| Professor: | Douglas Anderson, Ph.D. |
| Ivers 234G | |
| 299-4453 (office), 299-4151 (math department) | |
| andersod@cord.edu |
Office Hours: TTh 1:00-3:30, MWF by discovery.
Text: J. David Logan, Applied Partial Differential Equations, Springer, New York, 1998.
Prerequisites: Math 210, 223, 311.
Content: In this course we explore some of the standard models of mathematical physics, including the heat equation, the wave equation, and Laplace's equation. Classical solution techniques involve transform methods for unbounded domains, and eigenfunction expansions on bounded domains. The course will be run like a seminar, with a heavy emphasis on problem solving and homework discussion. Before each class meeting, please read the section for that day, checking the work in the text and filling in missing mathematical steps as you read. Then begin the homework set.
Homework: Homework will be assigned each day for your practice in mastering the material, and will be due two class periods later. I will allow up to two (2) late submissions without penalty; after that late homework will not be accepted. Homework that is turned in should be neat and organized. You will not only be graded on correct answers but also on the neatness, organization, steps used to derive your answers, and the use of correct grammar and complete sentences.
Exam: There will be one take-home exam at the end of the block. You are allowed to use your text, class notes, homework, and Mathematica 5.0 where appropriate, but you must work independently. Solutions should first be written out on scratch paper, with the final submitted version neatly written without cross-outs, restarts, or eraser marks.
| Grading: | Points | Scale | |||
| Homework | 200 | A 90%--100% | |||
| B 80%--89% | |||||
| Exam | 100 | C 70%--79% | |||
| D 60%--69% | |||||
| F Below 60% |
| Date | Section | Exercises |
| Jan 7 | No Class | Joint Mathematics Meetings, Phoenix |
| 9 | 1.1 Mathematical Models | (7) 1,3,4,5,6,7 |
| 12 | 1.2 Conservation Laws | (14) 2,3,4,6 |
| 14 | 1.3 Diffusion | (18) 2,5,6,7 |
| 16 | 1.5 Vibrations of a String | (27) 2,3,4 |
| 19 | 1.7 Heat Flow in Three Dimensions | (35) 1,3,4,5 |
| 21 | 1.8 Laplace's Equation | (41) 1,2,3 |
| 23 | 2.2 Wave Equation | (59) 1,2,4,5 |
| 26 | 2.6 Laplace Transforms | (77) 1,2,6 |
| 28 | 2.7 Fourier Transforms | (82) 1,2,4,5,7 |
| 30 | 2.7 Fourier Transforms (cont) | (83) 8,11,12 |
| Feb 2 | 3.1 Fourier Method | (93) 1 |
| 4 | 3.2 Orthogonal Expansions | (101) 1,3,5 |
| 6 | 3.3 Fourier Cosine and Sine Series | (107) 2,4 |
| 9 | 3.4 Sturm-Liouville Problems | (114) 1,2,3,4,6 |
| 11 | 3.4 Eigenvalues, Eigenfunctions | (115) 7,9,11,12 |
| 13 | 4.1 Separation of Variables | (123) 2,3,4 |
| 16 | 4.2 Flux and Radiation Conditions | (130) 1,2 |
| 18 | 4.3 Laplace's Equation | (138) 2,5; Take-home Exam |
| 20 | 4.4 Potential inside a Sphere | |
| 23 | Legendre Polynomials | |
| 25 | No Class | |
| 27 | Block III ends |