Course: CAAM 31100=STAT 31100, CMSC 37812, MATH 38309
Title: Mathematical Computation III: Numerical Methods for PDEs
Instructor(s): Jeremy Hoskins
Teaching Assistant(s): TBA
Class Schedule: Sec 1: MW 10:30 AM-11:50 PM in TBA
Textbook(s): Larsson, Thomee, Partial Differential Equations with Numerical Methods
Description: This course covers important classes of numerical methods for partial differential equations, notably finite differences and finite element methods. The emphasis is on understanding the accuracy of these methods with a view on the role they play in today's science and engineering problems. The class is suitable for graduate students from all departments who have affinities with applied mathematics.
(Superset of the) topics:
1. Short review of the theory of ODEs and PDEs
2. Finite differences approaches: stability, consistency, convergence
3. Finite element methods: theory, numerical analysis, implementation
4. Some basic numerical approaches for problems with multiple time and/or space scales
5. A quick incursion into simulations of equations with random parameters
Prerequisites: Numerical linear algebra at the level of STAT 24300/30750 and basic Fourier series.