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Introduction to Mathematical Modeling Using Discrete Dynamical Systems

ISBN-10: 0495014176
ISBN-13: 9780495014171
Edition: 2006
List price: $359.95
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Description: 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  More...

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Book details

List price: $359.95
Copyright year: 2006
Publisher: Brooks/Cole
Publication date: 8/4/2005
Binding: Hardcover
Pages: 400
Size: 7.25" wide x 9.25" long x 0.75" tall
Weight: 1.584
Language: English

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.

Mathematical Modeling and Dynamical Systems
Modeling Reality
Discrete Dynamical Systems
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
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
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
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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