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.
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- Introduction (Fourier transforms, derivation of conservation laws, parabolic and hyperbolic PDEs)
- Numerical ODEs (briefly)
- Stability, accuracy, and convergence
- Von Neumann analysis
- Diffusion (reaction-diffusion) equation in multiple dimensions
- Nonrectangular geometry (logically quadrilateral grids and embedded grids)
- Methods for advection equation in 1D
- Dissipation and dispersion, modified equations
The first two topics (about 3-4 lectures) are covered in Chapter 5-8 of LeVeque. The rest of the course are covered in chapters 9 and 10 with elements from chapter 11. Instructors might want to supplement material presented from other sources. Table of contents of the relevant chapters are attached
This class will require writing computer programs. Typically four will be assigned for the quarter. You may use any language. If you do not have a strong preference of language, it is recommended that you use MATLAB.