This course involves using computers to study of physics problems that are not amenable to analytical calculations.
The topics covered are:
1. Finite differences and solution to ordinary differential equations
Projectile problem with air resistance, Kepler problem, Chaos in Lorenz model
2. Numerical Integration
Specific heat, Cornu spiral, ...
3. Random variables, Probability distribution functions, Monte Carlo Techniques
Relativistic kinematics, Simulation of experimental resolution
4. Linear Algebra
Resistor network, Steady states of various ODEs:Ginzburg-Landau, Lotka-Volterra
5. Nonlinear System of Equations
Newton's method, Solving transcendental equations, Quantum mechanics problems
6. Data Analysis
Least squares, Curve fitting, Nonlinear minimization, Fourier transform, FFT, Spectral analysis
7. Partial Differential Equations
Diffusion equation-Neutron diffusion, Relaxation equation-Electrostatics, Schrodinger Equation-Wave packet evolution
Physics 241 and 311. Math 320 or 340
Knowledge of programming
Recommended CS 412 (Numerical analysis)
This courses is designed to improve conceptual understanding of various physics processes by exploring them in a more quantitative and visual way. It will also provide computational skills - namely scientific programming, data analysis, numerical analysis and Monte Carlo techniques, that are necessary for graduate research or future career.
The course includes lectures on physics topics and numerical methods background, and are followed by extensive "lab"work where students modify or write programs to study physics.
Text used in Fall 2001
Numerical Methods for Physics, Second Edition, Alejandro L. Garcia, Prentice Hall