Handout for APMA E6302: Numerical Methods in PDEs
World Wide Web:
Instructor: Guillaume Bal
Office: Mudd 206
Office Hours: by appointment
Office Phone: (212) 854 4731
Class meeting: MW 11:00-12:15 in Mudd 545
Course Structure: Textbooks:
For the analysis of finite difference and finite element methods, I recommend
For the analysis of spectral methods and implementation in Matlab, I recommend
- S. Larsson and V. Thomee, "Partial Differential Equations
with Numerical Methods", Springer Verlag, 2003.
I will provide lecture notes as well. They are available in their
current form at NumAnal.pdf
Syllabus: This course will cover classical algorithms to
discretize and solve (linear) partial differential equations.
After a brief review of differential equations and linear algebra
relevant to the course, the techniques of finite differences, finite
element methods, and spectral methods will be covered. Students
attending this course are expected to combine a theoretical
understanding of the numerical techniques with a practical
implementation of the algorithms in Matlab. A very good introduction
to Matlab is the "Matlab guide" by Higham and Higham, SIAM, 2000.
L.N. Trefethen, "Spectral methods in Matlab", SIAM, 2000.
There will be a number of take-home homeworks. These homeworks
will count for 70% of the final grade.
The remaining 30%
will be given based on a written project analysing a numerical
algorithm and its Matlab implementation in a field of your