Unit · year 3
MU-305 · Partial Differential Equations
Threads change · space5 theorems
The heat, wave and Laplace equations and the methods that solve them.
Theorems in this unit
T-100
Separation of variables
Reducing a PDE to ODEs via product solutions.
T-101
d'Alembert's solution
The 1D wave equation solved by travelling waves.
T-102
The maximum principle
A harmonic function attains its extrema on the boundary.
T-103
Convergence of Fourier series
When and how a periodic function equals its Fourier series.
T-104
The method of characteristics
First-order PDEs solved along characteristic curves.