The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.
| Day | Date | Sections in Text | Description | Practice Problems |
|---|---|---|---|---|
| 1 | (W) Jan 4 | 1.1, 1.2 |
What are differential equations? DirectionFields.nb |
§1.1: #1, 2, 26 §1.2: # 1(a), 2(a) |
| 2 | (F) Jan 6 | 1.3, 2.1 |
Classification and linear first-order ODEs DirectionFields2.nb |
§2.1: #1, 9, 12 |
| 3 | (M) Jan 9 | 2.2, 2.4 |
Separable equations and existence-uniqueness theorems DirectionFields3.nb |
§2.2: #9, 11 §2.4: #5, 11 |
| 4 | (W) Jan 11 | 2.3 |
Modeling with differential equations MixingPlot.nb, WorksheetSlopeFields.nb |
§2.3: Solve the IVPs in Examples 2 and 3 §2.3: #9, 10 |
| 5 | (F) Jan 13 | 2.5 | Autonomous equations and population dynamics | §2.5: #9, 23 Review multivariable chain rule |
| 6 | sec1 (T) X-hour sec2 (W) Jan 18 |
2.6 |
Exact equations LastExamplePlot.nb |
§2.6: #23, 26, 30, 31 |
| 7 | sec1 (W) Jan 18 sec2 (Th) X-hour |
3.1, 3.2 | Second order constant coefficient with distinct real roots; the Wronskian |
§3.1: #2, 4 §3.2: #2, 4, 14 |
| 8 | (F) Jan 20 | 3.3 |
Complex conjugate roots SolutionPlots.nb |
§3.2: #25 §3.3: #8, 27 |
| 9 | (M) Jan 23 | 3.4 | Repeated roots and reduction of order | §3.4: #2, 16, 24 |
| 10 | (W) Jan 25 | 3.5 | Method of undetermined coefficients | §3.5: #5, 19 |
| 11 | (F) Jan 27 | 3.6 | Variation of parameters | §3.6: #9, 13 |
| 12 | (M) Jan 30 | 3.7, 3.8 | Modeling of vibrations Demos: 1, 2, 3, 4 ForcedVibrationsPlot.nb |
§3.7: #19 §3.8: #17 |
| 13 | (W) Feb 1 | 7.2 | Review of matrices, part 1 | |
| 14 | (F) Feb 3 | 4.1, 4.2 | Order n homogeneous linear equations with constant coefficients |
§4.1: #7, 8, 19(c) §4.2: #14, 17 |
| 15 | (M) Feb 6 | 4.3, 4.4 | Undetermined coefficients and variation of parameters for order n equations |
§4.3: #2, 4 §4.4: #2 |
| (W) Feb 8 | Midterm: covers 1.1-4.2 | Past exams Practice Problems Mid-Term Solutions |
||
| 16 | (W) Feb 8 | 7.1, 7.3 |
Review of matrices, part 2. Systems of ODEs. Demo |
§7.1: #10, 14 §7.3: #17, 18 |
| 17 | (F) Feb 10 | 7.4 | Existence and uniqueness of solutions of systems of ODEs | |
| 18 | (M) Feb 13 | 7.5 |
Constant coefficients systems with distinct real eigenvalues Example2Plots.nb, Example3Plots.nb, EigenManipulate.nb |
§7.5: #3, 12 |
| 19 | (W) Feb 15 | 7.6 |
Constant coefficient systems with complex conjugate eigenvalues ComplexEigenPlot.nb |
§7.6: #2, 6 |
| 20 | (F) Feb 17 | 7.8 | Repeated eigenvalues | §7.8: #1, 18 |
| 21 | (M) Feb 20 | 5.1, 5.2 | Power series review and solution near an ordinary point Some frequently seen Taylor series |
§5.2: #10, 12, 20 |
| 22 | (W) Feb 22 | 5.3, 5.4 |
Convergence of power series solutions; the Euler equation TaylorConvergencePlots.nb |
§5.3: #17 §5.4: #3, 8 |
| 23 | (F) Feb 24 | 10.1 | Boundary value problems; eigenfunctions | §10.1: #5, 8 |
| 24 | (M) Feb 27 | 10.2 | Fourier series | §10.2: #14, 15 |
| 25 | (W) Mar 1 | 10.3 |
Fourier convergence theorem FourierPlots.nb |
§10.3: #11 |
| 26 | (F) Mar 3 | 10.4 | Even and odd functions | §10.4: #17 |
| 27 | (M) Mar 6 | 10.5 |
The heat equation HeatEqnPlot.nb |
§10.5: #7, 10 |
| 28 | (W) Mar 8 | Wrap up | ||
| (Sat) Mar 11 | Final Exam: comprehensive | Past exams Practice Problems |