MAT 304: Computational Methods for Design

2 Feb 2004 — 7 Feb 2004

Old Main 403 Canisius College from 5:30pm — 8pm Daily

Instructor:   John A. Burns
Hatcher Professor of Mathematics
Interdisciplinary Center for Applied Mathematics
Virginia Tech
Blacksburg, VA 24061

Course Archives
All files below are MS PowerPoint (.ppt).  File size as indicated.

 Short Course Content and Prerequisites: It is assumed that the student has some background in differential equations and multivariable calculus. The course will focus on the application of numerical methods to solve design, control and optimization problems that arise in bioinformatics, aerospace engineering and nanotechnology.

The goal is to introduce undergraduate students in the mathematical sciences to practical computational techniques for modeling and design of such systems.

Review of Elementary Ordinary Differential Equations

Linear Equations
Non-linear Equations
Equilibrium
Stability

Applications to Biological Systems

Population Dynamics
Epidemiology
A Model for the Spread of Gonorrhea
Models of Cell Cycles

Applications to Nano-Technology and Engineering Design

Molecular Dynamics
Design of the Atomic Force Microscope
Smart Materials
Control of Wing Flutter
Design of Scram Jet Engines

Numerical Methods for Simulation of Ordinary Differential Equations

Euler’s Method
Runge-Kutta Methods
Multistep Methods
Long Time Behavior

Numerical Methods for Modeling, Optimization and Control

Optimization Methods — Derivative Methods, Computing Derivatives
Parameter Identification for Mathematical Modeling — Least squares
Methods, Sensitivity Computations
Optimal Design and Control — Control of Infectious Diseases, Wing
Flutter Control
Workshop on Using MATLAB to Solve Some Real Problems

Biographical Information: Prof. Burns, Hatcher Professor of Mathematics, has been the director of the Center for Optimal Design and Control at Virginia Polytechnic Institute and State University since 1993. Burns has held numerous distinguished visiting posts and has been a consultant to ICASE, NASA Langley Research Center, since 1985.

Prof. Burns’ research interests include Optimal Control Theory; Differential Equations; Approximation, Control, Identification and Optimization of Functional and Partial Differential Equations; Aeroelastic Control Systems; Fluid/Structural Control Systems; Smart Materials; and Optimal Design. Burns has published approximately 100 research articles in an array of elite applied mathematics journals and has directed 16 graduate theses, including 13 Ph.D.’s.

Prof. Burns received Virginia Tech’s “Teaching Excellence Award” in 1978 and 1981.