| 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 |
|