Laplace Transforms in Differential Equations 📚

In this lecture we look at Laplace transforms which gives a way to turn certain differential equation problems into algebra problems (in particular partial fractions). While the definition can be unwieldy to use we will find that we can build up a table of rules that lets us handle many common cases and so we also start populating our table of Laplace transform rules.

More information: https://www.calc4.org/flipped-fall-2023
Presenter: https://www.stevebutler.org/

0:00 Introduction to Laplace transforms
8:13 Basic properties of Laplace transforms
14:59 Laplace transform of exponential functions
22:02 Laplace transform of function times an exponential
27:00 Laplace transform of sine/cosine
33:35 Laplace transform of sine/cosine (alternative)
37:57 Laplace transform of t^a and Gamma function
51:13 Example (combining some rules)
55:01 Table of what we have so far