Differential Equations

Course Number:

Math 4100

Prerequisite: Math 2300 (Calculus 3)

**Course Topics and Core Homework Problems**

The following information is provided for illustrative purposes. Details are subject to change.

**Textbook**__Elementary Differential Equations with Boundary Value Problems__ by William Boyce, Richard DiPrima, and Douglas Meade, eleventh edition.

The text is available electronically and enrolled students will be billed automatically. Please see your instructor’s syllabus for details.

**Supplementary Notes (downloadable pdf file)****Planar Systems of Differential Equations**** **

The supplementary planar systems notes linked above are also (optionally) available at the bookstore: ask for the 4100 course packet.

Elementary Differential Equations with Boundary Value Problems (Boyce, DiPrima, Meade, 11th edition) | ||

Section | Topic | Homework |

2.1 | Linear Equations; Method of Integrating Factors | 2c, 4c, 6c, 9, 12, 14(b,c), 21 |

2.2 | Separable Differential Equations | 2, 3, 5, 10(a,c), 14(a,c), 18 |

2.3 | Modeling with First-Order Differential Equations | 1, 2, 5, 17(a,b),18(a,b) |

2.6 | Exact Equations and Integrating Factors | 1, 2, 4, 7, 11, 15, 19, 20 (see problem 17) |

3.1 | Homogeneous Differential Equations with Constant Coefficients | 3, 6, 10, 13, 15, 17 |

3.2 | Solutions of Linear Homogeous Equations; the Wronskian | 3, 7, 9, 10, 12, 13, 14, 15, 18, 19, 21, 24, 25, 27, 28 |

3.3 | Complex Roots of the Characteristic Equation | 1, 6, 11, 12, 13, 15, 19 |

3.4 | Repeated Roots; Redution of Order | 1, 2, 6, 10, 13, 19, 20 |

3.5 | Nonhomogeneous Equations; Method of Undetermined Coefficients | 1, 2, 5, 12, 14 |

3.6 | Variation of Parameters | 4, 6, 9, 10, 13 |

3.7 | Mechanical Vibrations | 1, 4, 5, 8, 17, 18(a,b) |

3.8 | Forced Periodic Vibrations | 4, 5, 7, 8 |

6.1 | Definition of the Laplace Transform | 1-3, 4(a,c), 6, 10, 12, 16 |

6.2 | Solution of Initial Value Problems | 3, 6, 7, 11, 15, 16, 17 |

6.3 | Step Functions | 1, 2, 5, 7, 9, 10, 14, 15, 16, 30 |

6.4 | Differential Equations with Discontinuous forcing functions | 1-4, 9, 11(a,b) |

6.5 | Impulse Functions | 1, 3, 4, 6, 10(a,b) |

6.6 | The Convolution Integral | 1(a), 4, 5, 7, 9, 11, 12 |

2.7 | Numerical Approrixmations: Euler's Method | 1,2,4 |

8.1 | The Euler or Tangent Line Method | 4, 5, 8, 22 |

Planar systems of Differential Equations (supplementary notes) | ||

1 | Introduction | 1.1, 1.2 |

2 | Some Concepts from Matrix Theory and Linear Algebra | 2.1, 2.2(1,4,6,7,8), 2.3(1),2.4(3),2.5(1,2,3) |

3 | General Theory of Linear 2x2 Systems | 3.1, 3.3, 3.4 |

4 | Case 1 (homogeneous, linear, constant coefficient) | 4.1, 4.2, 4.4, 4.5 |

5 | Case 2 | 5.1, 5.2, 5.3 |

6 | Case 3 | 6.1, 6.2, 6.4, 6.5 |

7 | Solutions of Nonhomegeous systems | 2.6(1,3), 7.1, 7.3, 7.4 |

8 | Qualitative Methods | 8.1, 8.2, 8.3 |

9 | Linearization of Nonlinear Systems at Isolated Rest Points (as time permits) | 9.1, 9.4, 9.5, 9.7 |