Definition of derivative: +$$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$
+ +Gaussian integral: +$$\int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}$$
+ +Product rule: $\dfrac{d}{dx}\bigl[f(x)\,g(x)\bigr] = f'(x)\,g(x) + f(x)\,g'(x)$
+ +Greek letters
+ +Euler's identity: $e^{i\pi} + 1 = 0$
+ +$\alpha,\ \beta,\ \gamma,\ \delta,\ \varepsilon,\ \zeta,\ \eta,\ + \theta,\ \iota,\ \kappa,\ \lambda,\ \mu,\ \nu,\ \xi,\ \pi,\ + \rho,\ \sigma,\ \tau,\ \upsilon,\ \phi,\ \chi,\ \psi,\ \omega$
+ +Fourier transform: +$$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\,e^{-2\pi i x \xi}\,dx$$
+ +Physics
+ +Einstein: $E = mc^2$
+ +Schrödinger equation: +$$i\hbar\frac{\partial\psi}{\partial t} = \hat{H}\psi$$
+ +Maxwell in free space: +$$\nabla \cdot \mathbf{E} = 0 \qquad \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$
+ +Piecewise definitions (stretchy {)
+
+Two rows (short brace): +$$|x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases}$$
+ +Four rows (tall brace): +$$f(x) = \begin{cases} + \dfrac{\sin x}{x}, & \text{if } x > 0 \\[6pt] + \displaystyle\sum_{k=0}^{\infty} \frac{(-1)^k x^{2k}}{(2k+1)!}, & \text{if } x = 0 \\[6pt] + -\sqrt{|x|}, & \text{if } -1 \leq x < 0 \\[4pt] + \infty, & \text{otherwise} +\end{cases}$$
+ +Stretchy delimiters
+ +Two-high (\binom):
+$$\binom{n}{k}$$
Around a fraction: +$$\left( \dfrac{\frac{a}{b}}{\frac{c}{d}} \right)^{n} \qquad + \left[ \dfrac{\frac{a}{b}}{\frac{c}{d}} \right]^{n}$$
+ +3×3 matrix: +$$\begin{pmatrix} + a_{11} & a_{12} & a_{13} \\ + a_{21} & a_{22} & a_{23} \\ + a_{31} & a_{32} & a_{33} +\end{pmatrix} \qquad +\begin{bmatrix} + a_{11} & a_{12} & a_{13} \\ + a_{21} & a_{22} & a_{23} \\ + a_{31} & a_{32} & a_{33} +\end{bmatrix}$$
+ +Stretchy arrows
+ +Vector accents: $\vec{v},\ \vec{F},\ \vec{p},\ \vec{\mathbf{0}},\ \vec{\mathbf{B}},\ \vec{ABC},\ \overrightarrow{ABC},\ \overleftarrow{ABC}$
+ +Stretchy operators with labels: +$A \xrightarrow{f} B \xrightarrow{n+\mu-1} C \qquad X \xleftarrow{g} Y$
+ +AMScd commutative diagram: +$$\begin{CD} A @>f>> B \\ @VgVV @VVhV \\ C @>>k> D \end{CD}$$
+ +