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Mathematical and Computational Physics using Mathematica

Daniel Dubin
Organization: University of California, San Diego
Department: Department of Physics
Education level


A first course in mathematical and computational physics for undergraduates at the junior level. Students learn to solve real-world 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. Malek-Madani

A combined analytic and Mathematica-based numerical approach to the solution of common applied mathematics problems in physics and engineering.

This is a 2-quarter 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.


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, ray-tracing and wavepackets; nonlinear waves, solitons and shocks; random systems, probability densities; random walk with and without bias, the rejection method, the Fokker-Planck equation, thermal equilibrium and the Boltzmann distribution; Einstein relations; the Monte-Carlo method.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations
*Science > Physics