# MA 422 Mathematical Modeling

### Syllabus

## Office Hours

Monday 2-4, Friday 2-4 (no appointment necessary). Feel free to make an appointment if you cannot come to my regular office hours.

## Textbook

**No textbook required.** Handouts with class material and practice problems will be distributed for each course topics. The textbooks used for the class preparation include the following:

**D. Edwards and M. Hamson**, Guide to Mathematical Modeling, Published by CRC Press, 1990.

**Giordano, Weir, and Fox**, First Course in Mathematical Modeling , Thomson Brooks/Cole, 2003.

## Technology

Matlab will be used extensively. All students are also recommended to have a calculator.

## Topics Covered

1. Basic ideas and techniques of mathematical modeling.2. Programming in Matlab. M-files.

3. Modeling with differential equations. Continuous dynamical systems.

4. Modeling with difference equations. Discrete dynamical systems.

5. Dimensional analysis.

6. Empirical (experimental) models. Effectiveness and validity.

7. Interpolation and model fitting.

8. Simulation modeling. Monte Carlo simulations.

9. Discrete and continuous optimization modeling.

10. Modeling with systems of difference and differential equations.

11. Report writing and result presentation.

## Grading

Assignment 1 | 25% |

Assignment 2 | 25% |

Assignment 3 | 25% |

Project | 25% |

TOTAL | 100% |

A+ | A | A- | B+ | B | B- | C+ | C | C- | D+ | D | D- | F | |

grade | 97-100 | 93-96 | 90-92 | 87-89 | 83-86 | 80-82 | 77-79 | 73-76 | 70-72 | 67-69 | 63-66 | 60-62 | 0-59 |

## Prerequisites

MA201 or the permission of instructor.

## Attendance

Since the course is mostly based on material covered in class handouts and classwork, it is absolutely**imperative that students attend all classes**. Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.

## Assignments, Projects

There will be**three assignments**plus a

**student project + presentation**. No assignment grade will be dropped. Assignments turned in after their due date will receive an automatic reduction in grade.

## More on Mathematical Modelling

- Mathematical models are used widely in the natural, health and social sciences. The course will cover a variety of topics related to mathematical modeling and modeling techniques: discrete and continuous models, dynamical systems, stability of solutions, steady states.
- Algebra, trigonometry, and calculus techniques that students have encounter in previous courses will be used for successful mathematical modeling of more complex phenomena. Because of this, the course can be considered a continuation of earlier mathematics courses and the next step in building students' problem solving skills.
- The course provides the students interested in continuing their education at a graduate level wem with mathematical techniques that certain graduate programs use.
- The course emphasizes research ideas, not just mastering various techniques or methods. These ideas of problem solving are often used in various fields and will be a useful concept for students to acquire.

## Course Objectives

- identify a problem and choose an appropriate mathematical model,
- create a model that adequately describes the problem, using the appropriate technology if necessary,
- test the validity of the model,
- solve the problem using the appropriate technology if necessary,
- present the results orally, on computer and in a form of a written report.

## Learning outcomes

Students will:- acquire knowledge of various mathematical concepts and modeling techniques required for successful application of mathematics;
- be able to model data using the language and techniques of mathematics;
- be able to understand and solve multidisciplinary application problems;
- know how to use appropriate technology to solve problems applying techniques of mathematics;
- demonstrate a proficiency in using mathematical software;
- demonstrate ability to present their results in an oral presentation using a computer;
- demonstrate ability to present their findings in a form of a written report.