View source for 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 [[Help:Formula|Wikimarkup for mathematical formulas]].

''Week of [[23 October]] [[2005]]:''
:'''[[Simpson's rule|Simpson's One-Third Rule]]'''
:<math>\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]</math>

''Week of [[16 October]] [[2005]]:''
:'''[[Newton's method|Multidimensional Newton-Raphson method]]'''
:<math> \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}</math>

''Week of [[9 October]] [[2005]]:''
:'''[[Momentum#Conservation_of_momentum|Conservation of momentum]] for a [[control volume]]'''
:<math> {\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</math>

''Week of [[2 October]] [[2005]]:''
:'''[[Bernoulli's equation]]'''<br>
:<math> p+{\rho v^2 \over 2}+{\gamma z}=\mathrm{constant} </math>