Below are the lecture notes for every lecture session along with links to the Mathlets used during lectures.
LEC# | TOPICS | RELATED MATHLETS |
---|---|---|
I. First-order 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. Second-order 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) |
|
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 |