Announcements

There will be no class in the week of Dec 10. Two make-up classes will be held in the evening of Tuesday, Dec 4, from 7pm to 9:45pm (with a 15 minute break between two 75 classes) at Van Vleck B 139.

Syllabus:

• Numerical Methods for Ordinary Differential Equations
  - Basic ODE Theory
  - Explicit and implicit methods, stability, Runge-Kutta and multistep methods, stiff problems
• Finite Difference Methods for Parabolic Partial Differential Equations
  - Numerical differentiations
  - Consistency, stability and convergence
  - Multidimensional problems
• Finite Difference Methods for Hyperbolic Partial Differential Equations
  - Linear hyperbolic equations and their numerical discretizations
  - Basic theory for nonlinear hyperbolic equations: shock formation, weak solution and entropy condition, Riemann problem
  - Shock capturing methods: Godnov and Roe methods, high resolution methods (TVD and ENO), kinetic and relaxation methods
  - Hamilton-Jacobi equations and the level set method for front propagation
• Finite Volume Methods for Partial Differential Equations
• Spectral Methods for Partial Differential Equations
  - Fast Fourier transform
  - Fourier spectral method, pseudospectral methods