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
January 6 |
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 Plotting slope fields and trajectories | ||||
Wednesday
January 8 |
1.3, 2.1 |
Classification and linear first-order ODEs
DirectionFields2.nb |
§2.1: #1, 9, 12 | ||||
Friday
January 10 |
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 January 13 | 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
January 15 |
2.5 | Autonomous equations and population dynamics |
§2.5: #9, 23
Review multivariable chain rule KA - Slope fields & solutions |
||||
Friday
January 17 |
2.6 |
Exact equations
LastExamplePlot.nb |
§2.6: #23, 26, 30, 31 | ||||
Tuesday
January 21 (x-hour) |
3.1, 3.2 |
Second order constant coefficient equations
with distinct roots; the Wronskian |
§3.1: #2, 4
§3.2: #2, 4, 14 |
||||
Wednesday
January 22 |
3.3 |
Complex conjugate roots
SolutionPlots.nb |
§3.2: # 25
§3.3: # 2, 16, 24 | ||||
Thursday
January 23
4:30 - 6:30, Kemeny 008 7:00 - 9:00, Kemeny 108 (alternative time) |
1st Midterm | 1st Midterm:material through 2.6. | Past exams | ||||
Friday
January 24 |
3.4 | Repeated roots and reduction of order | §3.4: # 2, 16, 24 | ||||
Monday
January 27 |
3.5, 3.6 | Method of undetermined coefficients; Variation of parameters |
§3.5: #5, 19
§3.6: #9, 13 | ||||
Wednesday
January 29 |
7.1, 7.2 |
Review of matrices.
Demo |
§7.1: #10, 14 | ||||
Friday
January 31 |
7.3, 7.4 | Systems of ODEs; Existence and uniqueness of solutions of systems of ODEs. |
§7.3: #17, 18
§7.4: #6 |
||||
Monday
February 3 |
7.5 |
Constant coefficients systems with distinct real eigenvalues Example2Plots.nb, Example3Plots.nb, EigenManipulate.nb |
§7.5: #3, 12 | ||||
Wednesday
February 5 |
7.6 |
Constant coefficient systems with complex conjugate eigenvalues ComplexEigenPlot.nb |
§7.6: #2, 6 | ||||
Friday
February 7 |
7.8 | Repeated Eigenvalues | §7.8: #1, 18 | ||||
Monday
February 10 |
7.8 & 9.1 | Repeated eigenvalues; Phase plane; linear systems | §9.1: #1, 8 | ||||
Wednesday
February 12 | 9.1; begin 7.9. | Phase Plane; Linear Systems | §9.1: # 1, 8 | ||||
Thursday
February 13
4:30 - 6:30, Kemeny 008 7:00-9:00, Kemeny 108 (alternative time) |
2nd Midterm |
2nd Midterm
Material from 3.1 through 7.8. |
Past exams | ||||
Friday
February 14 |
7.9 | Nonhomogeneous Linear Systems | §7.9: # 1, 3, 15 | ||||
Monday
February 17 |
9.2 | Autonomous Systems and Stability | §9.2: # 1, 3, 5 Plotting slope fields and trajectories Direction field plotter |
||||
Wednesday
February 19 |
9.3 9.4 | Locally Linear Systems | §9.3: # 1, 3, 5 | ||||
Friday
February 21 |
9.4 and 9.5 | Competing Species and Predator-Prey Equations | §9.4: # 1, 8 §9.5: # 1, 3, 11 | ||||
Monday
February 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
February 26 |
6.3 | IVPs and Step functions | KA: Laplace/step function differential equation | ||||
Friday
February 28 |
6.4, 6.5 | Discontinuous forcing functions, Impulse Functions | KA: The convolution integral | ||||
Monday
March 2 |
6.6 | The convolution integral | §6.6: # 9, 13 KA: The convolution integral | ||||
Wednesday March 4 | Course Wrap Up | ||||||
Friday
March 6 |
Course wrap up | Course instruction ends. | |||||
Thursday March 12 Room Kemeny 008 |
3:00 pm |
Final
The exam is cumulative and covers material from the whole term. |
Past exams |