**MATH 651**

CLN 28422, MWF 10:00-11:00, EH 3096
# Topics in Applied Mathematics (Multiple Scales and Singular Perturbation Metho)

(Prerequisites: MATH 316 or 404 and vector calculus)

## Instructor:

Dr. Patrick Nelson

East Hall 5860

tel: 763-3408

fax: 763-0937

pwn@umich.edu

office hours: Wednesday, 11:00-12:00; Tuesday, 1:00-2:00

## Course Description

The primary purpose of this class is to analyze the formulation and solution of problems that arise in the
physical sciences, engineering, and medicine and are modeled by partial differential equations. The emphasis
is on deriving explicit analytical results, rather than on the abstract properties of the solutions. Proofs
will be omitted but the underlying concepts will be carefully explained.

## Textbook

__Partial Differential Equations (Analytical solution techniques)__, J. Kevorkian, *Springer*,

## Mathematical Concepts to be covered

- Heat equation
- Dimensional Analysis
- Laplace and Wave equations
- Formulation of models from basic principles
- Quasi-linear first order equations, (Weak solutions, shocks and fans)
- Non-linear first order equations
- Hamilton-Jacobi equations
- Computation with matlab and fortran
- Interpretation of results

## Homeworks

## Learning Objectives and Instructor Expectations

Although the subject matter of applied partial differential equations 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 formulating the mathematical solutions.
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 each will count for 1/3 of the grade. Each quiz will be take home and at least 48 hours will
be given for completion