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Quizzes, once administered, will uploaded to the schedule. Solutions will appear on Sakai . As MATLAB sets are assigned, they will be posted in the HW section with a link to the MATLAB page, where all further information can be found.
All sections listed refer to the main textbook. Letters indicate supplementary material, which can be found under Resources.
| Lecture | Date | Topic | Readings | Suggested HW and additional comments |
|---|---|---|---|---|
| Week 1 | ||||
| 1 | Tue 09/06 | Introduction to course, modeling, exponential growth | IPP(Section 1), 1.1, 1.2 | |
| 2 | Thu 09/08 | Logistic growth, more examples, separation of variables (begin) | IPP(Section 1), 1.1, 1.2 | 1.1: 3, 5, 15, 17, 19, 21. 1.2: 1, 3, 7, 13. MATLAB 1 posted (due 09/22, in Sakai) |
| Week 2 | ||||
| 3 | Tue 09/13 | Separation of variables (continued) | 1.2 | 1.2: 25, 29, 31, 35. |
| 4 | Thu 09/15 | Slope fields, introduction to numerical methods for ODEs (Euler's method) | E, 1.3, 1.4 | 1.3: all odd 1-17. 1.4: 1, 7, 8, 13, 15. Quiz 1 given. |
| Week 3 | ||||
| 5 | Tue 09/20 | Finish Euler's method, existence and uniqueness of solutions of ODEs, phase line (begin) | L, 1.4, 1.5, 1.6 (begin) | 1.5: 2, 3, 5, 6, 11, 13. 1.6: all odd 1-15, 23, 25, 31, 35, 39, 43. |
| 6 | Thu 09/22 | Finish phase line, bifurcations | L, 1.6, 1.7 | 1.7: 1, 3, 5, 9, 11, 17. MATLAB 2 posted (due 10/04, in Sakai) |
| Week 4 | ||||
| 7 | Tue 09/27 | Linear first order ODEs, and their solution (integrating factor) | 1.8, 1.9 | 1.8: all odd 1-13, 17, 21, 23. 1.9: all odd 1-11, 21, 25. Quiz 2 given. |
| 8 | Thu 09/29 | Systems of differential equations, modeling via systems, geometry of systems | 2.1, 2.2 | 2.1: 1, 2, 3, 7(a), 9, 17, 19, 21, 23, 25, 26, 27, 29. 2.2: all odd 1-27 (you can skip the technology parts if you'd like). |
| Week 5 | ||||
| 9 | Tue 10/04 | Finish systems introduction, damped harmonic oscillator, additional systems techniques | IPP(Section 2), finish 2.1-2.2, 2.3, 2.4 | 2.3: 1(b,c), 3(b,c), 7. 2.4: all odd 1-7, 13 (a-c). MATLAB 3 posted (due 10/11, in Sakai) |
| 10 | Thu 10/06 | Finish additional systems techniques, existence and uniqueness (briefly mentioned), epidemic modeling | 2.6, 2.7 (did not get to 2.7, will cover briefly next class) | 2.7: 1, 3, 6(a-c), 7. Quiz 3 given. |
| Week 6 | ||||
| 11 | Tue 10/11 | Epidemic modeling (briefly), introduction to linear systems and their properties | LS, finish 2.7, 3.1 | 3.1: all odd 5-9, all 15-29, 35. MATLAB 4 posted (due 10/27, in Sakai) |
| 12 | Thu 10/13 | Exam 1, in class | ||
| Week 7 | ||||
| 13 | Tue 10/18 | Finished linear system properties, relation to eigenvalues/eigenvectors of coefficient matrix | LS, finish 3.1, 3.2 | 3.2: all odd 1-19 (a-d). |
| 14 | Thu 10/20 | Matrix exponentials, real eigenvalue case for linear systems | IPP (Section 3), ME, 3.3 (start) | IPP (Section 3): all problems. 3.3: all odd 1-15. Quiz 4 given. |
| Week 8 | ||||
| 15 | Tue 10/25 | Finished real eigenvalue case, begin complex eigenvalues | 3.3 (finish), 3.4 (begin) | 3.4: all odd 1-15, 21, 23. |
| 16 | Thu 10/27 | Finish complex eigenvalues | 3.4 | See lecture 15 above. Quiz 5 given. MATLAB 5 posted (due 11/08, in Sakai) |
| Week 9 | ||||
| 17 | Tue 11/01 | Linear systems with repeated and zero eigenvalues | 3.5 | 3.5: all odd 1-21. |
| 18 | Thu 11/03 | Second-order linear equations | 3.6 | 3.6: 1, 5, 11, all odd 13-27. Quiz 6 given. |
| Week 10 | ||||
| 19 | Tue 11/08 | Analysis of the trace-determinant plane, 3-dimensional linear systems (just introduction) | 3.7, 3.8 | 3.7: 3, 5, 7, 11, 12, 13. Nothing from Section 3.8. MATLAB 6 posted (due 11/22, in Sakai) |
| 20 | Thu 11/10 | Forced harmonic oscillations | 4.1 | 4.1: 1, 5, 9, 13, 23, 29, 35, 39. Quiz 7 given. |
| Week 11 | ||||
| 21 | Tue 11/15 | Finish forced oscillations, sinusoidal forcing | 4.1 (finish), 4.2 | 4.2: 1 - 13 odd (put solutions in polar form as well, i.e. pure sine or cosine), 19. |
| 22 | Thu 11/17 | Exam 2, in class | ||
| Week 12 | ||||
| 23 | Tue 11/22 | Finish sinusoidal forcing, undamped oscillator and resonance | 4.2 (finish), 4.3 | 4.3: 1, 5, 9, 13, 15, 17, 21. MATLAB 7 posted (due 12/06, in Sakai) |
| N/A | Thu 11/24 | Thanksgiving!! | Eat turkey (or meal of choice) | |
| Week 13 | ||||
| 24 | Tue 11/29 | Finish beats and resonance | 4.3 (finish) | See Lecture 23 above. Quiz 8 given. |
| 25 | Thu 12/01 | Introduction to nonlinear systems and linearization | 5.1 (beginning) | 5.1: 1-17 odd, 18, 23. |
| Week 14 | ||||
| 26 | Tue 12/06 | Finish linearization | 5.1 (finish) | See Lecture 25 above. MATLAB 8 (last one) posted (due 12/14, in Sakai) |
| 27 | Thu 12/08 | Nullcline analysis | 5.2 | 5.2: 1-19 odd. Quiz 9 given. |
| Week 15 | ||||
| 28 | Tue 12/13 | Introduction to special nonlinear systems (Hamiltonian, dissipative) | 5.3, 5.4 | 5.3: 1, 3, 9, 11, 13, 14, 18. 5.4: 1, 3, 13, 18, 19, 21. |