E6302 Handout

Handout for APMA E6302: Numerical Methods in PDEs

World Wide Web: http://www.columbia.edu/~gb2030

Instructor: Guillaume Bal

  • Office: Mudd 206
  • Office Hours: by appointment
  • Office Phone: (212) 854 4731
  • e-mail: gb2030@columbia.edu
  • 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
    • S. Larsson and V. Thomee, "Partial Differential Equations with Numerical Methods", Springer Verlag, 2003.
    For the analysis of spectral methods and implementation in Matlab, I recommend
    • L.N. Trefethen, "Spectral methods in Matlab", SIAM, 2000.
    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.
  • Grading:

  • 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 choice.

  • Guillaume Bal