The readings referred to in the table are from the text: Borrelli, R. and C. Coleman. Differential Equations: A Modeling Perspective. Wiley Text Books, 2nd ed., New York, 2003. ISBN: 0471433322.
| SES # | TOPICS | READINGS |
|---|---|---|
| Unit I : First-order ODE’s | ||
| 1 | Modeling and Terminology | Chapter 1 |
| 2 | Linear Differential Equations | Chapter 2: Sections 2.1 and 2.2 |
| 3 | Existence and Uniqueness of Solutions: Uniqueness | Chapter 2: Sections 2.3 and A.1 |
| 4 | Existence and Uniqueness of Solutions: Picard Iterates | Chapter 2: Section A.2 |
| 5 | Extension of Solutions | Chapter 2: Section A.3 |
| 6 |
Slope Fields
Separable Equations |
Chapter 2: Sections 2.4 and 2.5 |
| 7 | Qualitative Analysis | Chapter 2: Section 2.8 |
| 8 | Approximate Numerical Solutions | Chapter 2: Page 122 |
| 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 | Chapter 3: Sections 3.1 and 3.2 |
| 12 |
Direction Fields
Brief Review of Complex Numbers |
Chapter 3: Section 3.3 |
| 13 | Inhomogeneous 2nd Order Linear ODE’s | Chapter 3: Sections 3.5 and 3.6 |
| 14 | Theory of 2nd Order Linear and Nonlinear ODE’s | Chapter 3: Sections 3.7 and 3.8 |
| 15 | Beats, Resonance, and Frequency Response Modeling | Chapter 4: Sections 4.1 and 4.3 |
| 16 | Extra Topics | |
| Unit III: Fourier Series | ||
| 17 | Fourier Trigonometric Series | Chapter 10: Sections 10.1 and 10.2 |
| 18 | Half-range and Exponential Fourier Series | Chapter 10: Section 10.3 |
| 19 | In-class Exam 2 | |
| 20 | The Dirac Delta Function | Chapter 10: Page 328 |
| Unit IV: The Laplace Transform | ||
| 21 | The Laplace Transform: Solving IVP’s | Chapter 5: Section 5.1 |
| 22 | Properties of the Transform | Chapter 5: Sections 5.2 and 5.3 |
| 23 | Convolution | Chapter 5: Section 5.4 |
| 24 | Extra Topics | |
| Unit V: Linear Systems of ODE’s | ||
| 25 |
Compartment Models
Introduction to Linear Algebra |
Chapter 6: Section 6.1 and page 421 |
| 26 | Eigenvalues, Eigenvectors and Eigenspaces | Chapter 6: Section 6.2 |
| 27 | Homogeneous Linear Systems: Real Eigenvalues Case | Chapter 6: Section 6.3 |
| 28 | Homogeneous Linear Systems: Complex Eigenvalues Case | Chapter 6: Section 6.4 |
| 29 | Inhomogeneous Linear Systems: Exponentials of Matrices | Chapter 6: Section 6.6 |
| 30 | Theory of General Linear Systems of ODE’s | Chapter 6: Section 6.8 |
| 31 | Extra Topics and/or Review | |
| 32 | In-class Exam 3 | |
| Unit VI: Nonlinear Systems of ODE’s | ||
| 33 | The Fundamental Theorem | Chapter 7: Section 7.1 |
| 34 |
Autonomous Systems
Interacting Species Models |
Chapter 7: Sections 7.2 and 7.3 |
| 35 | Stability of Linear and Nonlinear Autonomous Systems | Chapter 8: Sections 8.1 and 8.2 |
| 36 |
Conservative Systems
Lyapunov Functions |
Chapter 8: Sections 8.3 and page 508 |
| 37 | Limit Cycles and Planar Autonomous Systems | Chapter 9: Sections 9.1 and 9.2 |
| 38 | Extra Topics | |
| 39 | Review | |
| 40 | Final Exam | |
