J. Rauch
4834 East Hall
Email: rauch@umich.edu
Office Hours: Tuesdays, and Wednesdays, 2:00-3:00 PM.
Textbook: Elementary Differential Equations, 8th Edition, by W. E. Boyce and R. C. DiPrima, John Wiley and Sons.
| Week | Meeting | Date | In Class | Remarks/Web Postings |
|---|---|---|---|---|
| 1 | Lecture 1 | Tues, Sept. 4 | § 1.1, § 1.2 | course info., and, 216 dfield HW handouts |
| Lecture 2 | W, Sept. 5 | § 1.3, § 2.1 | integrating factor handout | |
| Lecture 3 | F, Sept. 7 | § 2.2, § 2.3 | ||
| 2 | Lecture 4 | M, Sept. 10 | § 2.5 (phase line, 1/2 Thm 2.8.1 uniqueness) | |
| Lecture 5 | T, Sept. 11 | § 2.6 (exact equations) | no integrating factor. See also Lecture 47. | |
| Lecture 6 | W, Sept. 12 | § 2.7, § 8.1 (Euler's algorithm) | no backward Euler, eulertest.m | |
| Lecture 7 | F, Sept. 14 | § 2.4, 2.8 (existence, nonuniuqeness, explosion) | HW1 due, no successive approx. | |
| 3 | Lecture 8 | M, Sept. 17 | § 3.1 | |
| Lecture 9 | T, Sept. 18 | § 3.2 | ||
| Lecture 10 | W, Sept. 19 | § 3.3 | ||
| Lecture 11 | F, Sept. 21 | § 3.4 | HW2 due | |
| 4 | Lecture 12 | M, Sept. 24 | § 3.5 | |
| Lecture 13 | T, Sept. 25 | Annihilators, pp. 236-237. | Instead of ډ.6 | |
| Lecture 14 | W, Sept. 26 | § 3.7 | ||
| Lecture 15 | F, Sept. 28 | § 3.8, Matlab ODE45 | HW3 due, gravity spring m-files | |
| 5 | Lecture 16 | M, Oct. 1 | § 3.9 | |
| Lecture 17 | T, Oct. 2 | Overflow Chap 3. Second order geometry. | plotting options for gravity spring | |
| Lecture 18 | W, Oct. 3 | Review | ||
| EXAM 1 | F, Oct. 5 | EXAM 1 | ||
| 6 | Lecture 19 | M, Oct. 8 | § 4.1 | HW4 due, Wronskian handout |
| Lecture 20 | T, Oct. 9 | § 4.2 | ||
| Lecture 21 | W, Oct. 10 | § 4.3, Annihilators | ||
| Lecture 22 | F, Oct. 12 | overflow Chapter 4 | HW5 due | |
| 7 | Study Day | M, Oct. 15 | Linear Algebra, Matthews Chapter 1 (Gauss elimination) | |
| Study Day | T, Oct. 16 | Linear Algebra, Row operations in Matlab | gauss.m posting | |
| Lecture 23 | W, Oct. 17 | Pert. Thry. I, Taylor's Thm., Differentiable Dependence | HW6 due, Taylor posting, | |
| Lecture 24 | F, Oct. 19 | Perturbation Theory II, Weakly nonlinear spring) | Instead of § 5.1, Perturbation Steps posting | |
| 8 | Lecture 25 | M, Oct. 22 | Perturbation Theory III, Nonlinear pendulum | Instead of § 5.2 |
| Lecture 26 | T, Oct. 23 | § 6.1, Conditional convergence | ||
| Lecture 27 | W, Oct. 24 | § 6.1, 6.2 | ||
| Lecture 28 | F, Oct. 26 | § 6.3 | HW7 due | |
| 9 | Lecture 29 | M, Oct. 29 | Linear Algebra | |
| Lecture 30 | T, Oct. 30 | Linear Algebra | ||
| Lecture 31 | W, Oct 31 | Linear Algebra | ||
| Lecture 32 | F, Nov. 2 |
Linear Albebra | HW8 due | |
| 10 | Lecture 33 | M, Nov. 5 | Linear Algebra | |
| Lecture 34 | T, Nov. 6 | Linear Algebra | ||
| Lecture 35 | W, Nov. 7 | § 7.1 | ||
| Lecture 36 | F, Nov. 9 | Review, Review Session 5-6PM 4088 EH | HW9 due | |
| 11 | EXAM 2 | M, Nov. 12 | EXAM 2 | |
| Lecture 37 | T, Nov. 13 | § 7.4 | ||
| Lecture 38 | W, Nov. 14 | § 7.5, (+ pplane.m) | ||
| Lecture 39 | F, Nov. 16 | § 7.6 | HW10 due, Exam sols. | |
| 12 | Lecture 40 | M, Nov. 19 | § 7.8 | No Jordan, Multiple roots algorithm posting |
| Lecture 41 | T, Nov. 20 | § 7.7, § 7.9 variation of parameters | No diagonalizable | |
| Lecture 42 | W, Nov. 21 | § 8.1 (truncation errors, order of accuracy) | ||
| Thanksgiving | F, Nov. 23 | Thanksgiving Holiday | ||
| 13 | Lecture 43 | M, Nov. 26 | § 8.2, § 8.5 (improved Euler, roundoff) |
HW11 due, |
| Lecture 44 | T, Nov. 27 | § 9.1, § 9.3 | structural stability | |
| Lecture 45 | W, Nov. 28 | § 9.2, (stability, centers) | Math 216 pplane lab | |
| Lecture 46 | F, Nov. 30 | Linearization, (pendulum, damped and undamped) | Linearization and Perturbation Theory | |
| 14 | Lecture 47 | M, Dec. 3 | Integrals of Motion (trajectories, energy, chemistry) | HW12 due |
| Lecture 48 | T, Dec. 4 | § 8.2 pg 455 (variation of step size, the heart of ODE45) | postponed till after HW12 due | |
| Lecture 49 | W, Dec. 5 | § 9.4 | Bimolecular Reacton posting | |
| Lecture 50 | F, Dec. 7 | § 9.5 | ||
| 15 | Lecture 51 | M, Dec. 10 | § 9.6 | HW13 due |
| Lecture 52 | T, Dec. 11 | § 9.6, Elbow Room and/or Review | ||
| Review session | W, Dec 12 | 4:10-5:10. 4088 EH | ||
| Fri, Dec. 14 | 1:30-3:30 PM. 1360 EH. |