# Math 220: Differential Equations

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## Course Information Heading link

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### Course Prerequisites

Grade of C or better in MATH 210 (Calculus III)

### Course Description

The course covers techniques and applications of differential equations, first and second order equations, Laplace transforms, series solutions, graphical and numerical methods, and partial differential equations.

### Credit Awarded

3 hours

### Course Materials

### Course Materials

#### Textbook

Nagle, Saff, and Snider, *Fundamentals of Differential Equations*, 9th edition, with MyLab Math (printed textbook is optional).

#### MyLab Math

MyLab Math access for this title is required and **must be purchased through Blackboard**. MyLab Math already includes an electronic version of the textbook, so buying a printed copy is optional.

## List of Topics Heading link

Section | Topic(s) |
---|---|

1.1 | Background: Introduction to ODEs |

1.2 | Solutions and IVPs |

1.3 | Direction Fields |

1.4 | Euler's Method |

2.1 | Introduction: Falling body |

2.2 | Separable Equations |

2.3 | First Order Linear Equations |

2.4 | Exact Equations |

3.2 | Mixing Problems and Population Models |

3.4 | Newtonian Mechanics |

3.5, 5.7 (optional) | RLC Circuits |

3.6-3.7 (optional) | Numerical Methods |

4.1 | The Mass-spring oscillator |

4.2 | Homogeneous Linear Equations |

4.3 | Auxiliary Equations with Complex Roots |

4.4 | Method of Undetermined Coefficients |

4.5 | The Superposition Principle and Undetermined Coefficients Revisited |

4.6 | Variation of Parameters |

4.7 | Cauchy-Euler Equations and Reduction of Order |

4.9-4.10 (optional) | Mechanical Vibrations |

5.2 | Differential Operators, Method of Elimination for Systems |

5.4 (optional) | Phase Plane |

7.2 | Laplace Transform |

7.3 | Properties of Laplace Transforms |

7.4 | Inverse Laplace Transform |

7.5 | Solving Initial Value Problems by Laplace Transforms |

7.6 | Transforms of Discontinuous Functions |

7.9 | Dirac Delta Function |

10.1 | Introduction to Partial Differential Equations |

10.2 | Separation of Variables, Boundary Value Problems, and Eigenvalue Problems |

10.3 | Fourier Series |

10.4 | Fourier Sine and Cosine Series |

10.5 | Heat Equation |

10.6 | Wave Equation |