Physics 329: Introduction to Computational Physics: Proposed Syllabus

Unix: 2 weeks

• Week 1: Overview, Unix basics (filesystems, commands, standard I/O, X-interface ...)
• Week 2: Basic shell programming and Web authoring.

Maple/Mathematica: 3 weeks

• Week 3: Introduction, command-line and GUI interfaces, basic commands and interactive problem solving.
• Week 4: Basic Maple/Mathematica programming.
• Week 5: Plotting facilities, interfacing with other systems, sample applications.

Scientific Programming (F77/F90/C): 3 weeks

• Week 6: Use of target language in Unix environment (compilation, linking, make, RCS ...), basic programming elements (variables, basic statement types, control structures ...)
• Week 7: Modularization (functions/subroutines), arrays and other data structures useful in scientific programming.
• Week 8: Integration and interaction of programs with other tools (plotting packages, visualization packages, Maple/Mathematica ...), porting and testing codes on different architectures/machines.

Solution of Linear Systems: 1 week

• Week 9: The LU decomposition algorithm, using "canned" software for solving full linear systems, applications (circuit analysis ...)

Elementary Finite Difference Methods: 2 weeks

• Week 10: The nature of discrete equations derived from continuum systems, expected behaviour of FD approximations (convergence & accuracy), polynomial interpolation.
• Week 11: Numerical differentiation and numerical integration, applications.

Non-linear Equations (Root Finding): 1 week

• Week 12: Bisection (binary search), Newton's method, Newton's method for systems of non-linear equations.

Particle Simulations: 1 week

• Week 13: Typical equations of motion for interacting particle systems, discretization of EOM, applications (n-body gravitational problem ...).

Solution of ODEs: 1 week

• Week 14: Using "canned" software to solve ODEs and simple systems of ODEs.

Random Numbers, Monte Carlo and Stochastic Methods: 1 week

• Week 15: Random number generators, generating non-uniformly distributed random numbers, simple Monte Carlo simulations (diffusion limited aggregation ...).