Physics 410: Computational Physics: Final Exam Review Topics and Course Wrap Up

Final Exam

1. Linear Systems
   • Definition
   • Outline of solution via LU decomposition
   • 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) that were discussed.
2. 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.
3. 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.
4. Root Finding & Non Linear Equations
   • 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 2.5 hours, it will be designed to take roughly the same amount of time as the midterm, i.e. you should be able to complete it in 1.5 hours or less.

Course Wrap Up

1. If you have not yet done so, send me a message if you do not intend to complete Homework 5
2. If you do intend to complete Homework 5, send me a message when you have completed it.
3. Deadline for submission of HW 5 is Wednesday, December 3, 12 noon. This deadline is absolutely firm; at that time, hard copy of the key to HW 5 will be available outside my office. I will endeavour to have comments back to those of you who have completed the assignment by Friday, December 5, 12 noon.
4. Deadline for submission of term projects is Monday, December 8, 4:00 PM. This deadline is also absolutely firm. Term projects are either to be submitted to me in person, or left in my mailbox in the physics main office. Do not attempt to slide the projects under my office door. Hard copies of term projects must be provided (i.e. electronic-only submissions are not accepted), and these copies will not be returned. Should you wish to get feedback on your project, you are welcome to do so once the grades have been submitted (i.e. preferably next term).
5. You are welcome and in fact encouraged to supplement your written report with "multi-media" materials (e.g. mpeg animations), published via your web page for the course. These web pages will remain active for at least the duration of the academic year.