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The class meets for lecture on Monday, Wednesday, and Friday. This schedule contains the material covered in each lecture.
It is generally one chapter per lecture.
This schedule is tentative, and may be adjusted as necessary.
| Week |
Date |
Chapters |
Topics |
Homework assignment |
| 1 |
1/5 - 1/9 |
1, 2, 3 |
Intro to ODE's, first order ODE's, dynamic perspective
|
Homework 1 (due 1/14)
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| 2 |
1/12 - 1/16 |
4, 5, 6 |
Phase lines, complex numbers, second order linear ODEs
|
Homework 2 (due 1/21)
|
| 3 |
1/19 - 1/23 |
7, 8 |
Linear ODE systems, eigenvalues
|
Homework 3 (due 1/28)
|
| 4 |
1/26 - 1/30 |
9, 10, 11 |
2D linear ODE systems, inhomogeneous first and second order linear ODE's
|
Homework 4 (due 2/4)
|
| 5 |
2/2 - 2/6 |
12, 13, 14 |
Chaos, nonlinear ODE systems, linearization, monotonic quantities
|
Homework 5 (due 2/11)
|
| 6 |
2/9 - 2/13 |
15, 16, 17 |
Power series methods, numerical methods, stiff ODE's
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Homework 6 (due 2/18)
|
| 7 |
2/16 - 2/20 |
18, 19 |
Intro to PDE's, separation of variables: heat equation
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Homework 7 (due 2/25)
|
| 8 |
2/23 - 2/27 |
20, 21, 22 |
Fourier series: periodic functions, solving PDE's: separation of variables and Fourier series
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Homework 8 (due 3/4)
|
| 9 |
3/2 - 3/6 |
23, 24, 25 |
Exponential Fourier series, transform perspective, Fourier transform, solving PDE's with Fourier transform
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Homework 9 (due 3/11)
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| 10 |
3/9 - 3/13 |
26, 27, Final review |
Convolution and the wave equation on a line, applications of Fourier analysis (Chapter 27 not on final)
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