Laplace Transforms

This course introduces the Laplace transform through definitions and examples, then covers inverse transforms, translation theorems, unit step functions, convolution, and solving an initial value problem.

Syllabus

The Definition of the Laplace Transform and Three Basic Examples.
Linearity Property of the Laplace Transform and 7 Useful Transforms to Know! Full Example..
Find the Laplace Transform of cos(kt) using the Definition.
Laplace Transform of a Piecewise Function Using the Definition.
Inverse Laplace Transform and Linearity of Inverse Laplace :: With Examples.
Use Laplace Transform to Solve Initial Value Problem :: Full Example with Partial Fraction Decomp.
Inverse Laplace Transform :: Completing the Square :: First Translation Theorem in Reverse.
Inverse Laplace Partial Fraction Decomposition :: Overall Strategy.
Shifting Laplace Transforms :: The First Translation Theorem for Laplace Transforms.
Laplace Transform With Unit Step Functions :: Second Shifting/Translation Theorem.
Proof of the Convolution Theorem :: Laplace Transforms.