### Mathematics

Resources related to mathematics

## Differential Equations

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

The play-list consisting of 32 videos can be found on YouTube.

Derivates:
 $e^{\alpha x} = F(x); \frac{dF}{dx} = \alpha F$ $\frac{d \sin(kx)}{d x} = k \cos(x)$ $\frac{d \cos(kx)}{d x} = -k \sin(x)$ $\frac{d [ \cos(kx)+ i \sin(k x)]}{d x} = i k [\cos(kx)+ i \sin(k x) ]$