Physics 381C: Computational Physics: Course Topics

Unix: 2 lectures

• Unix fundamentals
• Unix as a programming environment for scientific computation

Maple: 2 lectures

• Overview of Maple features for day-to-day symbolic computation
• Introduction to Maple programming

Scientific Programming and Analysis: 2 lectures

• Importance of using and building tools
• Data abstraction and program organization
• Program verification
• Program/program and program/user communication.

Solution of ODEs and Applications: 3 lectures

• Review of pertinent theory
• Using canned ODE software
• Sample applications from non-linear dynamics.

Solution of Linear Systems: 2 lectures

• Review of pertinent theory
• Using canned software for solving linear systems
• Tridiagonal and banded solvers

Fast Fourier Transforms: 1 lecture

• Review of DFT.
• Overview of FFT algorithm, canned software

Overview of Finite Difference Approximations (FDAs): 2 lectures

• Derivation of FDAs
• Consistency, accuracy, convergence, stability

Finite Difference Methods for Elliptic PDEs: 4 lectures

• Model problem, discretization
• Relaxation, over-relaxation, convergence analysis
• The Multi-grid method

Finite Difference Methods for Parabolic PDEs: 3 lectures

• Model problem, discretization
• Stability analysis
• Implicit schemes, ADI schemes
• Visualization

Finite Difference Methods for Hyperbolic PDEs: 5 lectures

• Model problem, discretization
• Stability analysis
• Boundary conditions
• Introduction to RNPL
• Visualization

Miscellaneous Topics and Student Presentations: 4 lectures