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 |