# Maths Screencasts

### Cauchy's Residue Theorem

### Complex variable (function of)

- Taylor Series of a function of a complex variable
- Cauchy's Residue Theorem: Example 1
- Cauchy's Residue Theorem: Example 2
- Rouche's Theorem

### Differential Equations: First Order

- Solution of first order ODE using an integrating factor
- Solution of first order ODE by separation of variables

### Differential Equations: Second Order

- Introduction to the Frobenius method for solving a second order linear ordinary differential equation
- Solution of a second order ordinary differential equation with constant coefficients
- Solution of Euler's Equation (a second order nonlinear ordinary differential equation)
- Solution of a second order linear ordinary differential equation using the Frobenius method

### Differentiation

### Forces

### Integration

- ...by substitution
- ...contour integration
- ...hyperbolic functions
- ...line integrals
- ...over an area
- ...trigonometric functions
- Integration of sin x from 0 to π/2
- Integration involving sin
^{2}x - Integration involving sin
^{3}x - Integration involving tan
^{3}x - Integration involving products of sin x and cos x
- ...partial fractions
- ...repeated integration