We use MathJax to include mathematical formulas in Axional Docs documents. LaTeX or AsciiMath notation can be used, and the mathematics will be processed using JavaScript to produce HTML for viewing in any modern browser.

# 1 Putting mathematics in a document

To put mathematics in your web page, you can use TeX and LaTeX notation, AsciiMath notation, or a combination of all three within the same page.

Mathematics that is written in TeX or LaTeX format is indicated using math delimiters that surround the mathematics, telling MathJax what part of your page represents mathematics and what is normal text.

# 2 Sample: The Quadratic Formula

The following code

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$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$

Shows the formula

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$

# 3 Sample: Cauchy's Integral Formula

The following code

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$f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz$

Shows the formula

$$f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz$$

# 4 Sample: Double angle formula for Cosines

The following code

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$\cos(θ+φ)=\cos(θ)\cos(φ)−\sin(θ)\sin(φ)$

Shows the formula

$$\cos(θ+φ)=\cos(θ)\cos(φ)−\sin(θ)\sin(φ)$$

# 5 Sample: Gauss' Divergence Theorem

The following code

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$\int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS$

Shows the formula

$$\int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS$$

# 6 Sample: Curl of a Vector Field

The following code

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$\vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}$

Shows the formula

$$\vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}$$

# 7 Sample: Standard Deviation

The following code

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$\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}$

Shows the formula

$$\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}$$

# 8 Sample: Definition of Christoffel Symbols

The following code

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$(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)$

Shows the formula

$$(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)$$