The problems are designed to be worked on by students in groups in recitation.
| REC # | TOPICS | PROBLEMS | SOLUTIONS |
|---|---|---|---|
| I. First-order differential equations | |||
| 1 | Natural growth, separable equations | (PDF) | (PDF) |
| 2 | Direction fields, integral curves, isoclines, separatrices, funnels | (PDF) | (PDF) |
| 3 | Euler's method; linear models | (PDF) | (PDF) |
| 4 | First order linear ODEs; integrating factors | (PDF) | (PDF) |
| 5 | Complex numbers; complex exponentials | (PDF) | (PDF) |
| 6 | Review for exam I | ||
| II. Second-order linear equations | |||
| 7 | Solutions to second order ODEs | (PDF) | (PDF) |
| 8 | Homogeneous 2nd order linear constant coefficient equations | (PDF) | (PDF) |
| 9 | Exponential and sinusoidal input signals | (PDF) | (PDF) |
| 10 | Gain and phase lag; resonance; undetermined coefficients | (PDF) | (PDF) |
| 11 | Frequency response | (PDF) | (PDF) |
| 12 | Review for exam II | ||
| III. Fourier series | |||
| 13 | Fourier series: introduction | (PDF) | (PDF) |
| 14 | Fourier series | (PDF) | (PDF) |
| 15 | Fourier series: harmonic response | (PDF) | (PDF) |
| 16 | Step and delta functions, and step and delta responses | (PDF) | (PDF) |
| 17 | Convolution | (PDF) | (PDF) |
| 18 | Laplace transform | (PDF) | (PDF) |
| 19 | Laplace transform II | (PDF) | (PDF) |
| 20 | Review for exam III | ||
| IV. First order systems | |||
| 21 | First order linear systems | (PDF) | (PDF) |
| 22 | Eigenvalues and eigenvectors | (PDF) | (PDF) |
| 23 | Linear phase portraits | (PDF) | (PDF) |
| 24 | Matrix exponentials | (PDF) | (PDF) |
| 25 | Autonomous systems | (PDF) | (PDF) |
| 26 | Reviews | ||