| Topics |
Chapter/Section |
Lectures |
|
| A Single First Order Equation: |
1 |
11 |
| Some comments on modeling |
1.1 |
1.5 |
Mathematical introduction to ODE;
Integrating equations;
the simplest equations |
1.2 |
1 |
| Geometry of solution space |
1.3 |
1 |
| Euler's method |
1.4 |
1 |
| Some comments on existence and uniqueness |
1.5 |
1 |
| Equilibrium points |
1.6 |
1 |
| Bifurcation |
1.7 |
1 |
| First order linear ODE |
1.8 |
1 |
| |
|
|
Autonomous Systems of
Two First Order Equations |
2 |
7 |
| Examples |
2.1 |
2 |
| Direction fields in the phase plane |
2.2 |
1 |
| Explicit solutions |
2.3 |
2 |
| Euler's method; comment on existence and uniqueness |
2.4 |
1 |
| Lorenz equations |
2.5 |
1 |
| |
|
|
Linear autonomous systems
of two equations |
3 |
10 |
| |
|
|
Non-homogeneous and
non-autonomous equations;
Forcing and Resonance |
4 |
5 |
| |
|
|
| Nonlinear systems |
5 |
6 |
| |
|
|
| Laplace Transforms |
6 |
4 |
|
|
|
|
|
43 |
