| 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 |