# 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)"

$x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$

$Q=\frac{{\left[D\right]}^{d}{\left[C\right]}^{c}}{{\left[A\right]}^{a}{\left[B\right]}^{b}}$

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

$\mathrm{ln}\left(I\right)=\mathrm{ln}\left({I}_{0}\right)+\left(\frac{q}{nkT}\right)$

${\rho }_{\square }=\frac{\rho }{t}$

${n}_{1}\mathrm{sin}{\theta }_{1}={n}_{2}\mathrm{sin}{\theta }_{2}$

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

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

$aA+bB\to cC+dD$

$Sunrise=12-\frac{1}{{15}^{0}}{\mathrm{cos}}^{-1}\left(\frac{-\mathrm{sin}\phi \mathrm{sin}\delta }{\mathrm{cos}\phi \mathrm{cos}\delta }\right)-\frac{TC}{60}$

$Sunrise=12-\frac{1}{{15}^{0}}{\mathrm{cos}}^{-1}\left(-\mathrm{tan}\phi \mathrm{tan}\delta \right)-\frac{TC}{60}$

$Sunset=12+\frac{1}{{15}^{0}}{\mathrm{cos}}^{-1}\left(\frac{-\mathrm{sin}\phi \mathrm{sin}\delta }{\mathrm{cos}\phi \mathrm{cos}\delta }\right)-\frac{TC}{60}$

$Sunset=12+\frac{1}{{15}^{0}}{\mathrm{cos}}^{-1}\left(-\mathrm{tan}\phi \mathrm{tan}\delta \right)-\frac{TC}{60}$

$\frac{1}{{\tau }_{bulk}}=\frac{1}{{\tau }_{band}}+\frac{1}{{\tau }_{Auger}}+\frac{1}{{\tau }_{SRH}}$