| 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 | |
When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.