# Math 512 - Methods in Applied Mathematics - Spring 2005

TR 9:40-10:55 - Ayres 309A

### Course Information:

In this course we will study the fundamental ideas and techniques
of mathematics associated with continuous models of physical,
engineering and other systems. In contrast to the typical
'methods' course, in this course we will first derive
the various ordinary and partial differential equations
before we develop the techniques to solve them.

The main focus will be on differential equations, both ODEs and
PDEs. We will study the basic theory, some solution techniques
involving substitution and transforms, and the stability of
the solutions. As time permits we will also look into
different transforms (Fourier, wavlet, etc.) and time-series
analysis.

The prerequisites for this course are multivariable calculus,
begining ordinary differential equations, some linear algebra, some
advanced mathematics (proofs) and some computer skills.
### Resources:

- Text(s): Any basic books on ordinary and partial differential equations.
The texts used at UT for 231 or 431 and 435 are fine. Here are some
inexpensive alternatives:

Elementary Differential Equations and Boundary Value Problems
by Boyce and DiPrima (any edition).

Ordinary Differential Equations and Stability Theory: An Introduction by Dave A. Sanchez, Dover, 1979. (only available used)

A First Course in Partial Differential Equations with Complex
Variables and Transform Methods by Hans F. Weinberger, Dover, 1995.

Introduction to PDEs with Applications by E.C. Zachmanoglou and
Dale W. Thoe, Dover, 1986.
- Class Outline/Schedule Contains the topics
covered, links to handouts and homework problems & solutions. Updated
regularly.

### Grading:

### Instructor:

Dr. Charles Collins

312B Ayres Hall

974-4269 or 974-2461

ccollins@math.utk.edu
Office Hours: TBA and by appointment

ccollins@math.utk.edu