The following equations are represented in the HTML source code as LaTeX expressions.

The Lorenz Equations

\[\begin{aligned}

\dot{x} & = \sigma(y-x) \\

\dot{y} & = \rho x - y - xz \\

\dot{z} & = -\beta z + xy

\end{aligned} \]

The Cauchy-Schwarz Inequality

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

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}{\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+\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{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}

\]

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.

seems to work great!

ReplyDeleteThis page works with Firefox 3.6.6.

ReplyDeleteSuper duper in Google Chrome, buddy! Not quite sure what th'hell it all means, tho...

ReplyDelete