Physics 410 - Computational Physics - Fall 2000

Physics 410: Computational Physics: Final Exam Review Topics

Last update: Wednesday December 13, 6:00 AM

For the final exam on Monday, December 18 , 3:30-5:00 PM, HEBB 12, you are responsible for the following:

Linear Systems
- Derivation and solution of various types of linear systems arising from finite difference approximations of boundary value problems---you do not need to memorize specific LAPACK routine names and/or calling sequences, but be aware of the different types of systems (tridiagonal and banded) which were discussed.
Finite Difference Methods
- Centred, O(h^2) approximations to first and second derivatives
- Construction of finite difference approximations for:
  - Linear and non-linear boundary value problems
  - Simple dynamical problems (such as the simple harmonic oscillator)
- Expected convergence behaviour for solutions of difference equations
- Richardson expansions, Richardson extrapolation, and applications of extrapolation techniques in, e.g., derivation of higher-order difference approximations.
Root Finding & Non Linear Equations
- Bisection (binary search) for a single non-linear equation.
- Newton's method for a single non-linear equation.
- Newton's method for systems of non-linear equations.
Solution of ODEs
- Casting of systems of ODEs into canonical, first-order form

IMPORTANT NOTES:

The exam is CLOSED BOOK---NO reference materials (i.e. no cheat-sheets) may be used during the exam.
Be sure to review Homeworks 4, 5 and 6, including the keys for those cases where you had difficulty
Although the exam is scheduled for 90 minutes, it has been designed to take less time to complete than the midterm, i.e. you should be able to complete it in an hour or less.