Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems. The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems. This book will be particularly useful to advanced students and practitioners in higher mathematics.

Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)

Science & Math

Hirsch, Morris W.

Smale, Stephen

Devaney, Robert L.

Mathematics

Academic Press

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Hirsch, Devaney, and Smale’s classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.

This book attempts to understand processes in motion such as the movement of stars, the ups and downs of the stock market, the changes in weather, the changes chemicals undergo, and the motion of a pendulum. Students are introduced to chaos, fractals and dynamics, three exciting contemporary mathematics topics, through a combination of precalculus mathematics and hands-on computer experimentation that produced graphic images of Julia sets, the Mandelbrot set, and fractals.

Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics

Computers & Technology

Programming

Addison-Wesley

A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented.Chaotic Dynamical Systems Software, Labs 1?6 is a supplementary laboratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems, it leads to a rich understanding of this emerging field.

A First Course In Chaotic Dynamical Systems: Theory And Experiment (Studies in Nonlinearity)

Westview Press

A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition The long-anticipated revision of this well-liked textbook offers many new additions.In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics. The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to students and also offers a wide variety of interesting open questions for students at the undergraduate level to pursue. The only prerequisite for students is a one-year calculus course (no differential equations required); students will easily be exposed to many interesting areas of current research. This course can also serve as a bridge between the low-level, often non-rigorous calculus courses, and the more demanding higher-level mathematics courses. Features <ul>
<li>More extensive coverage of fractals, including objects like the Sierpinski carpet and others that appear as Julia sets in the later sections on complex dynamics, as well as an actual chaos "game."</li> <li>More detailed coverage of complex dynamical systems like the quadratic family and the exponential maps.</li> <li>New sections on other complex dynamical systems like rational maps.</li> <li>A number of new and expanded computer experiments for students to perform. 
</li> </ul>
About the Author Robert L. Devaney is currently professor of mathematics at Boston University. He received his PhD from the University of California at Berkeley under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.

A First Course In Chaotic Dynamical Systems (Advances in Applied Mathematics)

Routledge

An Introduction To Chaotic Dynamical Systems

Chapman and Hall/CRC

Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topics that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.

Differential Equations (with CD-ROM)

Hall, Glen R.

Blanchard, Paul.

Brooks/Cole

Written by the authors, the Student Solutions Manual contains worked solutions to all of the odd-numbered exercises in the text.

Student Solutions Manual for Blanchard/Devaney/Hall’s Differential Equations, 3rd

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom.

Differential Equations

Blanchard, Paul (Paul Blanchard)

See the best price to sell, buy, or rent books by Devaney, Robert L.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Devaney, Robert L.

See the best price to sell, buy, or rent books by Devaney, Robert L.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics

A First Course In Chaotic Dynamical Systems: Theory And Experiment (Studies in Nonlinearity)

A First Course In Chaotic Dynamical Systems (Advances in Applied Mathematics)

An Introduction To Chaotic Dynamical Systems

Differential Equations (with CD-ROM)

Student Solutions Manual for Blanchard/Devaney/Hall’s Differential Equations, 3rd

Differential Equations