Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 228A: Numerical Methods for Partial Differential Equations
Approved: 2011-06-02,

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
R. J. LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. SIAM, 2007.
http://epubs.siam.org/doi/book/10.1137/1.9780898717839
Search by ISBN on Amazon: 978-0-89871-629-0

Course Description:

The first quarter (228A) will focus on elliptic problems. The topics proposed are:
  • Introduction to Poisson equation
  • Finite differences
  • Basics of Finite elements (if time allows)
  • Convergence and accuracy
  • Iterative methods
  • Multigrid
  • Krylov subspace methods, CG & GMRES
  • FFT

      These topics are covered in chapters 1,2,3 and 4 or LeVeque and Chapters 1-5 of Briggs. See Table of contents attached.

      Programming

      This class will require writing computer programs. You may use any language. If you do not have a strong preference of language, it is recommended that you use MATLAB. Four programming exercises that include analytic solution to problems will be assigned each quarter.