(DiffEQ, Fall 23) 24 - Introduction to Laplace transforms
Автор: Beard Meets Calculus
Загружено: 2023-10-31
Просмотров: 2679
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
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