LaTeX (math equations) examples

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LaTeX (math equations) examples[ Edit ]

This article has been created to serve as a collection of reference examples for equations on Commonlounge editor. You can see the source code by clicked "Edit" above.

Fractions, sqrt, exponents

\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }

Derivatives, fractions

\frac{\partial X}{\partial u}

Summation, subscript, superscript

\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)

Summation

\displaystyle\sum_{i=1}^{k+1}i

Choose, superscript

P(E) = {n \choose k} p^k (1-p)^{ n-k}

Integration, derivatives

\int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx

Multiple equations

\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}

Matrix, determinants

\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}

Vectors

\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}

More matrix

\begin{pmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{pmatrix}

More matrix

\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}

more here: Function Support in KaTeX