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PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation

Steve Brunton via YouTube

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Overview

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This course demonstrates separation of variables for solving Laplace’s equation in two dimensions and finding the steady-state heat distribution on a rectangular plate. It connects the resulting ordinary differential equations with sine and cosine eigenfunctions and Fourier coefficients.

Syllabus

Overview and Problem Setup: Laplace's Equation in 2D.
Linear Superposition: Solving a Simpler Problem.
Separation of Variables.
Reducing the PDE to a system of ODEs.
The Solution of the PDE.
Recap/Summary of Separation of Variables.
Last Boundary Condition & The Fourier Transform.

Taught by

Steve Brunton

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