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Solving PDEs with the Laplace Transform - The Heat Equation

Steve Brunton via YouTube

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Overview

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This course demonstrates how to solve the heat equation on a semi-infinite domain using Laplace transforms in time. It covers homogeneous and particular solutions, initial and boundary conditions, and interpreting the result in frequency and time domains.

Syllabus

Overview and Problem Setup
How Classic Methods e.g., Laplace Relate to Modern Problems
Laplace Transform with respect to Time
Solving ODE with Forcing: Homogeneous and Particular Solution
The Particular Solution and Initial Conditions
The Homogeneous Solution and Boundary Conditions
The Solution in Frequency and Time Domains

Taught by

Steve Brunton

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