MathJax Demo

This is a demo page for MathJax syntax

Testing SimpleMathJax

Please take a look at this beautiful equation.

<math>\int (x+y+z) \, dc</math>

<math>\hat{x}_{k|k-1} = A\hat{x}_{k-1|k-1} + Bu_{k-1}</math>

<math>P_{k|k-1} = AP_{k-1|k-1}A^{T} + Q</math>

<math>K_{k} = P_{k|k-1}H^{T}\left(HP_{k|k-1}H^{T}+R\right)^{-1}</math>

<math>\hat{x}_{k|k} = \hat{x}_{k|k-1} + K_{k}\left(y_{k} - H\hat{x}_{k|k-1}\right)</math>

<math>P_{k|k} = \left(I-K_{k}H\right)P_{k|k-1}</math>

Following this Mathematical Equation:

<math>\vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i}

       + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial
       F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}</math>

Its' source code is shown here:

<source language="TeX"> \vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i}

       + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial
       F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}

</source>

Finite Element

<math> \varepsilon = \frac{\left\langle \displaystyle\sum_{i=1}^N c_i\Psi_i \right| \hat{H} \left| \displaystyle\sum_{i=1}^Nc_i\Psi_i \right\rangle}{\left\langle \left. \displaystyle\sum_{i=1}^N c_i\Psi_i \right| \displaystyle\sum_{i=1}^Nc_i\Psi_i \right\rangle} = \frac{\displaystyle\sum_{i=1}^N\displaystyle\sum_{j=1}^Nc_i^*c_jH_{ij}}{\displaystyle\sum_{i=1}^N\displaystyle\sum_{j=1}^Nc_i^*c_jS_{ij}} \equiv \frac{A}{B}. </math>

<math>\sum_{j=1}^N c_j \left( H_{kj} - \varepsilon S_{kj} \right) = 0 \quad \text{for} \quad k = 1,2,\dots,N. </math>