10. The wave equation in higher dimensions

Part 1: The Euler–Poisson–Darboux equation. Solution for n=3 via spherical means and reduction of the EPD equation to the 1-dimensional wave equation. Solution for n=2 via descent from n=3.

Part 2 (optional): Solution for odd n>3 via reduction of the EPD equation with parameter n to the EPD equation with parameter n-2. Solution for even n>3 via descent.

Correction: In the formula for V(r,t) at 29:13, "r ± t" should be "t ± r" everywhere (this is corrected later in the video, at 31:20).

Sidansvarig: Hans Lundmark
Senast uppdaterad: 2023-02-27