# List of Equations

The equations below are formatted with MathML. They are rendered in MathJax so should work across all browsers, mobile phones etc.

### Copying an equation.

• Right click on the equation
• From the popup menu chose: Show Math As, MathML Code.
• A new window will open. Select and copy the MathML code.

### To convert to other formats such as GIF

Paste the mathml code into http://www.mathmlcentral.com/Tools/FromMathML.jsp

### Paste into Microsoft word

In most word versions a shortcut is to right-click within the word document and select "Keep Text Only (T)"

• Insert, equation
• Paste the MathML code
• It should magically turn into a word equation that you can also edit
• If you still see MathML code, click on the drop down menu in word and change it to "Keep Text Only (T)"

$L=\sqrt{D\tau }$

$R=| r 2 |= r 1 2 + r 2 2 + r 3 2 + r 1 2 r 2 2 r 3 2 +2 r 1 r 2 ( 1+ r 3 2 )cos2 θ 1 +2 r 2 r 3 ( 1+ r 1 2 )cos2 θ 2 +2 r 1 r 3 cos2( θ 1 + θ 2 )+2 r 1 r 2 2 r 3 cos2( θ 1 − θ 2 ) 1+ r 1 2 r 2 2 + r 1 2 r 3 2 + r 2 2 r 3 2 +2 r 1 r 2 ( 1+ r 3 2 )cos2 θ 1 +2 r 2 r 3 ( 1+ r 1 2 )cos2θ+2 r 1 r 3 cos2( θ 1 + θ 2 )+2 r 1 r 2 2 r 3 cos2( θ 1 − θ 2 )$

$\alpha ={\mathrm{sin}}^{-1}\left[\mathrm{sin}\delta \mathrm{sin}\phi +\mathrm{cos}\delta \mathrm{cos}\phi \mathrm{cos}\left(HRA\right)\right]$

$FF=\frac{{V}_{MP}{I}_{MP}}{{V}_{OC}{I}_{SC}}$

$FF=\frac{{V}_{MP}{I}_{MP}}{{V}_{OC}{I}_{SC}}$

$FF=\frac{{v}_{oc}-\mathrm{ln}\left({v}_{oc}+0.72\right)}{{v}_{oc}+1}$

$R={\left(\frac{{n}_{0}-{n}_{Si}}{{n}_{0}+{n}_{Si}}\right)}^{2}$

${R}_{\parallel }=\frac{{\mathrm{tan}}^{2}\left({\theta }_{1}-{\theta }_{2}\right)}{{\mathrm{tan}}^{2}\left({\theta }_{1}+{\theta }_{2}\right)}$

${R}_{\perp }=\frac{{\mathrm{sin}}^{2}\left({\theta }_{1}-{\theta }_{2}\right)}{{\mathrm{sin}}^{2}\left({\theta }_{1}+{\theta }_{2}\right)}$

${R}_{T}=\frac{{R}_{\perp }+{R}_{\parallel }}{2}$

$G=\alpha {N}_{0}{e}^{-\alpha x}$

$2{H}^{+}\left(aq\right)+2{e}^{-}\to {H}_{2}\left(g\right)$

${I}_{0}=qA\frac{D{n}_{i}^{2}}{L{N}_{D}}$

$W={x}_{p}+{x}_{n}=\sqrt{\frac{2\epsilon }{q}{V}_{o}\left(\frac{1}{{N}_{A}}+\frac{1}{{N}_{D}}\right)}$