#### Prerequisites & Bulletin Description

#### Course Objectives

The principal aim of Ordinary Differential Equations is for students to learn the fundamental techniques for solving first order and linear second order ordinary differential equations. Upon completion of this course a student should be able to:

- Solve a first order differential equation exactly.
- Solve a second order linear differential equations with constant coefficients.
- Solve second order linear non-homogeneous differential equations using the Method of Undetermined Coefficients and the Method of Variation of Parameters.
- Solve homogeneous linear systems of first equations using eigenvalues and eigenvectors.
- Construct a phase plane analysis of autonomous systems.
- Construct series solutions of first and second order linear equations and solve equations near ordinary and regular singular points; reproduce Special Functions.
- Apply existence theorems to determine if a first order initial value problem can be solved.

#### Evaluation of Students

Students will be graded on their ability to devise, organize and present in correct mathematical English solutions to problems. While instructors may design their own methods of evaluation student performance, these methods must include in-class examinations, graded homework assignments and a final exam.

#### Course Outline

Topics |
Number of Weeks |

First Order Equations | 4 |

Linear Second Order Equations | 3 |

Systems of Linear Equations and Phase Plane Analysis | 3 |

Series Solutions of First and Second Order Equations | 3 |

Existence and Uniqueness Theorems | 1 |

#### Textbooks & Software

*Elementary Differential Equations and Boundary Value Problems, 8th Edition*, by Boyce and DiPrima

*Mathematica*, by Wolfram Research

Submitted by: David Ellis

Date: December 2008