| Lecture |
Date |
Chapter |
Topics |
Homework assignment |
| 1 |
1/6 |
1 |
Course information and introduction to ODEs
|
|
| 2 |
1/8 |
2 |
First order ODEs I: autonomous and separable equations
|
Homework 1 (due 1/15)
|
| 3 |
1/10 |
3 |
First order ODEs II: dynamical perspective
|
|
| 4 |
1/13 |
4 |
First order ODEs III: stationary values, stability, phase lines
|
|
| 5 |
1/15 |
5 |
Mathematical Topics I: complex numbers
|
Homework 2 (due 1/22)
|
| 6 |
1/17 |
6 |
Second Order ODEs
|
|
| |
1/20 |
|
MLK Jr. Day, no class
|
|
| 7 |
1/22 |
7 |
Systems of ODEs I: linear systems
|
Homework 3 (due 1/29)
|
| 8 |
1/24 |
8 |
Systems of ODEs II: solving first order systems
|
|
| 9 |
1/27 |
9 |
Systems of ODEs III: phase portraits and dynamics
|
|
| 10 |
1/29 |
10 |
Inhomogeneous ODEs I: integrating factors and variation of parameters
|
Homework 4 (due 2/5)
|
| |
1/30 |
|
MIDTERM 1 (covers lectures 1--8)
|
|
| 11 |
1/31 |
11 |
Inhomogeneous ODEs II: inhomogeneous systems
|
|
| 12 |
2/3 |
12 |
Nonlinear Systems I: chaos and bifurcation
|
|
| 13 |
2/5 |
13 |
Nonlinear Systems II: linearization
|
Homework 5 (due 2/12)
|
| 14 |
2/7 |
14 |
Nonlinear Systems III: monotone and conserved quantities
|
|
| 15 |
2/10 |
15 |
Numerical Methods I: power series methods
|
|
| 16 |
2/12 |
16 |
Numerical Methods II: euler's method
|
Homework 6 (due 2/19)
|
| 17 |
2/14 |
17 |
Numerical Methods III: stiff ODEs
|
|
| |
2/17 |
|
Presidents Day, no class
|
|
| 18 |
2/19 |
18 |
PDEs I: definitions and examples
|
Homework 7 (due 2/26)
|
| |
2/20 |
|
MIDTERM 2 (covers lectures 9--17)
|
|
| 19 |
2/21 |
19 |
PDEs II: separation of variables
|
|
| 20 |
2/24 |
20 |
Fourier Series I: orthogonality and coefficients
|
|
| 21 |
2/26 |
21 |
Fourier Series II: solving ODEs and PDEs
|
Homework 8 (due 3/5)
|
| 22 |
2/28 |
22 |
Fourier Series III: higher-dimensional examples
|
|
| 23 |
3/3 |
23 |
Mathematical Topics II: complex Fourier series and transforms
|
|
| 24 |
3/5 |
24 |
Fourier Transforms I: definition and examples
|
Homework 9 (due 3/12)
|
| 25 |
3/7 |
25 |
Fourier Transforms II: solving ODEs and PDEs
|
|
| 26 |
3/10 |
26 |
Fourier Transforms III: convolution and integral formulas
|
|
| 27 |
3/12 |
na |
Numerical Methods IV: method of lines and spectral methods
|
Study for exam
|
| 28 |
3/14 |
na |
Exam Review
|
|
| |
3/18 |
|
Final Exam (covers lectures 1-26, emphasis on 18-26)
|
|
