User:Scm83x/Engineering Equations

Engineering Equations of the Week is my personal page to document the particular engineering equation that I am using the most that week or holds special significance for the moment. It is also a method for me to improve my familiarity with the Wikimarkup for mathematical formulas.

Week of 23 October 2005:

Simpson's One-Third Rule

$\underset{a}{\overset{b}{\int }}f(x)dx\approx \frac{h}{3}[f(x_0)+2\sum _{i=1}^{n/2-1}f(x_{2i})+4\sum _{j=1}^{n/2}f(x_{2j-1})+f(x_n)]$

Week of 16 October 2005:

Multidimensional Newton-Raphson method

$\left[\begin{array}{c}{x}_{i+1}\\ y_{i+1}\end{array}\right]=\left[\begin{array}{c}{x}_i\\ y_i\end{array}\right]-{\left[\begin{array}{cc}\frac{\partial f}{\partial x}& \frac{\partial f}{\partial y}\\ \frac{\partial g}{\partial x}& \frac{\partial g}{\partial y}\end{array}\right]}^{-1}\left[\begin{array}{c}f(x_i,y_i)\\ g(x_i,y_i)\end{array}\right]$

Week of 9 October 2005:

Conservation of momentum for a control volume

$\frac{\partial }{\partial t}\underset{CV}{\overset{}{\int }}\overrightarrow{V}\rho d\mathbb{𝕍}+\underset{CS}{\overset{}{\int }}\overrightarrow{V}\rho (\overrightarrow{V}\cdot \hat{n})dA=\mathrm{\Sigma }\overrightarrow{F}$

Week of 2 October 2005:

Bernoulli's equation

$p+\frac{\rho v^2}{2}+\gamma z=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}$