%mathjax

<h4>In-line Mathematics</h4>

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.

<h4>The Lorenz Equations</h2>
\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}

<h4>The Cauchy-Schwarz Inequalitys</h2>
\[
\left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq
 \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\]


<h4>A Cross Product Formula</h4>
\[
  \mathbf{V}_1 \times \mathbf{V}_2 =
   \begin{vmatrix}
    \mathbf{i} & \mathbf{j} & \mathbf{k} \\
    \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
    \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\
   \end{vmatrix}
\]


<h4>The probability of getting \(k\) heads when flipping \(n\) coins is:</h4>
\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]

<h4>An Identity of Ramanujan</h4>
\[
   \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =
     1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
      {1+\frac{e^{-8\pi}} {1+\ldots} } } }
\]

<h4>A Rogers-Ramanujan Identity</h4>

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

<h4>Maxwell's Equations</h4>

\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}