Introduction to Mathematical Modeling Using Discrete Dynamical Systems, International Edition 1e

ISBN-13: 9780495018650 / ISBN-10: 0495018651

Frederick R. Marotto, Fordham University
400pp
Published by Cengage Learning, ©2006
Available Now
£69.00

Using discrete dynamical systems, this book introduces powerful mathematical modeling techniques, both standard analytical and modern computational, to students in mathematics, the natural sciences, and the social sciences. With minimal mathematical background, students will quickly progress from the traditional study of exponential growth and decay that simple linear equations always exhibit, to an investigation of recently discovered chaotic dynamics often associated with nonlinear systems. A wide diversity of applications demonstrates the usefulness and relevance of topics that have often been viewed as excessively theoretical or abstract, such as sequences, limits, linear algebra, complex variables, and more. By taking advantage of discrete dynamical systems, students will have the opportunity to experience some fascinating areas of mathematical discovery.

Features

  • Introduces exciting areas of current research, such as dynamical systems, that show that mathematics is a vibrant and evolving discipline.
  • Emphasizes the determination of the dynamics of solutions as the primary focus beginning in Chapter 3, since this is intended for a course in discrete dynamical systems and not differential equations.
  • Begins Chapters 2 through 5 with the construction of a host of simple iterative models of the type that is to be investigated later in that chapter. These models motivate the analysis that is to follow and ensures that applications will not be sacrificed if time runs short.
  • Contains an ample supply of exercises at varying levels of difficulty with many answers provided, and numerous suggested computer projects with specific instructions for their completion.
  • Includes an appendix that explains how most computer projects can be done using either a spreadsheet program such as Microsoft Excel? or the powerful software package of Mathematica?.

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