| Week |
Date |
Chapter |
Homework Assignment |
| 1 |
March 31
April 2
April 4 |
1: What is a differential equation?
2: First-order ODE's: autonomous, separable, and initial value problems
3: First-order ODE's: dynamic perspectives |
Homework 1
(due April 9) |
| 2 |
April 7
April 9
April 11 |
4: Stationary values, stability, and phase line
5: Complex numbers
6: Second-order linear ODE's and initial value problems |
Homework 2
(due April 16) |
| 3 |
April 14
April 16
April 18 |
7: Homogeneous linear ODE systems and eigenvectors
8: Further applications of eigenvalues to ODE's
9: Two-dimensional homogeneous linear ODE systems and eigenvalues |
Homework 3
(due April 23) |
| 4 |
April 21
April 23
April 25 |
10: Solving inhomogeneous first-order linear ODE's
11: Solving inhomogeneous second-order linear ODE's
12: Chaos, bifurcation, and sensitive dependence on initial conditions & parameters |
Homework 4
(due April 30) |
| 5 |
April 28
April 30
May 2 |
13: Non-linear ODE systems: the role of linearization
14: Monotone and conserved quantities
15: Power series methods |
Homework 5
(due May 7) |
| 6 |
May 5
May 7
May 9 |
16: Introduction to numerical methods
17: Runge-Kutta methods and stiff ODE's
18: Introduction to PDE's |
Homework 6
(due May 14) |
| 7 |
May 12
May 14
May 16 |
19: Separation of variables for the heat equation
20: Fourier series for periodic functions
21: Solving PDE's via separation of variables and Fourier series |
Homework 7
(due May 21) |
| 8 |
May 19
May 21
May 23 |
22: More applications of separation of variables and Fourier series
23: Exponential Fourier series and transform perspective
24: Introduction to the Fourier transform |
Homework 8
(due May 28) |
| 9 |
May 26
May 28
May 30 |
No Class: Memorial Day
25: Gaussians and the heat equation on a line
26: Convolution and the wave equation on a line |
Homework 9
(due June 4) |
| 10 |
June 2
June 4 |
27: Applications of the Fourier transform
Final Exam Review |
|
