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.
Enrollment: The course is open to any SJSU student; others should enroll through Open University.
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.
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 (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: Exercises will be assigned continuously. Most of the exercises involve programming projects. The homework will count 85% of the course grade. Homework exercises may be turned in by fax (408-924-2917) or by e-mail sent as PDF files (please limit attachments to less than 2 Megabytes). Late homework will not be accepted.
Exams: There will be one midterm exam that counts for 15% of the grade; there is no final exam.
Computer Access: You may use any computers at your disposal.
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.
| Assignment | Exercises | Due date |
|---|---|---|
| 1 | 1.9 | Tuesday 1/30 |
| 2 | 1.3a | Thursday 2/1 |
| 3 | 1.7, 1.15, 1.18 | Tuesday 2/6 |
| 4 | 1.21 | Thursday 2/8 |
| 5 | 2.1, 2.3, 2.6a | Tuesday 2/13 |
| 6 | 2.12(a,b) | Thursday 2/15 |
| 7 | 2.15, 2.21, 3.3 | Tuesday 2/20 |
| 8 | 3.8, 3.10(a) | Thursday 2/22 |
| 9 | 3.15, 3.23, 3.25 | Tuesday 2/27 |
| 10 | 4.2, 4.5 | Thursday 3/1 |
| 11 | 4.8, 4.9, 4.11, 4.14 | Tuesday 3/6 |
| 12 | 4.17 | Thursday 3/8 |
| 13 | 5.4, 5.7(b), 5.11 | Tuesday 3/13 |
| 14 | 5.15, 5.16 | Thursday 3/15 |
| 15 | 5.17(d), 5.20, 5.27 | Tuesday 3/20 |
| --- | MIDTERM (No homework due) | Thursday 3/22 |
| --- | Spring Break | --- |
| 16 | 6.1 | Tuesday 4/3 |
| 17 | 6.7(a,b,d) | Thursday 4/5 |
| 18 | 6.8, 6.11(a), 6.12(a) | Tuesday 4/10 |
| 19 | 7.5 | Thursday 4/12 |
| 20 | 7.7, 7.8, 7.11 | Tuesday 4/17 |
| 21 | 8.2 | Thursday 4/19 |
| 22 | 8.10, 8.13, 8.14 | Tuesday 4/24 |
| 23 | 9.2 | Thursday 4/26 |
| 24 | 9.12, 9.13(a), 9.14(a,c) | Tuesday 5/1 |
| 25 | 10.3 | Thursday 5/3 |
| 26 | 10.13, 10.15, 10.18 | Tuesday 5/8 |
| 27 | 11.4 | Thursday 5/10 |
| 28 | 11.7, 11.13, 11.18 | Tuesday 5/15 |
| Lecture | Topics | Sections |
|---|---|---|
| 1 | Basic elements of MATLAB | 1.2 |
| 2 | Basic elements of C++ | 1.3 |
| 3 | Simple programs; Precision & round-off | 1.4-5 |
| 4 | Projectile motion; Simple methods for ODEs | 2.1 |
| 5 | Simple pendulum; Verlet's method | 2.2 |
| 6 | Kepler problem | 3.1 |
| 7 | Runge-Kutta methods | 3.2 |
| 8 | Adaptive methods | 3.3 |
| 9 | Lorenz model | 3.4 |
| 10 | Steady states; Linear systems of equations | 4.1-2 |
| 11 | Linear systems of equations (cont.) | 4.2-3 |
| 12 | Solving nonlinear equations | 4.4 |
| 13 | Analysis of data; Curve fitting | 5.1 |
| 14 | Fast Fourier transforms (FFTs) | 5.2 |
| 15 | Normal modes; Leeway | 5.3 |
| 16 | Midterm | Ch. 1-5 |
| 17 | Fundamentals of PDEs | 6.1 |
| 18 | Diffusion equation; FTCS scheme | 6.2-3 |
| 19 | Hyperbolic equations | 7.1 |
| 20 | Traffic flow | 7.2 |
| 21 | Laplace's equation; Relaxation methods | 8.1 |
| 22 | Poisson's equation; Spectral methods | 8.2 |
| 23 | Von Neumann stability | 9.1 |
| 24 | Implicit methods | 9.2 |
| 25 | Special functions | 10.1 |
| 26 | Quadrature; Romberg algorithm | 10.2 |
| 27 | Gaussian integration | 10.3 |
| 28 | Random number generators | 11.1-2 |