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
 * $$\int_a^b f(x) dx\approx

\frac{h}{3}\bigg[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) \bigg]$$

Week of 16 October 2005:
 * Multidimensional Newton-Raphson method
 * $$ \begin{bmatrix} x_{i+1} \\ y_{i+1} \end{bmatrix} = \begin{bmatrix} x_{i}  \\ y_{i} \end{bmatrix} - \begin{bmatrix} {\partial f \over \partial x} & {\partial f \over \partial y} \\ {\partial g \over \partial x} & {\partial g \over \partial y} \end{bmatrix}^{-1} \begin{bmatrix} f(x_i,y_i) \\ g(x_i,y_i) \end{bmatrix}$$

Week of 9 October 2005:
 * Conservation of momentum for a control volume
 * $$ {\partial \over \partial t} \int_{CV}^{} {\vec V \rho}\, d\mathbb{V} + \int_{CS}^{} {\vec V \rho (\vec V \cdot \hat n)}\, dA = \Sigma \vec F$$

Week of 2 October 2005:
 * Bernoulli's equation
 * $$ p+{\rho v^2 \over 2}+{\gamma z}=\mathrm{constant} $$