Chapter 18 · Partial Differential Equations
18.04
Fourier Series Solutions
Any reasonable starting profile on [0, L] is an infinite sum of sines (or cosines). Orthogonality gives each coefficient as an integral, and then each term evolves on its own.
About 16 minutes
You'll learn to
- →Compute Fourier sine and cosine coefficients on [0, L]
- →Use orthogonality to explain the coefficient formulas
- →Know what a series converges to at jumps and endpoints
- →Solve the heat equation for general initial data