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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 09/05 | Introduction to course and ODEs | IPP(Section 1), 1.1, 1.2 | |
| 2 | Thu 09/07 | More examples of ODEs, exponential and logistic growth | IPP(Section 1), 1.1 | 1.1: 3, 5, 15, 17, 19, 21. MATLAB 1 posted (due 09/21, in Sakai) |
| Week 2 | ||||
| 3 | Tue 09/12 | More modeling examples, separation of variables | IPP(Section 1), 1.1, 1.2 | 1.2: 1, 3, 7, 13, 25, 29, 31, 35. |
| 4 | Thu 09/14 | 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 (Due: Tuesday, September 19, in class) |
| Week 3 | ||||
| 5 | Tue 09/19 | Finish Euler's method, existence and uniqueness of solutions of ODEs | L, 1.4, 1.5, 1.6 (begin) | 1.5: 2, 3, 5, 6, 11, 13. |
| 6 | Thu 09/21 | Phase line | L, 1.6 | 1.6: all odd 1-15, 23, 25, 31, 35, 39, 43. MATLAB 2 posted (due 10/03, in Sakai) |
| Week 4 | ||||
| 7 | Tue 09/26 | Bifurcations, introduction to linear first order ODEs, and their solution | 1.7, 1.8 | 1.7: 1, 3, 5, 9, 11, 17. |
| 8 | Thu 09/28 | Method of undetermined method and integrating factor (begin) for first-order linear ODEs | 1.8, 1.9 | 1.8: all odd 1-13, 17, 21, 23. 1.9: all odd 1-11, 21, 25. Quiz 2 given. |
| Week 5 | ||||
| 9 | Tue 10/03 | Finish integrating factor, systems of differential equations, modeling via systems, geometry of systems | 1.9, 2.1, 2.2 | 1.9: all odd 1-11, 21, 25. 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). MATLAB 3 posted (due 10/10, in Sakai) |
| 10 | Thu 10/05 | Finish systems introduction, different methods of visualizing solutions (components in time, phase plane), second-order equations as first-order systems | Finish 2.1-2.2 | See assignments from Lecture 9. Quiz 3 given. |
| Week 6 | ||||
| 11 | Tue 10/10 | Damped harmonic oscillator | IPP(Section 2), 2.3, 2.4, 2.6 | 2.3: 1(b,c), 3(b,c), 7. MATLAB 4 posted (due 11/02, in Sakai). Quiz 4 given. |
| 12 | Thu 10/12 | Exam 1, in class | ||
| Week 7 | ||||
| 13 | Tue 10/17 | Additional systems techniques, existence and uniqueness (briefly mentioned), epidemic modeling, introduction to linear systems | IPP (Section 2), LS, finish 2.4, 2.6, 2.7, 3.1 | 2.4: all odd 1-7, 13 (a-c). 2.7: 1, 3, 6(a-c), 7. |
| 14 | Thu 10/19 | Continue linear systems and properties | LS, finish 3.1, 3.2 | 3.1: all odd 5-9, all 15-29, 35. |
| Week 8 | ||||
| 15 | Tue 10/24 | Continue linear systems introduction, relation to eigenvalues/eigenvectors of coefficient matrix | 3.1 (finish), 3.2 | 3.2: all odd 1-19 (a-d). |
| 16 | Thu 10/26 | Finish straight-line solutions, general solution, introduction to matrix exponentials | IPP (Section 3), ME, 3.2 | IPP (Section 3): all problems. Quiz 5 given. |
| Week 9 | ||||
| 17 | Tue 10/31 | Finish matrix exponentials, distinct real eigenvalue phase portrait for linear systems | IPP (Section 3), ME, 3.3 | 3.3: all odd 1-15. |
| 18 | Thu 11/02 | Complex eigenvalues | 3.4, 3.5 (begin) | 3.4: all odd 1-15, 21, 23. 3.5: all odd 1-21. Quiz 6 (Due: Tuesday, November 7, in class) MATLAB 5 posted (due 11/14, in Sakai) |
| Week 10 | ||||
| 19 | Tue 11/07 | Finish complex eigenvalues, begin repeated eigenvalues | 3.4 (finish), 3.5 | 3.5: all odd 1-21. |
| 20 | Thu 11/09 | Finish repeated eigenvalues, zero eigenvalue systems | 3.5 | See assignments from Lecture 19. Quiz 7 given. |
| Week 11 | ||||
| 21 | Tue 11/14 | Second-order linear equations, analysis of the trace-determinant plane | 3.6, 3.7 | 3.6: 1, 5, 11, all odd 13-27. 3.7: 3, 5, 7, 11, 12, 13. MATLAB 6 posted (due 11/28, in Sakai) |
| 22 | Thu 11/16 | Exam 2, in class | ||
| Week 12 | ||||
| 23 | Tue 11/21 | Finish trace-determinant plane, 3-dimensional linear systems (just introduction), introduction to non-homogeneous linear systems | 3.7 (finish), 4.1 (begin) | 3.7: 3, 5, 7, 11, 12, 13. |
| N/A | Thu 11/23 | Thanksgiving!! | Eat turkey (or meal of choice) | |
| Week 13 | ||||
| 24 | Tue 11/28 | Forced harmonic oscillations | 4.1 | 4.1: 1, 5, 9, 13, 23, 29, 35, 39. |
| 25 | Thu 11/30 | Sinusoidal forcing, introduction to undamped oscillator and resonance | 4.2, 4.3 | 4.2: 1 - 13 odd (put solutions in polar form as well, i.e. pure sine or cosine), 19. 4.3: 1, 5, 9, 13, 15, 17, 21. MATLAB 7 posted (due 12/07, in Sakai). Quiz 8 (Due: Tuesday, December 5, in class) |
| Week 14 | ||||
| 26 | Tue 12/5 | Finish sinusoidal forcing and resonance | 4.2, 4.3 | See assignments from Lecture 25. |
| 27 | Thu 12/7 | Introduction to nonlinear systems and linearization | 5.1 | 5.1: 1-17 odd, 18, 23. MATLAB 8 (last one) posted (due 12/14, in Sakai). Quiz 9 given. |
| Week 15 | ||||
| 28 | Tue 12/12 | Finish linearization, nullcline analysis, some special nonlinear systems | 5.2, 5.3, 5.4 | 5.2: 1-19 odd. 5.3: 1, 3, 9, 11, 13, 14, 18. 5.4: 1, 3, 13, 18, 19, 21. |