MATH 450
CLN , TTh 9:30 - 11:30 2355 GGBL

(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 Textbook Syllabus Lecture Notes Objectives Schedule

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

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

Mathematical concepts to be covered

1. Review of sequences and series.
2. Fourier Series .
3. Partial Differential Equations.
4. Applications of PDE's to physics , engineering and biology.
5. Complex variables.
6. Conformal mapping.
7. Numerical analysis with Matlab

 Homework 1 450Hmwk1.ps 450Hmwk1.pdf Homework 2 450Hmwk2.ps 450Hmwk2.pdf Homework 3 450Hmwk3.ps 450Hmwk3.pdf Homework 4 450Hmwk4.ps 450Hmwk4.pdf Homework 5 450Hmwk5.ps 450Hmwk5.pdf Homework 6 450Hmwk6.ps 450Hmwk6.pdf Homework 7 450Hmwk7.ps 450Hmwk7.pdf Homework 8 450Hmwk8.ps 450Hmwk8.pdf

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.