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 | Practice Problems |
---|---|---|---|
Monday
March 27 |
1.1, 1.2 |
What are differential equations?
DirectionFields.nb |
§1.1: #1, 2, 26
§1.2: # 1(a), 2(a) KA - Differential equations intro KA - Slope fields & equations |
Wednesday
March 29 |
1.3, 2.1 |
Classification and linear first-order ODEs
DirectionFields2.nb |
§2.1: #1, 9, 12 |
Friday
March 31 |
2.2, 2.4 |
Separable equations and existence-uniqueness theorems
DirectionFields3.nb |
§2.2: #9, 11
§2.4: #3, 7, 11 KA - Separable equations KA - Exponential model equations |
Monday
April 03 |
2.3 |
Modeling with differential equations
MixingPlot.nb , WorksheetSlopeFields.nb |
§2.3: Solve the IVPs in Examples 2 and 3
§2.3: #9, 10 KA-Write differential equations |
Wednesday
April 05 |
2.5 | Autonomous equations and population dynamics |
§2.5: #9, 23
Review multivariable chain rule KA - Slope fields & solutions |
Friday
April 07 |
2.6 |
Exact equations
LastExamplePlot.nb |
§2.6: #23, 26, 30, 31 |
Monday
April 10 |
3.1, 3.2 | Second order constant coefficient with distinct real roots; the Wronskian |
§3.1: #2, 4
§3.2: #2, 4, 14 |
Wednesday
April 12 |
3.3 |
Complex conjugate roots
SolutionPlots.nb |
§3.2: #25
§3.3: #8, 27 |
Friday
April 14 |
3.4 | Repeated roots and reduction of order | §3.4: #2, 16, 24 |
Monday
April 17 |
3.5 | Method of undetermined coefficients | §3.5: #5, 19 |
Wednesday
April 19 |
3.6 | Variation of parameters | §3.6: #9, 13 |
Friday
April 21 |
3.7, 3.8 |
Modeling of vibrations
Demos: 1 , 2 , 3 , 4 ForcedVibrationsPlot.nb |
§3.7: #19
§3.8: #17 |
Monday
April 24 |
6.1, 6.2 | Laplace Transform and the IVP |
KA: Laplace transform intro
KA: Properties of the Laplace transform KA: Laplace transform to solve a differential equation |
Wednesday
April 26 |
6.3, 6.4 | IVPs with discontinuous forcing functions | KA: Laplace/step function differential equation |
Friday
April 28 |
6.5, 6.6 | Impulse Functions and the convolution integral | KA: The convolution integral |
Monday
May 01 |
7.1, 7.2 |
Review of matrices
Demo |
§7.1: #10, 14 |
Wednesday May 03
4 - 6 pm, Silsby 028 |
Midterm |
Midterm
Coverage: from the beginning to the end of 6.4 |
Past exams |
Wednesday
May 03 |
7.3 | Review of matrices and systems of ODEs. | §7.3: #17, 18 |
Friday
May 05 |
7.4 | Existence and uniqueness of solutions of systems of ODEs | |
Monday
May 08 |
7.5 |
Constant coefficients systems with distinct real eigenvalues Example2Plots.nb, Example3Plots.nb, EigenManipulate.nb |
§7.5: #3, 12 |
Wednesday
May 10 |
7.6 |
Constant coefficient systems with complex conjugate eigenvalues ComplexEigenPlot.nb |
§7.6: #2, 6 |
Friday
May 12 |
7.8 | Repeated eigenvalues | §7.8: #1, 18 |
Monday
May 15 |
7.9 | Variation of parameters | §7.9: # 1, 3, 15 |
Wednesday
May 17 |
9.1 | The Phase Plane: Linear Systems | §9.1: # 1, 13 |
Friday
May 19 |
9.2 | Autonomous Systems and Stability |
§9.2: # 1, 3, 5
Plotting slope fields and trajectories |
Monday
May 22 |
9.3 | Locally Linear Systems | §9.3: # 1, 3, 5 |
Wednesday
May 24 |
9.4 | Competing-Species equations | §9.4: # 1 |
Friday
May 26 |
9.5 | Predator-Prey equations | §9.5: # 1, 3 |
Monday
May 29 |
No class! | Memorial day | |
Thursday June 01 Kemeny 008 |
11:30 am | Final: covers TBA | Past exams |