| Unit I : First-order ODE's |
| 1 | Modeling and Terminology | |
| 2 | Linear Differential Equations | |
| 3 | Existence and Uniqueness of Solutions: Uniqueness | |
| 4 | Existence and Uniqueness of Solutions: Picard Iterates | |
| 5 | Extension of Solutions | Problem set 1 due |
| 6 | Slope Fields
Separable Equations | |
| 7 | Qualitative Analysis | |
| 8 | Approximate Numerical Solutions | Problem set 2 due |
| 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 Some Instructions on Plotting Functions in MATLAB® | |
| 12 | Direction Fields
Brief Review of Complex Numbers | |
| 13 | Inhomogeneous 2nd Order Linear ODE's | |
| 14 | Theory of 2nd Order Linear and Nonlinear ODE's | Problem set 3 due |
| 15 | Beats, Resonance, and Frequency Response Modeling | |
| 16 | Extra Topics | |
| Unit III: Fourier Series |
| 17 | Fourier Trigonometric Series | Problem set 4 due |
| 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 | |
| 23 | Convolution | Problem set 5 due |
| 24 | Extra Topics | |
| Unit V: Linear Systems of ODE's |
| 25 | Compartment Models
Introduction to Linear Algebra | |
| 26 | Eigenvalues, Eigenvectors and Eigenspaces | Problem set 6 due |
| 27 | Homogeneous Linear Systems: Real Eigenvalues Case | |
| 28 | Homogeneous Linear Systems: Complex Eigenvalues Case | |
| 29 | Inhomogeneous Linear Systems: Exponentials of Matrices | Problem set 7 due |
| 30 | Theory of General Linear Systems of ODE's | |
| 31 | Extra Topics and/or Review Supplementary Notes on Jordan Normal Form | Problem set 8 due |
| 32 | In-class Exam 3 | |
| Unit VI: Nonlinear Systems of ODE's |
| 33 | The Fundamental Theorem | |
| 34 | Autonomous Systems
Interacting Species Models | Problem set 9 due |
| 35 | Stability of Linear and Nonlinear Autonomous Systems | |
| 36 | Conservative Systems
Lyapunov Functions | |
| 37 | Limit Cycles and Planar Autonomous Systems | Problem set 10 due |
| 38 | Extra Topics | |
| 39 | Review | |
| 40 | Final Exam | |