CHAPTER 20
Partial Differential Equations
What a PDE describes
Functions of several variables and equations involving partial derivatives.
Classification
First- and second-order equations; elliptic, parabolic and hyperbolic types.
Heat equation
Diffusion, initial and boundary conditions.
Wave equation
Propagation, vibrating systems and characteristic behaviour.
Laplace equation
Steady states, harmonic functions and boundary-value problems.
Separation and Fourier methods
Eigenfunction expansions and classical solution techniques.