Laplace Transforms and Solving ODEs

This course introduces Laplace transforms and their properties, then applies them to solve ordinary differential equations. It emphasizes inverse transforms, convolution, piecewise and periodic functions, discontinuities, and impulse modeling with the Dirac delta function.

Syllabus

Intro to the Laplace Transform & Three Examples.
3 Properties of Laplace Transforms: Linearity, Existence, and Inverses.
The Laplace Transform of Derivatives and Integrals.
Using Laplace Transforms to solve Differential Equations ***full example***.
Translation and Inverse Laplace Transforms.
Inverse Laplace Transform Example using Partial Fractions.
How to use Laplace Transform to solve Differential Equations ** Full Example **.
The Convolution of Two Functions | Definition & Properties.
Laplace Transform and Piecewise or Discontinuous Functions.
Periodic Functions and the Laplace Transform.
The Dirac Delta 'Function': How to model an impulse or infinite spike.
Solving ODEs with Delta functions using Laplace Transforms.