Our homepage is configured to use MathJax’s HTML-CSS mode with web fonts to display the equations, which produces uniform layout and typesetting across browsers. But MathJax can also be configured to use native MathML rendering when available in a browser, and only fall back to HTML-CSS mode when native rendering is not available. You can try the various output modes using the MathJax context Menu (which you access by ctrl+clicking / alt-clicking an equation) or the button below.

Select the rendering mode:

$x = − b ± b 2 − 4 a c 2 a$

### Cauchy’s Integral Formula

$f ( a ) = 1 2 π i ∮ γ f ( z ) z − a d z$

### Double angle formula for Cosines

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

### Gauss’ Divergence Theorem

$∫ D ( ∇⋅ F ) d V = ∫ ∂ D F ⋅ n d S$

### Curl of a Vector Field

$∇ → × F → = ( ∂ F z ∂ y − ∂ F y ∂ z ) i + ( ∂ F x ∂ z − ∂ F z ∂ x ) j + ( ∂ F y ∂ x − ∂ F x ∂ y ) k$

### Standard Deviation

$σ = 1 N ∑ i = 1 N ( x i − μ ) 2 .$

### Definition of Christoffel Symbols

$( ∇ X Y ) k = X i ( ∇ i Y ) k = X i ( ∂ Y k ∂ x i + Γ i m k Y m )$