s4aysnek's Website

I really like sigma

First Impressions

\oint_C {E \cdot d\ell = - \frac{d}{{dt}}} \int_S {B_n dA} \\ V = IR = I\left( {\frac{L}{{\sigma A}}} \right) = I\left( {\frac{{\rho L}}{A}} \right)

\bar{x} = \lim_{n\to\infty}[\frac{\sum_{i=1}^n \bar{x}_if(\bar{x_i})\Delta{x}}{\sum_{i=1}^n f(\bar{x}_i)\Delta{x}}] \quad \bar{y} = \frac{1}{2}\lim_{n\to\infty}[\frac{\sum_{i=1}^n f(\bar{x}_i)^2 \Delta x}{\sum_{i=1}^n f(\bar{x}_i) \Delta x}] \\~\\ \bar{x} = \frac{\int_a^b xf(x) \,dx}{\int_a^b f(x) \,dx} \quad \bar{y} = \frac{\frac{1}{2} \int_a^b f(x)^2 \,dx}{\int_a^b f(x) \,dx}

\begin{align} \frac{dy}{dx} &= xy = \frac{x}{\frac{1}{y}}\\ \frac{1}{y} \,dy &= x \,dx\\ \int{\frac{1}{y} \,dy} &= \int{x \,dx}\\ \ln|y| &= \frac{x^2}{2} + C\\ |y| &= e^{\frac{x^2}{2} + C}\\ y &= \pm e^{\frac{x^2}{2} + C}\\ &= \pm e^C e^{\frac{x^2}{2}} \end{align}