## Math 441. Differential Equations

Instructor Syllabus

**Text:** Boyce and DiPrima, *Elementary Differential Equations and Boundary Value Problems, 10th Edition*, John Wiley & Sons, Inc., 2012.

Subject | Chapter-Section | Class Hours |

Introduction | 1.1, 1.2, 1.3 | 1 |

First order linear equations | 2.1 (Exercise 38 on pg. 41) | 1 |

Separable and exact equations |
2.2, 2.6 |
1 |

Integrating factors and homogeneous equations |
2.6 (Exercise 30 on pg. 49) | 2 |

Differences between linear and nonlinear equations | 2.4, Bernoulli Equations | 1 |

Modeling with first order equations | 2.3 | 2 |

Autonomous equations and population dynamics | 2.5 | 2 |

The Picard existence and uniqueness theorem | 2.8 | 4 |

The basic theory or n^{th} order linear differential equations |
3.1, 3.2, 3.3, 4.1 | 6 |

n^{th} order linear equations with constant coefficients |
3.1, 3.3, 3.4, 4.2 | 3 |

Undetermined coefficients and variation of parameters for n^{th} order equations |
3.5, 3.6, 4.3, 4.4 | 2 |

Applications | 3.7, 3.8 | 1 |

Review of power series | 5.1 | 1 |

Series solutions near an ordinary point | 5.2, 5.3 | 2 |

Regular singularities, Euler equations | 5.4 | 2 |

Series solutions near a regular singular point (I, II) | 5.5, 5.6 | 2 |

Bessel's equation | 5.7 | 2 |

Introduction to systems | 7.1 | 1 |

Solving linear systems with constant coefficients | 7.5 | 1 |

Stability and Liapunov's Method | 9.2, 9.6 | 3 |

Leeway and Exams | 4 | |

Total number of lectures | 40 |

Approved by R. Muncaster 7/16/12.