Numerical Methods II - spring 2007
Prof. Varley: Tues and Thurs 7:00-8:15PM
The course will focus on the numerical solution of some representative partial differential equations occurring in physics (e.g. the wave equation, the diffusion equation, and the Poisson equation). The numerical solution of partial differential equations uses methods that are different from the methods used to solve ordinary differential equations so Numerical Methods I, PHYS 385/685 is NOT a pre-requisite. Also, the techniques for the numerical solution of partial differential equations are easier, more direct, and different from the analytical or formula solution methods so PHYS 301/605 or MATH 301 Mathematical Methods for the Physical Sciences is NOT a prerequisite. Implicit and explicit numerical methods will be examined as well as relaxation methods. Also the conditions for the stability of the numerical solution will be derived and discussed. Curve fitting techniques and the numerical form of the Fourier series and especially the so-called Fast Fourier Transform will be learned.
Mathematica will be used for programming and graphing but it is NOT assumed the student already knows Mathematica.
The course grade will be based on workshops, a term paper, and a take home exam.
Recommended Textbook: Numerical Methods for Physics by Alejandro Garcia, 2nd Edition (Prentice Hall, 2000) ISBN 0-13-906744-2