Laplace transform for solving IVPS

Inverse Laplace transform

Introduction to Laplace transforms

Power series method, example of 2nd order ODE

Radius of convergence

The power series method

Termwise differentiation of a power series

Intro and review of power series

2nd Order, non-homogeneous, constant coefficients (Variation of Parameters)

Mathematical Models using 1st order ODEs

Exact Differential equations

Benoulli equations

Substitution methods part 2

Substitution Methods part 1

Infinite series - The Geometric series

Infinite Series - Partial sums

Sequences - Increasing, decreasing, bounded and monotonic sequences

Convergence and Divergence of a sequence - The squeeze theorem and another short theorem

Approximate Integration - Midpoint rule

integration and partial fractions - Some more examples

Partial fractions - Cases 3 and 4

Trigonometric Substitutions

Integration by parts - Do's and don'ts

Factorisation - Difference of two squares

Factorisation - General quadratics case 2

Factorisation - General quadratics

Composite Simpsons Rule - how to use the formula

Numerical Integration - Gaussian-Legendre Quadrature

Numerical Integration - Gaussian Quadrature

Newton's method for solving nonlinear systems of Algebraic equations