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 |
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