Introduction to PDEs; first-order PDEs and characteristics, the advection equation. Finite-difference methods for ODEs, truncation error. The wave equation: exact solution, reflection of waves. The heat equation: exact solution, fixed and insulating boundary conditions. Forward, backward and Crank-Nicholson numerical methods for the heat equation, truncation errors and stability analysis. Types of second-order PDEs; boundary and/or initial conditions for well-posed problems. Exact solutions of Laplace's equation. Iterative methods for Laplace's equation; convergence. Numerical methods for the advection equation; upwind differencing. Separation of variables for the wave and heat equations. -- Course Website
Instructor: Associate Professor Michael Page
Prerequisites: MTH2010 or MTH2015, and MTH2032, or equivalent
