General information for the course is at the course website
This the syllabus for the first 7 weeks of class. It is subject to revision as the class progresses. The full syllabus will appear after we gauge class progress.
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Section numbers and exercises refer to the course text :
Paul Blanchard, Robert L. Devaney & Glen Hall; Differential Equations,
(fourth edition); Cengage, 2011 (864
pp.); (ISBN: 978-0495561989 or 9781133109037) Supplementary notes are denoted S1, S2, ... Homework to be turned in is marked with *. |
| Syllabus and textbook homework problems for 640:252:04 | |||
|---|---|---|---|
| Lecture | Topic(s) and text sections | Problems | Due Date |
| 1 (9/3) | S1 Modeling | Section 8* |
9/11/20 |
| 2 (9/8) | 1.1 Modeling
(continued) 1.2 Separation of Variables |
1.1: 4*, 5, 7, 10*, 17,18*, 19, 21, 23 1.2: 1, 3, 7, 15 |
9/16/20 |
| 3 (9/9) | 1.2 Separation of Variables (continued) | 1.2: 29, 33, 36* | 9/16/20 |
| 4 (9/14) | 1.3 Slope Fields | 1.3: 1,6,5,7,9,11,13,14*, 16, 18* | 9/23/20 |
| 5 (9/16) | 1.4 Euler's Method 1.5 Existence and Uniqueness 1.6 Equilibria and Phase Line |
1.4 1, 11, 16 1.5: 1, 3, 5, 8, 10*,14* 1.6: 1, 3, 4*, 7, 13, 16*, 23, 25, 27, 31, 33, 37, 39 |
9/23/20 |
| 6 (9/21) |
S2 Bifurcations 1.7 Bifurcations |
1.7: 1, 3, 5, 8*, 10* |
9/30/20 |
| 7 (9/23) | 1.8 Linear Differential
Equations 1.9 Integrating Factors |
1.8: 4*,7, 21, 22*, 23 1.9:5,9,12*, 21, 23 | 9/30/20 |
| 8 (9/28) | 2.1 Modelling via Systems | 2.1 1, 2, 7, 8, 9, 17, 19, 20*, 23, 25, 26, 28*, 29 | 10/7/20 |
| 9 (9/30) | 2.2 Geometry of Systems | 2.2: 3, 4, 8(a,b)*, 10*, 11, 12*, 21 | 10/7/20 |
| 10 (10/5) | 2.4 Analytic Methods 2.5 Euler's Method |
2.4: 1, 7, 10* 2.5: 1, 2*, 3, 5, | 10/14/20 |
| 11 (10/7) | Exam 1 covering through section 2.2 | ||
| 12 (10/12) | S3 Phase plane | 1*,2,3,4*,5 | 10/14/20 |
| 13 (10/14) | 3.1 Linear Systems Matrix Exponentials |
3.1: 5,7,9, 13, 16*, 19, 21, 27, 29, 33, 35* | 10/21/20 |
| 14 (10/19) | S4 Matrix Exponentials (continued) | 1b,3b*,5* | 10/21/20 |
| 15 (10/21) | 3.2 Straight-Line Solutions | 3.2 14*, 17,19,20* | 10/28/20 |
| 16 (10/26) | 3.3 Phase Plane: Real Eigenvalues | 3.3 12*, 21, 22* | 10/28/20 |
| 17 (10/28) | 3.4 Phase plane: Complex Eigenvalues | 3.4: 1, 4(a,d)*,, 10*, 19, 21, 22*, 23 | 11/4/20 |
| 18 (11/2) | 3.5 Repeated and Zero Eigenvalues | 3.5: 1,5, 17, 2*, 6*, 18 | 11/4/20 |
| 19 (11/4) | 3.7 The Trace-Determinant
Plane (emphasizing one-parameter families) |
1, 3c , 6c* 12* | 11/11/20 |
| 20 (11/9) | 3.6 Second-Order Linear Equations | 3.6: 13, 14*, 36(a,b)* | 11/11/20 |
| 21 (11/11) | 3.8 3-Dim Linear System | 3.8: 4*, 5, 6*, 7 | 11/18/20 |
| 22 (11/16) | 4.1 Forced Harmonic
Oscillators 4.2 Sinusoidal Forcing |
4.1: 10*, 20*, 23, 30 4:2: 1, 12*, 15 | 11/18/20 |
| 23 (11/18) | Exam 2 covering through section 3.7 | ||
| 24 (11/23) | 4.4 Steady State | 4.4:4*, 5, 6* | 11/25/20 |
| 25 (11/30) | 4.3 Resonance | 4.3:9, 14*, 15, 18*, 21 | 12/2/20 |
| 26 (12/2 ) | 5.1 Equilibria, Linearization | 5.1: 1, 18*, 19, 27, 28* | 12/2/20 |
| 27 (12/7 ) | 8.1 Discrete Systems | 8.1: 1, 15, 20*, 23, 27, 31 | 12/9/20 |
| 28 (12/9 ) | 8.2 Fixed/Periodic points | 8.2: 1, 7, 9, 14*, 15 | 12/9/20 |