Chapter 18 · Partial Differential Equations
18.11
Fourier Transform Methods
On an infinite line, transform in x: the heat equation becomes an ODE for each frequency, and the solution is the start convolved with a spreading Gaussian, the heat kernel.
About 16 minutes
You'll learn to
- →Transform a PDE in x into ODEs in t
- →Derive and interpret the heat kernel
- →Solve the heat equation on the whole line by convolution
- →Relate Fourier methods to d'Alembert's formula and half-plane problems