Chapter 18 · Partial Differential Equations
18.03
Separation of Variables
Guess a solution that's a product u = X(x)T(t). The PDE splits into two ODEs linked by a separation constant, and the boundary conditions allow only special values of it: eigenvalues.
About 16 minutes
You'll learn to
- →Separate variables in a linear PDE
- →Solve the eigenvalue problem X'' + λX = 0 with zero boundary values
- →Write product solutions of the heat equation
- →Combine product solutions to match a finite sine sum