Lecture Plan
The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.
| Lectures | Sections in Text | Description | Additional comments |
|---|---|---|---|
| Monday January 5 |
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 January 7 |
Finish 1.2.
1.3 |
Solutions to some problems; Classification of differential equations.
Khan Academy - Exponential model equations |
|
| Friday January 9 | 2.1, 2.2 |
Linear first order differential equations; separable equations.
Khan Academy - Separable equations |
|
| Monday January 12 | 2.4 |
Existence-uniqueness theorems.
Khan Academy -Write differential equations |
|
| Wednesday January 14 | 2.3 |
Modeling with differential equations
Khan Academy - Slope fields & solutions |
Friday January 16 | 2.5 | Autonomous equations and population dynamics |
| Tuesday (Wednesday) January 20 (21) | 2.6 | Exact equations | |
| Wednesday (Thursday) January 21 (22) | 3.1, 3.2 |
Second order constant coefficient equations
with distinct roots; the Wronskian |
Friday January 23 | 3.3 | Complex conjugate roots |
| Monday January 26 | 3.4 | Repeated roots and reduction of order | |
| Wednesday January 28 | 3.5, 3.6 | Nonhomogeneous equations: Method of undetermined coefficients and variation of parameters | |
| Friday January 30 Time and Room TBD. | Exam 1 | material through 3.4. |
past exam practice problems |
| Friday January 30 | 7.1, 7.2 | Review of matrices. | |
| Monday February 2 | 7.3, 7.4 | Systems of ODEs; Existence and uniqueness of solutions of systems of ODEs. | |
| Wednesday February 4 | 7.5 |
Constant coefficients systems with distinct real eigenvalues |
|
| Friday February 6 | 7.6 |
Constant coefficient systems with complex conjugate eigenvalues |
|
| Monday February 9 | 7.7, 7.8 | Repeated Eigenvalues | |
| Wednesday February 11 | 7.9 | Nonhomogeneous Linear Systems | |
| Friday February 13 | 9.1 | The Phase Plane (Good review!) | |
| Monday February 16 | 9.2 | Autonomous Systems and Stability
Plotting slope fields and trajectories Direction field plotter |
|
| Wednesday February 18 | 9.3 | Locally Linear Systems | |
| Friday February 20 | 9.4 | Competing Species | |
| Monday February 23 | 9.5 | Predator-Prey Equations | |
|
Wednesday
February 25
Live Section 1 |
Review Chapter 9 | ||
| Friday February 27 | test 2 | Material from 3.4 through 9.3. | Old past exams |
| Friday February 27 | 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 |
|
| Monday March 2 | 6.3 | Step functions | |
| Wednesday March 4 | 6.4, 6.5 | Discontinuous forcing functions, Impulse Functions KA: Laplace/step function differential equation | |
| Friday March 6 | 6.6 |
The convolution integral
Khan Academy: The convolution integral |
|
| Monday March 9 | Review Chapter 6 | Review Chapter 6 | |
| Tuesday November 16 | No class scheduled | Last day of instruction | |
| Exam Date and Time TBD | Room TBD | Exam covers material from the whole course. | Old past exams |