Syllabus Detail

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 228C: 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
Prerequisites:
MAT 128C
Suggested Schedule:

Topics Covered

  • Hyperbolic conservation laws
  • Godunov method, wave propagation, and high-resolution methods

 

Detailed contents are attached and covered in Chapters 10-18 of “Numerical Methods for Conservation Laws” by LeVeque.

A computer assignment related to these topics is required.

  • Advanced in-depth topic to be chosen by the instructor in charge.

 

Students are required to submit a final project on the advanced topic covered. This could be a project assigned by the instructor or related to the student’s research but using techniques presented.

Advanced topics include but not limited to:

  • Level Set Methods
  • Spectral Methods
  • Immersed Boundary Methods and Irregular Geometry
  • Mesh Generation
  • Fast Multipole Method
  • Simulations and Stochastic Differential Equations
  • Computational Fluid Dynamics