







Mathematical and Computational Physics using Mathematica






Organization:  University of California, San Diego 
Department:  Department of Physics 






College






A first course in mathematical and computational physics for undergraduates at the junior level. Students learn to solve realworld problems using both analytic and numerical methods. The course assumes familiarity with introductory calculus, linear algebra and analytic solution of simple ODEs.






The Mathematica Book by S. Wolfram Advanced Engineering Mathematics by R. MalekMadani






A combined analytic and Mathematicabased numerical approach to the solution of common applied mathematics problems in physics and engineering. This is a 2quarter course sequence taught for the past two years in the physics department at UC San Diego. So far students have given the course high ratings, although they find the material rather demanding. The students particularly like being able to "see" the results of their analyses using the graphics and animation capabilities of Mathematica. Topics: In part A: an introduction to Mathematica; physical approach to ODEs and their numerical solution; initial and boundary value problems; chaotic systems and molecular dynamics; Fourier series and integrals; linear operators and eigenmodes; Green's functions; solution of heat, Poisson, wave and Schroedinger equations in various separable geometries. In part B: Numerical solution of PDEs using spectral and grid methods; waves in inhomogeneous media via the WKB method; dispersion, group and phase velocities, raytracing and wavepackets; nonlinear waves, solitons and shocks; random systems, probability densities; random walk with and without bias, the rejection method, the FokkerPlanck equation, thermal equilibrium and the Boltzmann distribution; Einstein relations; the MonteCarlo method.












http://sdphca.ucsd.edu/105a/105a.html http://sdphca.ucsd.edu/105b/105b.html

