Physics 410: Computational Physics: Course Topics

Unix & Overview: 4 lectures

• Overview of course goals, philosophy of scientific computing
• Unix fundamentals for scientific computing

Maple: 4 lectures

• Use of a modern "symbolic manipulation" language for routine computations
• Maple as a powerful environment for exploratory scientific programming

Scientific Programming in Fortran: 6 lectures

• Fortran 77 programming of simple scientific applications
• Numerical computation concerns: error analysis and bug-proofing strategies
• Integration and interaction of Fortran programs with other tools ("make", "sort", graphing programs, maple, etc.)
• Porting code to different architectures, portability.

Solution of Linear Systems: 3 lectures

• The LU decomposition algorithm
• Using "canned" software for solving linear systems
• Solution of tridiagonal and banded-systems

Finite Difference (FD) Methods: 8 lectures

• The nature of discrete equations derived from continuum systems
• Expected behaviour of FD approximations (convergence & accuracy)
• Polynomial Interpolation
• Numerical differentiation and numerical integration

Non-linear Equations (Root Finding): 3 lectures

• Bisection (binary search)
• Newton's method
• Newton's method for systems of non-linear equations

Solution of ODEs: 6 lectures

• Review of ODE theory
• Canonicalizing systems of ODEs
• Using "canned" software to solve systems of ODEs
• Applications

Random Numbers, Monte Carlo and Stochastic Methods: 3 lectures

• Random number generation and trustworthiness
• Generating non-uniformly distributed random numbers
• Simple Monte Carlo algorithms
• Simulation and visualization of diffusion-limited aggregation