**MATH 450**

CLN , TTh 9:30 - 11:30 2355 GGBL
# Advanced Mathematics for Engineers I

(Prerequisites: MATH 215 (or equivalent) and 216, 256, 286, or 316)

## Instructor:

Dr. Patrick Nelson

East Hall 3071

tel: 763-3408

fax: 763-0937

pwn@math.lsa.umich.edu

office hours: Tues 3-4:30, Wed 9:30 - 11:00, and by appt.

## Course Description

There are three main objectives to this class. First, we will introduce the concepts of
partial differential equations and complex variables and some basic techniques for analyzing
these problems. Second, by studying the application of PDE's to physics, engineering,
and biology, the student will begin to acquire intuition and expertise about how to
use these equations to model scientific processes. Finally, by utilizing numerous numerical
tecniques, the student will begin to visualize, hence better understand, what a PDE is and
how it can be used to study the Natural Sciences.

## Textbooks

- Advanced Engineering Mathematics (required),
Erwin Kreyszig,
* Wiley *, 1998.
__Elementary Applied PDE's with Fourier Series and Boundary Value Problems (good reference)__,
R. Haberman, *Prentice-Hall*, 1997.
__Partial Differential Equations (good reference)__, S.J. Farlow, * Wiley *,1982.

## Mathematical concepts to be covered

- Review of sequences and series.
- Fourier Series .
- Partial Differential Equations.
- Applications of PDE's to
physics , engineering and biology.
- Complex variables.
- Conformal mapping.
- Numerical analysis with Matlab

## Learning Objectives and Instructor Expectations

The objective of this course is to help young and
established scientists and engineers to build the skill necessary to analyze equations
that they encounter in the real world. This learning will be done using homework and
computer assignements as well as in class assignments that will be done in groups and
presented in class. Every week on Tuesday there will be a quiz or group project to be
done in class. Also, time during each class will be devoted to the discussion of
homework problems. Class attendance and participation is expected and is factored into
your final grade.

## Grading

Homework assignments will count as 30% of grade evaluation. Quizes and group projects will
count for 20%. There will also be one midterm worth 20% of the grade and a
**final (Fri Dec 21st, 10:30 - 12:30)** that counts for 25%.
The remaining 5% is student participation. There will be no make-up quizzes; instead I
will drop the lowest quiz score.