LECTURE 1: A model problem

A hyperbolic scalar PDE
A difference method
Dissipative approximations

LECTURE 2: Initial value problems for hyperbolic PDE

Systems in one space dimension
Systems in several space dimensions

LECTURE 3: Initial-boundary value problems (IBVP) for PDE

A model problem
Analysis of wellposedness
The energy method

LECTURE 4: Difference methods for IBVP, (I)

A semidiscrete model problem
The energy method for stability analysis
The Laplace transform technique
The Kreiss condition

LECTURE 5: Difference methods for IBVP, (II)

Error estimates
The method of lines
Fully discrete approximations