**MATH 462**

CLN 10473, MWF 9:00-10:00, EH 1060
# Mathematical Modeling

(Prerequisites: MATH 216, 256, 286, or 316 and Math 217, 417, or 419)

## Instructor:

Dr. Patrick Nelson

East Hall 3071

tel: 763-3408

fax: 763-0937

pwn@math.lsa.umich.edu

office hours: Monday, 10:00-11:00; Thursday, 1:30-3:00

## Course Description

Introductory survey of applied mathematics with emphasis on modeling
of physical, mechanical and biological problems in terms of differential equations.
Formulation, analysis, and interpretation of the results will be the theme of the
course. We will study analysis techniques common in dynamical systems such as linearization
theory, Liapunov functions and phase plane.

## Textbook

There are no required texts for this class. There will be a course packet that will
be available that will take notes from the following reference texts:

__Other references__:

- Mathematical Models,
Richard Haberman,
*Siam Classics in Applied Mathematics, 1998*,
__Nonlinear Dynamics__, P.G. Drazin, *Cambridge Press*,
__Dynamical Systems__, Arrowsmith and Place * Chapman and Hall *.

## Mathematical and Modeling Concepts to be covered

- Concepts of Modeling
- Dimensions, Units, Dimensional Analysis
- Differential equations
- Formulation of models from basic principles
- Concepts of equilibria and stability
- Nonlinearity, limit cycles, bifurcations
- Chaos
- Computation with matlab
- Parameter estimating techniques
- Interpretation of results

## Homeworks

## Learning Objectives and Instructor Expectations

Although the subject matter of Mathematical Modeling can be made rather difficult,
I will attempt to present the course material in as simple a manner as possible.
More theoretical aspects, such as proofs, will not be presented but I will present in
detail the mathematical techniques needed for mathematical modeling.
Applications will be emphasized and will come from areas of Physics, Engineering, Medicine,
and the Life Sciences.

## Grading

Homework assignments will count as 1/3 of grade evaluation. There will also be two quizzes
and will count for 1/3 of the grade. The remaining 1/3 will come from a
modeling project each student group will have to prepare and present
at the end of term.