Physics 410: Computational Physics: Final Exam Review Topics
Last update: Wednesday November 28, 12:00 PM
For the final exam on Friday, December 14, 8:30-10:00 AM, CHEM 124,
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 FDAs for linear and non-linear boundary value problems.
- Richardson expansions, expected behaviour of solution error, convergence testing.
- Solution of ODEs
- Casting of systems of ODEs into canonical, first-order form
- Initial-value problems vs boundary value problems.
- Calibration, independent-residual evaluation
- Applications:
- Definite integrals
- Dynamical systems
- Method-of-lines for time-dependent PDEs
- Solution of 2-pt BVPs via shooting
- 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.
IMPORTANT NOTES:
- The exam is CLOSED BOOK---NO reference materials may be used during the exam.
- Be sure to review Homeworks 4 and 5, including the keys for those cases
where you had difficulty
- Although the exam is scheduled for 90 minutes, it will be designed to take
less time to complete than the midterm, i.e. you should be able to
complete it in an hour or less.