Peter Blomgren
San Diego State University
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Math 693b: Advanced Numerical Analysis Spring 2017
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Video: Crazy surface waves on a torus!
If the embedded video does not work, here are direct links: [mp4, webm, mpeg]

Notes and Resources...

are linked from the schedule.

Catalog description

Methods for differential equations. Elliptic and parabolic partial differential equations. Stiff ordinary equations.

Prerequisites
  • 1. Math 531 (Partial Differential Equations)
  • 2. Math 537 (Ordinary Differential Equations)
  • 3. Math 693a (Numerical Matrix Analysis: Numerical Optimization)

Computational Resources:

You must have access to a somewhat modern version of Matlab, or some other computational environment that you are comfortable using. Class accounts for the labs will be available. You can also use SDSU's Rohan Sun Enterprise system or another capable system. [How to open a ROHAN account].

Students with Disabilities:

If you are a student with a disability and believe you will need accommodations for this class, it is your responsibility to contact Student Disability Services at (619)594-6473. To avoid any delay, please contact Student Disability Services as soon as possible. Please note that accommodations are not retroactive, and cannot be provided until an accommodation letter from Student Disability Services is received by the Professor.

Required Text and Reading Materials:

Finite Differences And Partial Differential Equations, 2nd edition. John C. Strikwerda, Society for Industrial and Applied Mathematics, November 2004. ISBN 0-8987-1567-9. [Errata] Note: SIAM Student Membership is (still, hopefully) FREE, which means you can get the member price! (30% off)

Class web page [http://terminus.sdsu.edu/SDSU/Math693b/], and handouts.

Course Outline (as of 1/17/2017):

Strikwerda: 1-Hyperbolic Partial Differential Equations; 2-Analysis of Finite Difference Schemes; 3-Order of Accuracy of Finite Difference Schemes; 4-Stability for Multistep Schemes; 5-Dissipation and Dispersion; 6-Parabolic Partial Differential Equations; 7-Systems of Partial Differential Equations in Higher Dimensions; 8-Second-Order Equations; 9-Analysis of Well-Posed and Stable Problems; 10-Convergence Estimates for Initial Value Problems; 11-Well-Posed and Stable Initial-Boundary Value Problems; 12-Elliptic Partial Differential Equations and Difference Schemes; 13-Linear Iterative Methods; 14-The Method of Steepest Descent and the Conjugate Gradient Method. Trefethen Spectral Methods. Other Sources: Mimetic Methods, The Finite Element Method.

Professor

Peter Blomgren
blomgren DOT peter AT gmail DOT com
Class hours: TuTh 12:30p – 1:45p, GMCS-325
Office hours: TuTh 11:00a – 11:50a, 2:00p – 2:50p, GMCS-587, and by appointment.

Copyright © 2017 Peter Blomgren.