Math 615 Applied Numerical Analysis

Spring 2012

instructor and contact info:
Ed Bueler
   Chapman 301C       474-7693
   elbueler@alaska.edu     www.dms.uaf.edu/~bueler
textbook:  Morton and Mayers, Numerical Solution of Partial
              Differential Equations
, 2nd ed., Cambridge, 2005.
 time:  MWF 1:00--2:00pm

room:   
Gruening 308

crn:   
38766

Numerical methods and analysis for approximating partial differential equations (PDEs) and related problems on computers.  How to do it in practice and how to determine how good a method is.  How to choose among algorithms when facing in hard problems

Students are encouraged to come with a particular problems in mind, and to do the class project on it.  Lots of computed examples.  Students will use Matlab/Octave to build algorithms and run them on concrete examples.  Emphasis on thinking with matrices and vectors.  We don't just list some finite difference schemes but try to think of them as simple matrix equations in which we write codes to build big matrices for computer solution.  Exposure to nonlinear examples because real problems are nonlinear.

Topics include:

Prerequisites:  Exposure to the use of computers to do mathematics. [= a numerical course of some kind like Math 310, ES 301, Phys 220, and perhaps programming like CS 201].  Undergraduate differential equations.  Undergraduate linear algebra [= Math 314].  Some exposure to Fourier series and the method of separation of variables. [= Math 421 or Math/Phys 611]