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 | ||||
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Wednesday
September 12 |
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 | ||||
Friday
September 14 |
1.3, 2.1 |
Classification and linear first-order ODEs
DirectionFields2.nb |
§2.1: #1, 9, 12 | ||||
Monday
September 17 |
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 |
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Thursday X hour September 20 (Section 1 Gelb) OR
Wednesday September 19 (Section 2 Lin) |
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 |
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Friday
September 21 |
2.5 | Autonomous equations and population dynamics |
§2.5: #9, 23
Review multivariable chain rule KA - Slope fields & solutions |
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Monday
September 24 |
2.6 |
Exact equations
LastExamplePlot.nb |
§2.6: #23, 26, 30, 31 | ||||
Wednesday
September 26 |
3.1, 3.2 |
Second order constant coefficient equations
with distinct roots; the Wronskian |
§3.1: #2, 4
§3.2: #2, 4, 14 |
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Friday
September 28 |
3.3 |
Complex conjugate roots; Runge-Kutta Method
SolutionPlots.nb |
§3.2:
§3.3: , 16, 24 | ||||
Monday
October 1 |
3.4 | Repeated roots and reduction of order | §3.4: , 16, 24 | ||||
Tuesday
October 2: 4:30 - 6:30 pm, Location Kemeny 008 |
1st Midterm | 1st Midterm:material through 3.2. | Past exams | ||||
Wednesday
October 3 |
3.5, 3.6 | Method of undetermined coefficients; Variation of parameters |
§3.5: #5, 19
§3.6: #9, 13 | ||||
Friday
October 5 |
7.1, 7.2 |
Review of matrices.
Demo |
§7.1: #10, 14 | ||||
Monday
October 8 |
7.3, 7.4 | Systems of ODEs; Existence and uniqueness of solutions of systems of ODEs. |
§7.3: #17, 18
§7.4: #6 |
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Wednesday
October 10 |
7.5 |
Constant coefficients systems with distinct real eigenvalues Example2Plots.nb, Example3Plots.nb, EigenManipulate.nb |
§7.5: #3, 12 | ||||
Friday
October 12 |
7.6 |
Constant coefficient systems with complex conjugate eigenvalues ComplexEigenPlot.nb |
§7.6: #2, 6 | ||||
Monday
October 15 |
7.7 | Fundamental Matrices | §7.7: #2, 12 | ||||
Wednesday
October 17 |
7.8 | Repeated eigenvalues | §7.8: #1, 18 | ||||
Friday
October 19 | 9.1 | Phase Plane: Linear Systems | §9.1: # 1, 8 | ||||
Monday
October 22 |
7.9 | Nonhomogeneous Linear Systems | §7.9: # 1, 3, 15 | ||||
Wednesday
October 24 |
9.2 | Autonomous Systems and Stability | §9.2: # 1, 3, 5 Plotting slope fields and trajectories Direction field plotter |
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Friday
October 26 |
9.3 9.4 | Locally Linear Systems | §9.3: # 1, 3, 5 | ||||
Monday
October 29 |
9.4 and 9.5 | Competing Species and Predator-Prey Equations | §9.4: # 1, 8 §9.5: # 1, 3, 11 | ||||
Tuesday
October 30: 4:30 - 6:30 pm, Kemeny 008. |
2nd Midterm |
2nd Midterm
Material from 3.5 through 9.3. |
Past exams | ||||
Wednesday
October 31 |
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 |
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Friday
November 2 |
6.3 | IVPs and Step functions | KA: Laplace/step function differential equation | ||||
Monday
November 5 |
6.4, 6.5 | Discontinuous forcing functions, Impulse Functions | KA: The convolution integral | ||||
Wedensday
November 7 |
6.6 | The convolution integral | §6.6: # 9, 13 KA: The convolution integral | ||||
Thursday X hour November 8 (Section 2 Lin) OR
Friday November 9 (Section 1 Gelb) |
Course Wrap Up | ||||||
Monday
November 12 |
Course wrap up | ||||||
Tuesday
November 13 |
Course instruction ends. | ||||||
Friday November 16 Room Kemeny 008 |
11:30 am |
Final
The exam is cumulative and covers material from the whole term. |
Past exams |