LaTeX samples / test page

LaTeX sample that uses upgreek

This equation is from PMC3117236, equation "(A1)".

Equation (from \begin{align*} \begin{split} \upvarepsilon_r^i &= a_{11}^i \sigma_r^i + \sigma_{12}^i \sigma_{\uptheta}^i \\ \upvarepsilon_{\uptheta}^i & = a_{12}^i \sigma_r^i + a_{22}^i \sigma_{\uptheta}^i \\ \gamma_{r \uptheta}^i & = a_{66}^i \tau_{r \uptheta}^i \\ \gamma_{rz}^i & = \gamma_{\uptheta z}^i = \tau_{rz}^i = \tau_{\uptheta z}^i = 0 \end{split} \end{align*}

For comparison, here's the image source on PMC: .

Here's the same equation but with standard characters (not upright): \begin{align*} \begin{split} \varepsilon_r^i &= a_{11}^i \sigma_r^i + \sigma_{12}^i \sigma_{\theta}^i \\ \varepsilon_{\theta}^i & = a_{12}^i \sigma_r^i + a_{22}^i \sigma_{\theta}^i \\ \gamma_{r \theta}^i & = a_{66}^i \tau_{r \theta}^i \\ \gamma_{rz}^i & = \gamma_{\theta z}^i = \tau_{rz}^i = \tau_{\theta z}^i = 0 \end{split} \end{align*}

Some simple LaTeX

• Inline: \(a + b = c\)
• Fractions: \[\frac{n!}{k!(n-k)!} = {n \choose k}\]
• Array: \[ \begin{array}{cc} a + \frac{b}{c} & \sqrt{a^b} \\ c & c \end{array} \]

The Lorenz Equations, LaTeX

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

The Cauchy-Schwarz Inequality, LaTeX

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

A Cross Product Formula

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

The probability of getting \(k\) heads when flipping \(n\) coins is:

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

An Identity of Ramanujan

\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]

A Rogers-Ramanujan Identity

\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for $|q|<1$}. \]

Maxwell's Equations

\begin{align} \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{align}

In-line Mathematics

Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.