Math222 Syllabus

Course Objectives:
This course continues the material presented in Math 221 by examining the theory and practical implementation of numerical methods for certain nonlinear partial differential equations. By the end of the course, students will understand the mathematical and computational issues that must be considered when designing a numerical method for the nonlinear PDE's typically found in physical applications.
Text:
Most of the material will come from class notes and selected papers. Other useful sources include:
- Randy LeVeque's ``Numerical Methods for Conservation Laws'' from the ETH Lectures in Mathematics Series
- Colella and Puckett's ``Finite Difference Methods for Computational Fluid Dynamics''
Intended Audience:
This is a ``second tier'' graduate course in mathematics intended for both students in the applied math program and other graduate programs in the applied sciences (e.g. Environmental Sciences, Marine Sciences, Physics, Chemistry, etc.)
Prerequisites:
This course will build on the material covered in Math 221.
Topics may include:
- Finite difference methods for one-dimensional gas dynamics
- Methods for the incompressible Navier-Stokes equations
  - Projection Methods
  - Vorticity-Stream Function Methods
  - Psuedo-Spectral Methods
- Particle methods and the N-body problem
- Integral equation and PDE's
  - Integral equations for elliptic PDE
  - Boundary integrals and layer potentials
  - Convolution integrals by the Fast Multipole Method
- Techniques for nonstandard computational domains
  - Adaptive Mesh Refinement
  - Cartesian and body fitted grids
  - Triangularization (for Finite Elements)
  - Moving Grids

Course Objectives:

Text:

Intended Audience:

Prerequisites:

Topics may include: