Unit I: First-order ODE's |
1 |
Modeling and Terminology (PDF) |
2 |
Linear Differential Equations (PDF) |
3 |
Existence and Uniqueness of Solutions: Uniqueness |
4 |
Existence and Uniqueness of Solutions: Picard Iterates |
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) |
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 |
Unit IV: The Laplace Transform |
21 |
The Laplace Transform: Solving IVP’s |
22 |
Properties of the Transform (PDF) |
23 |
Convolution (PDF) |
24 |
Extra Topics (PDF) |
Unit V: Linear Systems of ODE's |
25 |
Compartment Models
Introduction to Linear Algebra |
26 |
Eigenvalues, Eigenvectors and Eigenspaces |
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 |
31 |
Extra Topics and/or Review |
32 |
In-class Exam 3 |
Unit VI: Nonlinear Systems of ODE's |
33 |
The Fundamental Theorem (PDF) |
34 |
Autonomous Systems
Interacting Species Models (PDF) |
35 |
Stability of Linear and Nonlinear Autonomous Systems (PDF) |
36 |
Conservative Systems
Lyapunov Functions |
37 |
Limit Cycles and Planar Autonomous Systems |
38 |
Extra Topics |
39 |
Review |
40 |
Final Exam |