The lecture notes below represent a summary of the topics discussed and analyzed in class.
SES # | TOPICS |
---|---|
Unit I: First-order ODE’s | |
1 | Modeling and Terminology (PDF) |
2 | Linear Differential Equations (PDF) |
3 | Existence and Uniqueness of Solutions: Uniqueness (PDF) |
4 | Existence and Uniqueness of Solutions: Picard Iterates (PDF) |
5 | Extension of Solutions (PDF) |
6 |
Slope Fields
Separable Equations |
7 | Qualitative Analysis (PDF) |
8 | Approximate Numerical Solutions (PDF) |
9 | Extra Topics and/or Review |
10 | In-class Exam 1 |
Unit II: Second-order ODE’s | |
11 |
Homogeneous 2nd Order Linear ODE’s with Constant Coefficients (PDF) Some Instructions on Plotting Functions in MATLAB® (PDF) |
12 |
Direction Fields
Brief Review of Complex Numbers |
13 | Inhomogeneous 2nd Order Linear ODE’s (PDF) |
14 | Theory of 2nd Order Linear and Nonlinear ODE’s (PDF) |
15 | Beats, Resonance, and Frequency Response Modeling |
16 | Extra Topics (PDF) |
Unit III: Fourier Series | |
17 | Fourier Trigonometric Series (PDF) |
18 | Half-range and Exponential Fourier Series |
19 | In-class Exam 2 |
20 | The Dirac Delta Function (PDF) |
Unit IV: The Laplace Transform | |
21 | The Laplace Transform: Solving IVP’s (PDF) |
22 | Properties of the Transform (PDF) |
23 | Convolution (PDF) |
24 | Extra Topics (PDF) |
Unit V: Linear Systems of ODE’s | |
25 | Compartment Models and Introduction to Linear Algebra (PDF) |
26 | Eigenvalues, Eigenvectors and Eigenspaces (PDF) |
27 | Homogeneous Linear Systems: Real Eigenvalues Case (PDF) |
28 | Homogeneous Linear Systems: Complex Eigenvalues Case |
29 | Inhomogeneous Linear Systems: Exponentials of Matrices |
30 | Theory of General Linear Systems of ODE’s (PDF) |
31 |
Extra Topics and/or Review Supplementary Notes on Jordan Normal Form (PDF) |
32 | In-class Exam 3 |
Unit VI: Nonlinear Systems of ODE’s | |
33 | The Fundamental Theorem (PDF) |
34 | Autonomous Systems and Interacting Species Models (PDF) |
35 | Stability of Linear and Nonlinear Autonomous Systems (PDF) |
36 | Conservative Systems and Lyapunov Functions (PDF) |
37 | Limit Cycles and Planar Autonomous Systems |
38 | Extra Topics |
39 | Review |
40 | Final Exam |