Methods in Computational Physics, PHYS 510b

Intention:

Furnish beginning graduate students with computational techniques needed for their research, such as programming, data analysis, and use of scientific software. Provide numerical skills useful in today's academic job market.

Outline:

). Useful Software: Mathematica and Xmgrace.

1. Basic Numerical Techniques: interpolation, differentiation, integration, fitting, root finding.

2. Ordinary and Partial Differential Equations: Euler and Runge-Kutta methods, initial-value, and eigenvalue problems.

3. Chaotic Systems: driven damped pendulum, spectral analysis.

4. Monte Carlo Simulations: random number generators, multi-dimensional integrals, many-body systems, Ising model.

5. Matrix Manipulations: eigenvalue problems, multi-dimensional fitting.

6. Molecular Dynamic and Parallel Computing: atomic motion in a solid, message passing interface.

Syllabus:

The grade will be based 50% on homework, and 50% on the term project.

). Useful Software:	Mathematica and Xmgrace.
1. Basic Numerical Techniques:	interpolation, differentiation, integration, fitting, root finding.
2. Ordinary and Partial Differential Equations:	Euler and Runge-Kutta methods, initial-value, and eigenvalue problems.
3. Chaotic Systems:	driven damped pendulum, spectral analysis.
4. Monte Carlo Simulations:	random number generators, multi-dimensional integrals, many-body systems, Ising model.
5. Matrix Manipulations:	eigenvalue problems, multi-dimensional fitting.
6. Molecular Dynamic and Parallel Computing:	atomic motion in a solid, message passing interface.