**Instructors:** Matthew Ellison, Dimitrios Giannakis

**Course on canvas.dartmouth.edu.**⇗

## Course Schedule

Sections and problems are from Boyce & DiPrima, 11th edition.

Lectures | Sections | Description | Tentative Homework |

Week 1: Th Jan 4 |
1.1, 1.2, 1.3 | Introduction to differential equations; classification of ODEs | 1.1: #5, 6, 8, 18, 20 1.2: #5, 10 (Hint: do (b) first), 11 |

Week 2: T Jan 9 | 2.1, 2.2 | Integrating factors; separable equations | 2.1: #9, 12, 20, 23 2.2: #6,15, 20 |

Week 2: Th Jan 11 | 2.3, 2.4 | Modeling with differential equations; existence-uniqueness theorems | 2.3: #2, 6 (Hint: solve 6(c) numerically), 11 2.4: #8, 10, 18, 21, 24, 27 |

Week 3: T Jan 16 | 2.5, 2.6 | Autonomous equations; exact equations | 2.5: #3, 8, 15 2.6: #2, 10, 12 |

Week 3: Th Jan 18 | 3.1, 3.2 | Second-order constant coefficient equations with distinct roots; the Wronskian | 3.1: #11, 16, 17, 20 3.2: #8, 15, 17,21, 27 |

Week 4: T Jan 23 | 3.3, 3.4 | Complex conjugate roots; repeated roots and reduction of order | 3.3: #4, 8, 14, 26 3.4: #5, 9, 22 |

Week 4: Th Jan 25 | 3.5, 3.6 | Inhomogeneous equations; method of undetermined coefficients and variation of parameters |
3.5: #7, 10, 11, 22 |

Week 4: F Jan 26 |
Midterm Exam 1 | Material through 3.3 | |

Week 5: T Jan 30 | 7.1, 7.2 7.3 | Review of matrices; systems of ODEs | 7.1: #6,12 7.2: #2, 12, 16 7.3: #9, 19 |

Week 5: Th Feb 1 | 7.4, 7.5 | Existence and uniqueness of solutions of systems of ODEs; systems with distinct real eigenvalues | 7.4: #8 (only (a,b,c)), 11, 12(only (a,b)) 7.5: #6, 12, 18, 21 |

Week 6: T Feb 6 | 7.6, 7.7 | Systems with complex eigenvalues; fundamental solutions | 7.6: #8, 9, 23 7.7: (TBD) |

Week 6: Th Feb 8 | 7.8, 7.9 | Systems with repeated eigenvalues; inhomogeneous linear systems | 7.8: #8, 13, 17 (only (a,b,c,d)) 7.9: # 2, 3, 7, 10 (only verify the general solution of the corresponding homogeneous part) |

Week 7: T Feb 13 | 9.1, 9.2 | The phase plane; autonomous systems and stability | 9.1: #15, 17, 18 9.2: #3, 7 (only (a,b,c)), 19 |

Week 7: Th Feb 15 | 9.3 | Locally linear systems | 9.3: #3, 7, 17, 24 |

Week 7: F Feb 16 |
Midterm Exam 2 | Material from 3.4 through 7.9 | |

Week 8: T Feb 20 | 9.4, 9.5 | Competing species; predator-prey equations | 9.4: #3, 6 9.5: #4, 12 |

Week 8: Th Feb 22 | 6.1, 6.2 | Laplace transform and the IVP | 6.1: #2, 11, 18 6.2: #12, 18, 21, 24 |

Week 9: T Feb 27 | 6.3 | Step functions | 6.3: #12, 14, 17 |

Week 9: Th Feb 29 | 6.4, 6.5 | Discontinuous forcing functions, impulse functions | 6.4: #5, 12 6.5: #6, 10, 14 |

Week 10: T Mar 5 | 6.6 | The convolution integral | 6.6: #1, 2, 13, 16 |

March 8 | Final Exam | Exam covers material from the whole course |