Below are the lecture notes for every lecture session along with links to the Mathlets used during lectures.
LEC#  TOPICS  RELATED MATHLETS 

I. Firstorder differential equations  
1  Direction fields, existence and uniqueness of solutions (PDF)  Related Mathlet: Isoclines 
2  Numerical methods (PDF)  Related Mathlet: Euler’s method 
3  Linear equations, models (PDF)  
4  Solution of linear equations, integrating factors (PDF)  
5  Complex numbers, roots of unity (PDF)  
6  Complex exponentials; sinusoidal functions (PDF)  Related Mathlets: Complex roots, Complex exponential 
7  Linear system response to exponential and sinusoidal input; gain, phase lag (PDF)  Related Mathlet: Trigonometric identity 
8  Autonomous equations; the phase line, stability (PDF)  Related Mathlet: Phase lines 
9  Linear vs. nonlinear (PDF)  
10  Exam I  
II. Secondorder linear equations  
11  Modes and the characteristic polynomial (PDF)  
12  Good vibrations, damping conditions (PDF)  Related Mathlet: Damped vibrations 
13  Exponential response formula, spring drive (PDF)  Related Mathlet: Harmonic frequency response: Variable input frequency 
14  Complex gain, dashpot drive (PDF)  Related Mathlet: Amplitude and phase: Second order II 
15  Operators, undetermined coefficients, resonance (PDF)  
16  Frequency response (PDF)  Related Mathlets: Amplitude and phase: Second order II, Amplitude and phase: First order, Amplitude and phase: Second order III 
17  LTI systems, superposition, RLC circuits (PDF)  Related Mathlet: Series RLC circuit 
18 
Engineering applications (PDF) Video of the guest lecture by Prof. Kim Vandiver 

19  Exam II  
III. Fourier series  
20  Fourier series (PDF)  Related Mathlet: Fourier coefficients 
21  Operations on fourier series (PDF)  Related Mathlet: Fourier coefficients: Complex with sound 
22  Periodic solutions; resonance (PDF)  
23  Step functions and delta functions (PDF)  
24  Step response, impulse response (PDF)  
25  Convolution (PDF)  Related Mathlets: Convolution: Accumulation, Convolution: Flip and drag 
26  Laplace transform: basic properties (PDF)  
27  Application to ODEs (PDF)  
28  Second order equations; completing the squares (PDF)  
29  The pole diagram (PDF)  Related Mathlets: Amplitude response: Pole diagram, Poles and vibrations 
30  The transfer function and frequency response (PDF)  
31  Exam III  
IV. First order systems  
32  Linear systems and matrices (PDF)  
33  Eigenvalues, eigenvectors (PDF)  Related Mathlets: Linear phase portrait: Matrix entry, Matrix vector 
34  Complex or repeated eigenvalues (PDF)  Related Mathlet: Linear phase portrait: Matrix entry 
35  Qualitative behavior of linear systems; phase plane (PDF)  Related Mathlets: Linear phase portrait: Matrix entry, Linear phase portrait: Cursor entry 
36  Normal modes and the matrix exponential (PDF)  
37  Nonlinear systems (PDF)  
38  Linearization near equilibria; the nonlinear pendulum (PDF)  
39  Limitations of the linear: limit cycles and chaos (PDF)  Related Mathlet: Vector fields 
41  Final exam 