Introduction to Mathematical Modeling Using Discrete Dynamical Systems / Edition 1

by Frederick R. Marotto

Overview

MATHEMATICAL MODELING USING DISCRETE DYNAMICAL SYSTEMS! This mathematics text introduces powerful mathematical modeling techniques while providing you with the tools you need to succeed. Exercises with answers, suggested computer projects with specific instructions for their completion, and the book-specific website are just a few of the tools that will help you master the material. Coverage of current research, such as dynamical systems, shows you that mathematics is a vibrant and evolving discipline.

Product Details

ISBN-13:	9780495014171
Publisher:	Cengage Learning
Publication date:	08/04/2005
Edition description:	New Edition
Pages:	416
Product dimensions:	7.40(w) x 9.10(h) x 0.80(d)

About the Author

Frederick R. Marotto is Associate Professor of Mathematics at Fordham University.

Table of Contents

1. MATHEMATICAL MODELING AND DYNAMICAL SYSTEMS. Modeling Reality. Discrete Dynamical Systems. 2. LINEAR EQUATIONS AND MODELS. Some Linear Models. Linear Equations and Their Solutions. Homogenous Equations and Their Applications. Solutions of Non-Homogenous Equations. Applications of Non-Homogenous Equations. Dynamics of Linear Equations. Empirical Models and Linear Regression. 3. NONLINEAR EQUATIONS AND MODELS. Some Nonlinear Models. Autonomous Equations and Their Dynamics. Cobwebbing, Derivatives and Dynamics. Some Mathematical Applications. Periodic Points and Cycles. Parameterized Families. Bifurcation and Period-Doubling. Chaos. 4. MODELING WITH LINEAR SYSTEMS. Some Linear Systems Models. Linear Systems and Their Dynamics. Some Vector and Matrix Arithmetic. Stability and Eigenvalues. Repeated Real Eigenvalues. Complex Numbers and Their Arithmetic. Complex Eigenvalues. Non-Homogenous Systems. 5. MODELING WITH NONLINEAR SYSTEMS. Nonlinear Systems and Their Dynamics. Linearization and Local Dynamics. Bifurcation and Chaos. Fractals. Appendix. Answers to Odd-Numbered Exercises. Bibliography. Index.