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

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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 $a x^{2} + b x + c = 0$ $a x^{2} + b x + c = 0$ , the roots are given by $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

Complex formulas

Formula	Result
Bernoulli Trials	$P (E) Probability of event E: Get exactly k heads in n coin flips. = (\binom{n}{k}) Number of ways to get exactly k heads in n coin flips {p Probability of getting heads in one flip}_{}^{k Number of heads} {(1 - p) Probability of getting tails in one flip}_{}^{n - k Number of tails}$ $P (E) Probability of event E: Get exactly k heads in n coin flips. = (\binom{n}{k}) Number of ways to get exactly k heads in n coin flips {p Probability of getting heads in one flip}_{}^{k Number of heads} {(1 - p) Probability of getting tails in one flip}_{}^{n - k Number of tails}$
Cauchy-Schwarz Inequality	${(\sum_{k = 1}^{n} a_{k}^{} b_{k}^{})}_{}^{2} \leq (\sum_{k = 1}^{n} a_{k}^{2}) (\sum_{k = 1}^{n} b_{k}^{2})$ ${(\sum_{k = 1}^{n} a_{k}^{} b_{k}^{})}_{}^{2} \leq (\sum_{k = 1}^{n} a_{k}^{2}) (\sum_{k = 1}^{n} b_{k}^{2})$
Cauchy Formula	$f (z) \cdot {Ind}_{γ}^{} (z) = \frac{1}{2 π i} \oint_{γ}^{} \frac{f (ξ)}{ξ - z} d ξ$ $f (z) \cdot {Ind}_{γ}^{} (z) = \frac{1}{2 π i} \oint_{γ}^{} \frac{f (ξ)}{ξ - z} d ξ$
Cross Product	$V_{1}^{} \times V_{2}^{} = \| \begin{matrix} i & j & k \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{matrix} \|$ $V_{1}^{} \times V_{2}^{} = \| \begin{matrix} i & j & k \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{matrix} \|$
Vandermonde Determinant	$\| \begin{matrix} 1 & 1 & \dots & 1 \\ v_{1}^{} & v_{2}^{} & \dots & v_{n}^{} \\ v_{1}^{2} & v_{2}^{2} & \dots & v_{n}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ v_{1}^{n - 1} & v_{2}^{n - 1} & \dots & v_{n}^{n - 1} \end{matrix} \| = \prod_{1 \leq i < j \leq n}^{} (v_{j}^{} - v_{i}^{})$ $\| \begin{matrix} 1 & 1 & \dots & 1 \\ v_{1}^{} & v_{2}^{} & \dots & v_{n}^{} \\ v_{1}^{2} & v_{2}^{2} & \dots & v_{n}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ v_{1}^{n - 1} & v_{2}^{n - 1} & \dots & v_{n}^{n - 1} \end{matrix} \| = \prod_{1 \leq i < j \leq n}^{} (v_{j}^{} - v_{i}^{})$
Lorenz Equations	$\begin{array}{rcl} x_{}^{˙} & = & σ (y - x) \\ y_{}^{˙} & = & ρ x - y - x z \\ z_{}^{˙} & = & - β z + x y \end{array}$ $\begin{array}{rcl} x_{}^{˙} & = & σ (y - x) \\ y_{}^{˙} & = & ρ x - y - x z \\ z_{}^{˙} & = & - β z + x y \end{array}$
