This course on Laplace Transforms aims to teach students the definition and properties of Laplace transforms, how to find Laplace transforms of various functions, solve initial value problems, and understand the convolution theorem. Students will learn skills such as finding Laplace transforms of piecewise functions, using partial fraction decomposition, and applying shifting theorems. The teaching method includes theoretical explanations, step-by-step examples, and proofs of key theorems. This course is intended for learners interested in advanced mathematics, particularly in the field of differential equations and mathematical transformations.
Overview
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.
Taught by
Jonathan Walters
