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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

This course teaches the technique of Separation of Variables to solve Partial Differential Equations (PDEs), focusing on solving Laplace's equation in two dimensions for steady-state heat distribution on a rectangle. The learning outcomes include understanding linear superposition, reducing PDEs to systems of ODEs, and applying the Fourier Transform. The course is suitable for individuals interested in physics and engineering seeking to enhance their problem-solving skills in PDEs.

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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