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 |