Working examples

This is not a Government of Canada website

The purpose of this website is to provide a working example of the WET-BOEW-GCWeb theme created by TNG Consulting Inc. together with the Government of Canada for Moodle software . Demo courses are only available in English however multi-language courses are supported.

MathML formulas

If you need to do formulas, consider enabling formulas in Moodle and using the built-in editor for easier data entry.

Simple formulas

Given the quadratic equation $a{x}^{2}+bx+c=0$ , the roots are given by $x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$ .

Complex formulas

Formula Result
Bernoulli Trials $P\left(E\right)\text{Probability of event E: Get exactly k heads in n coin flips.}=\left(\genfrac{}{}{0}{}{n}{k}\right)\text{Number of ways to get exactly k heads in n coin flips}{p\text{Probability of getting heads in one flip}}_{}^{k\text{Number of heads}}{\left(1-p\right)\text{Probability of getting tails in one flip}}_{}^{n-k\text{Number of tails}}$
Cauchy-Schwarz Inequality ${\left(\sum _{k=1}^{n}{a}_{k}^{}{b}_{k}^{}\right)}_{}^{2}\le \left(\sum _{k=1}^{n}{a}_{k}^{2}\right)\left(\sum _{k=1}^{n}{b}_{k}^{2}\right)$
Cauchy Formula $f\left(z\right)\text{}·{\mathrm{Ind}}_{\gamma }^{}\left(z\right)=\frac{1}{2\pi i}\underset{\gamma }{\overset{}{\oint }}\frac{f\left(\xi \right)}{\xi -z}\text{}d\xi$
Cross Product ${V}_{1}^{}×{V}_{2}^{}=|\begin{array}{ccc}i& j& k\\ \frac{\partial X}{\partial u}& \frac{\partial Y}{\partial u}& 0\\ \frac{\partial X}{\partial v}& \frac{\partial Y}{\partial v}& 0\end{array}|$
Vandermonde Determinant $|\begin{array}{cccc}1& 1& \cdots & 1\\ {v}_{1}^{}& {v}_{2}^{}& \cdots & {v}_{n}^{}\\ {v}_{1}^{2}& {v}_{2}^{2}& \cdots & {v}_{n}^{2}\\ ⋮& ⋮& \ddots & ⋮\\ {v}_{1}^{n-1}& {v}_{2}^{n-1}& \cdots & {v}_{n}^{n-1}\end{array}|=\prod _{1\le i
Lorenz Equations $\begin{array}{rcl}\underset{}{\overset{˙}{x}}& =& \sigma \left(y-x\right)\\ \underset{}{\overset{˙}{y}}& =& \rho x-y-xz\\ \underset{}{\overset{˙}{z}}& =& -\beta z+xy\end{array}$
Maxwell's Equations $\left\{\begin{array}{rcl}\nabla \text{​}×\underset{}{\overset{↼}{B}}-\text{}\frac{1}{c}\text{}\frac{\partial \text{​}\underset{}{\overset{↼}{E}}}{\partial \text{​}t}& =& \frac{4\pi }{c}\text{}\underset{}{\overset{↼}{j}}\\ \nabla \text{​}·\underset{}{\overset{↼}{E}}& =& 4\pi \rho \\ \nabla \text{​}×\underset{}{\overset{↼}{E}}\text{}+\text{}\frac{1}{c}\text{}\frac{\partial \text{​}\underset{}{\overset{↼}{B}}}{\partial \text{​}t}& =& \underset{}{\overset{↼}{0}}\\ \nabla \text{​}·\underset{}{\overset{↼}{B}}& =& 0\end{array}$
Einstein Field Equations ${R}_{\mu \nu }^{}-\frac{1}{2}\text{}{g}_{\mu \nu }^{}\text{}R=\frac{8\pi G}{{c}_{}^{4}}\text{}{T}_{\mu \nu }^{}$
Ramanujan Identity $\frac{1}{\left(\sqrt{\phi \sqrt{5}}-\phi \right){e}_{}^{\frac{25}{\pi }}}=1+\frac{{e}_{}^{-2\pi }}{1+\frac{{e}_{}^{-4\pi }}{1+\frac{{e}_{}^{-6\pi }}{1+\frac{{e}_{}^{-8\pi }}{1+\dots }}}}$
Another Ramanujan identity $\sum _{k=1}^{\infty }\frac{1}{{2}_{}^{⌊k·\text{​}\phi ⌋}}=\frac{1}{{2}_{}^{0}+\frac{1}{{2}_{}^{1}+\cdots \frac{1}{{2}_{}^{1}+\frac{1}{{2}_{}^{2}+\cdots \frac{1}{{2}_{}^{3}+\frac{1}{{2}_{}^{5}+\dots }}}}}}$
Rogers-Ramanujan Identity