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

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