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MATH630: Mathematical Modeling
Revised: November 2006
Course Description
This course is an introduction to mathematical modeling of deterministic systems that can be represented by ordinary differential equations. The main thrust of the course is the study of the stability of models about equilibrium usi ng the two-dimensional software PHASE PORTRAITS which is introduced early in the course and seems to make phase-plane analysis very accessible. The student becomes familiar with the necessary background literature in ordinary differential equations to und erstand the different types and aspects of stability, Liapanov functions, and a sufficient understanding of phase plane analysis to make a complete analysis on nonlinear systems. Some of the models: predator/prey models, competition and combat models. In addition, students are required to make a presentation in class of a particular model with a detailed analysis furnished to the class. Three semsester hours.
Text
Beltrami, Edward. Mathematics for Dynamic Modeling. Academic Press, 1987.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
Chapter 1: Simple Dynamic Models(10 days)
The harmonic oscillator, stable equilibra I, simple conservative systemsChapter 2: Stable and Unstable Motion (15 days)
The pendulum, when is a linear system stable?; when is a nonlinear system stable?; the phase plane/PHASEPORTRAITS softwareChapter 3: Stable and Unstable Motion, II (10 days)
Liapanov functions, stable equilibria II, control of systems by feedbackChapter 4: Analysis of Specific Models (as time allows)
The logistic model; use of discrete/continuous analysis; quadratic models of predation, competition and combat, analysis of equilibria of model