The problems are designed to be worked on by students in groups in recitation.
Recitation files.
| 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 |
|
|
