Resources for Math 1360: Mathematical Modeling

Periodically, I teach the above course. This web page is intended
to bbegin collecting resources for students in Math 1360 for the
times that I teach it.

Contents:

I. A typical list of course topics
II. Previous Exams
III.Homework

I. Typical Course topics

Dynamic Modeling

William Layton
Department of Mathematics
University of Pittsburgh
Pittsburgh, PA 15260
U.S.A.

Wjl@pitt.edu
http://www.math.pitt.edu/~wjl

Notations
Introduction
I. Richardson's Model of Arms Races
I.1 Richardson's Model of Arms Races.
I.2. The General Case.
I.3. Testing the Model.

References for Chapter I.

II. Introduction to Phase Portraits of Nonlinear Systems.
II.1. Introduction.
II.2. Sketching a Phase Portrait by Hand.
II.3. Analysis of Phase Portraits near Critical Points.
II.4. The Nonlinear Problem.

References for Chapter II.

III. Modelling Population Growth.
III.1. the Exponential Model of Malthus.
III.2. The Logistic Equation.
III.3. Other Models of a Single Population.
III.4. Remarks

References for chapter III.

IV. Oscillations in Population Modelling:the Lotka-Volterra Equations.
IV.1. Interacting Species Models.
IV.2. The Predator - Prey Model.
IV.3. Oscillations in Nature and Models.

References for Chapter IV.

V. Modelling Epidemics.
V.1. Introduction.
V.2. Development of the SIR Model.
V.3. Analysis of the SIR Model: No Removals.
V.4. The Full SIR Model.

References for Chapter V.

VI. Limit Cycles and Poincare-Bendixon Theory.
VI.1. Introduction to Limit Cycles.
VI.2. Poincare-Bendixon Theory.
VI.3. The Birth of Limit Cycles: the Hopf Bifurcation.

References for Chapter VI.

VII. Oscillations in Nature: the Holling-Tanner Model.
VII.1. The Holling-Tanner model of predator-prey interactions.
VII.2. Analysis of the Holling-Tanner model.
VII.3. Hopf bifurcations in the Holling-Tanner model.

References for Chapter VII.

VIII. Buisness Cycles.