Maxwell's Equations	${\begin{array}{rcl} \nabla \times B_{}^{↼} - \frac{1}{c} \frac{\partial E_{}^{↼}}{\partial t} & = & \frac{4 π}{c} j_{}^{↼} \\ \nabla \cdot E_{}^{↼} & = & 4 π ρ \\ \nabla \times E_{}^{↼} + \frac{1}{c} \frac{\partial B_{}^{↼}}{\partial t} & = & 0_{}^{↼} \\ \nabla \cdot B_{}^{↼} & = & 0 \end{array}$ ${\begin{array}{rcl} \nabla \times B_{}^{↼} - \frac{1}{c} \frac{\partial E_{}^{↼}}{\partial t} & = & \frac{4 π}{c} j_{}^{↼} \\ \nabla \cdot E_{}^{↼} & = & 4 π ρ \\ \nabla \times E_{}^{↼} + \frac{1}{c} \frac{\partial B_{}^{↼}}{\partial t} & = & 0_{}^{↼} \\ \nabla \cdot B_{}^{↼} & = & 0 \end{array}$
Einstein Field Equations	$R_{μ ν}^{} - \frac{1}{2} g_{μ ν}^{} R = \frac{8 π G}{c_{}^{4}} T_{μ ν}^{}$ $R_{μ ν}^{} - \frac{1}{2} g_{μ ν}^{} R = \frac{8 π G}{c_{}^{4}} T_{μ ν}^{}$
Ramanujan Identity	$\frac{1}{(\sqrt{φ \sqrt{5}} - φ) e_{}^{\frac{25}{π}}} = 1 + \frac{e_{}^{- 2 π}}{1 + \frac{e_{}^{- 4 π}}{1 + \frac{e_{}^{- 6 π}}{1 + \frac{e_{}^{- 8 π}}{1 + \dots}}}}$ $\frac{1}{(\sqrt{φ \sqrt{5}} - φ) e_{}^{\frac{25}{π}}} = 1 + \frac{e_{}^{- 2 π}}{1 + \frac{e_{}^{- 4 π}}{1 + \frac{e_{}^{- 6 π}}{1 + \frac{e_{}^{- 8 π}}{1 + \dots}}}}$
Another Ramanujan identity	$\sum_{k = 1}^{\infty} \frac{1}{2_{}^{⌊ k \cdot φ ⌋}} = \frac{1}{2_{}^{0} + \frac{1}{2_{}^{1} + \dots \frac{1}{2_{}^{1} + \frac{1}{2_{}^{2} + \dots \frac{1}{2_{}^{3} + \frac{1}{2_{}^{5} + \dots}}}}}}$ $\sum_{k = 1}^{\infty} \frac{1}{2_{}^{⌊ k \cdot φ ⌋}} = \frac{1}{2_{}^{0} + \frac{1}{2_{}^{1} + \dots \frac{1}{2_{}^{1} + \frac{1}{2_{}^{2} + \dots \frac{1}{2_{}^{3} + \frac{1}{2_{}^{5} + \dots}}}}}}$
Rogers-Ramanujan Identity	$1 + \sum_{k = 1}^{\infty} \frac{q_{}^{k_{}^{2} + k}}{(1 - q) (1 - q_{}^{2}) \dots (1 - q_{}^{k})} \frac{q_{}^{2}}{(1 - q)} + \frac{q_{}^{6}}{(1 - q) (1 - q_{}^{2})} + \dots = \prod_{j = 0}^{\infty} \frac{1}{(1 - q_{}^{5 j + 2}) (1 - q_{}^{5 j + 3})} \frac{1}{(1 - q_{}^{2}) (1 - q_{}^{3})} \times \frac{1}{(1 - q_{}^{7}) (1 - q_{}^{8})} \times \dots, for \| q \| < 1 .$ $1 + \sum_{k = 1}^{\infty} \frac{q_{}^{k_{}^{2} + k}}{(1 - q) (1 - q_{}^{2}) \dots (1 - q_{}^{k})} \frac{q_{}^{2}}{(1 - q)} + \frac{q_{}^{6}}{(1 - q) (1 - q_{}^{2})} + \dots = \prod_{j = 0}^{\infty} \frac{1}{(1 - q_{}^{5 j + 2}) (1 - q_{}^{5 j + 3})} \frac{1}{(1 - q_{}^{2}) (1 - q_{}^{3})} \times \frac{1}{(1 - q_{}^{7}) (1 - q_{}^{8})} \times \dots, for \| q \| < 1 .$

Last modified: Monday, 26 August 2019, 10:08 AM

Date modified:: 2019-08-10

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WET-BOEW-GCWeb 4.0 for Moodle

Working examples

This is not a Government of Canada website

MathML formulas

Simple formulas

Complex formulas