Course description: This course will present an introduction to a variety of numerical methods applied to problems in physics. An undergraduate background in science or engineering and some familiarity with computer programming is required.
Textbook: Numerical Methods for Physics, 2nd Edition, A.L. Garcia, Prentice Hall (2000). For info on the text, go to http://www.algarcia.org/nummeth/nummeth.html. If you buy your copy online, be sure to get the SECOND EDITION (white cover). If you find an error in the book which is not listed in the current errata, I'll give you 5 points of homework extra credit (equal to one homework exercise). Naturally, only the first person to point out the error receives the extra credit; errors found will be announced in class.
Exams: There will be no midterms; the final exam (Monday, December 15, 1945-2200) counts for 10% of the grade.
Computer Access: You may use any computers at your disposal.
Language: You may use any language you wish to complete the assignments. I regularly use C, C++, FORTRAN and MATLAB but can also read several others. A student edition of MATLAB, which includes a manual, is available in the bookstore (if no copies are in the physics section then look under the computer science or engineering textbooks). For information on how to download the programs in the textbook go to http://www.algarcia.org/nummeth/nummeth.html
Homework: Some homework exercises are pencil and paper calculations, similar to those in your other physics classes, but the majority involve programming projects. For the latter you should turn in print-outs of your source code and sample outputs. Exercises will be assigned continuously, to be turned in at each class meeting. If you are unable to come to class, your homework exercises may be turned in by e-mail sent as PDF files (please limit attachments to less than 2 Megabytes per e-mail message and 10 Megabytes per assignment). The homework will count 90% of the course grade. Late homework will not be accepted. However, you may miss up to five exercises with no penalty.
Homework Points: Each homework exercise will be worth 5 points. Three points will be assigned based on producing the required results and two points will be assigned based on your organization and analysis of those results. Using a computer it is easy to vomit a large volume of paper, which you are strongly discouraged from doing. For the first few assignments I'll be lenient with regards to style but by the third week you are expected to turn in well-organized work. Hand-written comments are fine; substance is more important than typeset beauty.
Extra Credit: There is no specific extra credit however, on occasion, bonus points will be given when your homework solutions are exceptionally good, such as when you find and document some interesting results that go beyond the original scope of the problem. If I read your homework and say "Cool!" then you'll get a bonus point.
Ethics: Your own commitment to
learning, as evidenced by your enrollment at
Disabilities: If you need course adaptations or accommodations because of a disability, or if you need special arrangements in case the building must be evacuated, please make an appointment with me as soon as possible, or see me during office hours. Presidential Directive 97-03 requires that students with disabilities register with DRC to establish a record of their disability.
Emergencies: If you hear a continuous alarm or are told to evacuate the building, walk quickly to the nearest stairway at the end of each hall. Do not use the elevator. Take your personal belongings with you. Be quiet and follow instructions. Move away from the building and do not return until informed by police or coordinators.
|
Lecture |
Topics |
Sections |
Date |
|
1 |
Programming basics |
1.2-3 |
Mon. 8/23 |
|
2 |
Simple programs |
1.4 |
Wed. 8/27 |
|
* |
Labor Day |
* |
Mon. 9/1 |
|
3 |
Precision & round-off |
1.5 |
Wed. 9/3 |
|
4 |
Projectile motion; Simple methods for ODEs |
2.1 |
Mon. 9/8 |
|
5 |
Simple pendulum; Verlet's method |
2.2 |
Wed. 9/10 |
|
6 |
Kepler problem |
3.1 |
Mon. 9/15 |
|
7 |
Runge-Kutta methods |
3.2 |
Wed. 9/17 |
|
8 |
Adaptive methods |
3.3 |
Mon. 9/22 |
|
9 |
Lorenz model |
3.4 |
Wed. 9/24 |
|
10 |
Steady states; Linear systems of equations |
4.1-2 |
Mon. 9/29 |
|
11 |
Linear systems of equations (cont.) |
4.2-3 |
Wed. 10/1 |
|
12 |
Solving nonlinear equations |
4.4 |
Mon. 10/6 |
|
13 |
Analysis of data; Curve fitting |
5.1 |
Wed. 10/8 |
|
14 |
Fast Fourier transforms (FFTs) |
5.2 |
Mon. 10/13 |
|
15 |
Normal modes |
5.3 |
Wed. 10/15 |
|
16 |
Fundamentals of PDEs |
6.1 |
Mon. 10/20 |
|
17 |
Diffusion equation; FTCS scheme |
6.2-3 |
Wed. 10/22 |
|
18 |
Hyperbolic equations |
7.1 |
Mon. 10/27 |
|
19 |
Traffic flow |
7.2 |
Wed. 10/29 |
|
20 |
Traffic flow (cont.) |
7.2 |
Mon. 11/3 |
|
21 |
|
8.1 |
Wed. 11/5 |
|
22 |
Poisson's equation; Spectral methods |
8.2 |
Mon. 11/10 |
|
23 |
Von Neumann stability |
9.1 |
Wed. 11/12 |
|
24 |
Implicit methods |
9.2 |
Mon. 11/17 |
|
25 |
Special functions |
10.1 |
Wed. 11/19 |
|
26 |
Quadrature; Romberg algorithm |
10.2 |
Mon. 11/24 |
|
* |
Thanksgiving |
* |
Wed. 11/26 |
|
27 |
Probability & Statistical Mechanics |
11.1 |
Mon. 12/1 |
|
28 |
Random number generators |
11.2 |
Wed. 12/3 |
|
29 |
Kinetic Theory |
11.3 |
Mon. 12/8 |
|
30 |
Leeway |
--- |
Wed. 12/10 |