Lecture Plan
The following is a tentative schedule for the course.
| Lectures | Sections in Text | Description | Additional comments |
|---|---|---|---|
| Monday March 25 |
1.1.
Begin 1.2 |
Basic mathematical models; Solutions of some differential equations.
Khan Academy - Differential equations intro Khan AcademyA - Slope fields & equations Interactive website for plotting slope fields and trajectories |
|
| Wednesday March 27 |
Finish 1.2.
1.3 |
Solutions to some problems; Classification of differential equations.
Khan Academy - Exponential model equations |
|
| Friday March 29 | 2.1, 2.2 |
Linear first order differential equations; Separable equations.
Khan Academy - Separable equations |
|
| Monday April 1 | 2.4 |
Existence and uniqueness theorems.
Khan Academy -Write differential equations |
|
| Wednesday April 3 | 2.3 |
Modeling with differential equations
Khan Academy - Slope fields & solutions |
Friday April 5 | 2.5 | Autonomous equations and population dynamics |
| Monday April 8 | 2.6 | Exact equations | |
| Wednesday April 10 | 3.1, 3.2 |
Second order constant coefficient equations
with distinct roots; the Wronskian |
Friday April 12 | 3.3 | Complex conjugate roots |
| Monday April 15 | 3.4 | Repeated roots and reduction of order | |
| Wednesday April 17 | 3.5, 3.6 | Nonhomogeneous equations: Method of undetermined coefficients and variation of parameters | |
| Thursday April 18: 4:30 - 6:30 pm. | Midterm 1 | Old past exams: Others will be posted on CANVAS |
|
| Friday April 19 | 7.1, 7.2 | Review of matrices. | |
| Monday April 22 | 7.3, 7.4 | Systems of ODEs; Existence and uniqueness of solutions of systems of ODEs. | |
| Wednesday April 24 | 7.5 |
Constant coefficients systems with distinct real eigenvalues |
|
| Friday April 26 | 7.6 |
Constant coefficient systems with complex conjugate eigenvalues |
|
| Monday April 29 | 7.8 | Repeated Eigenvalues | |
| Wednesday May 1 | 7.9 | Nonhomogeneous Linear Systems | |
| Friday May 3 | 9.1 | The phase plane (Good review!) | |
| Monday May 6 | 9.2 | Autonomous Systems and Stability
Plotting slope fields and trajectories Direction field plotter |
|
| Wednesday May 8 | 9.3 | Locally Linear Systems | |
|
Thursday
May 9: 4:30 - 6:30 pm. |
Midterm 2 | Old past exams: Others will be posted on CANVAS | |
| Friday May 10 | 9.4 | Competing species | |
| Monday May 13 | 9.5 | Predator-prey equations | |
| Wednesday May 15 | 6.1, 6.2 |
Laplace transform and the IVP
Khan Academy: Laplace transform intro Khan Academy: Properties of the Laplace transform Khan Academy: Laplace transform to solve a differential equation |
|
| Friday May 17 | 6.3 | Step functions | |
| Monday May 20 | 6.4, 6.5 | Discontinuous forcing functions; Impulse Functions KA: Laplace/step function differential equation | |
| Wednesday May 22 | 6.6 |
The convolution integral
Khan Academy: The convolution integral |
|
| Friday May 24 | Review | Review of Laplace transform | |
| Monday May 27 | No class scheduled | ||
| Wednesday May 29 | Review | Last day of instruction | |
| Saturday June 1: 8:00 - 11:00 am. | Final exam | Exam covers material from the whole course. | Old past exams. Others will be posted on CANVAS |