**Prerequisites & Bulletin Description**

## Course Objectives

The principal aim of Mathematical Modeling is for students to learn the methods for representing specific real-world systems by mathematical constructs. Students who successfully complete this course should:

- Understand the basic principals of mechanical vibrations, population dynamics, and traffic flow.
- Be capable of solving first order linear partial differential equations, in particular equations modeling wave phenomena; be capable of presenting qualitative information concerning non-linear wave equations.
- Be capable of linearizing non-linear systems of equations and determining the stability properties of equilibria.
- Approximating the properties of targeted real-world systems from the properties of their appropriate mathematical models.

## Evaluation of Students

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

## Course Outline

Topics |
Number of Weeks |

Mechanical Vibrations & Phase Plane Analysis | 4 weeks |

Population Dynamics | 3 weeks |

Partial Differential Equations: 1st & 2nd order wave equations | 3 weeks |

Traffic flow | 4 weeks |

## Textbooks & Software

*Mathematical Models*, by Richard Haberman. * Partial Differential Equations for Scientists and Engineers*, by Stanley Farlow.

Submitted by: David Ellis

Date: September 22, 2006