Nonlinear Science: Emergence and Dynamics of Coherent Structures (Oxford Texts in Applied and Engineering Mathematics 8) [Hardcover]

Alwyn Scott (Author)

Book Description

ISBN-10: 0198528523 | ISBN-13: 978-0198528524 | Publication Date: December 4, 2003 | Edition: 2

Much mathematical modeling has involved the assumption that physical systems are approximately linear, leading to the construction of equations which although relatively easy to solve, are unrealistic and overlook significant phenomena. Models assuming nonlinear systems however lead to the emergence of new structures that reflect reality much more closely. This second edition of Nonlinear Science places a strong emphasis on applications to realistic problems. It includes numerous new topics such as empirical results in molecular dynamics, solid-state physics, neuroscience, fluid dynamics, and biophysics; numerous new exercises and solutions; updated sections on nerve impulse dynamics, quantum theory of pump-probe measures, and local modes on lattices. With over 350 problems, including hints and solutions, this is an invaluable resource for graduate students and researchers in the applied sciences, mathematics, biology, physics and engineering.

Editorial Reviews

Review

Review from previous edition 'The presentation in the book is based on concrete equations and the formulas are often derived from physical intuition'EMS

'..presents a suggestive panoramic view of the history and experimental motivation of nonlinear phenomena. The problems at the end of each chapter are a good training to get a better understanding of the topics and suggest new directions of research.....I recommend this book as a reference-text for undergraduate students of last year as well as a basic book for an interdisciplinary P.H.D.course in natural sciences and engineering. The book is a basic one for all the bridge studies with biology as the biophysics and biocomputing, and,in particular, for the emerging area of astrobiology.' MATH

About the Author

Alywn Scott is an Emeritus Professor at the Department of Mathematics at the University of Arizona and a Consultant at the Department of Informatics and Mathematical Modelling at the Technical University of Denmark. He is the editor of the forthcoming Encyclopedia of Nonlinear Science (Taylor and Francis (Routledge), New York). He is the chairman of in international committee for the Pnevmatikos Prize in Nonlinear Science, which is awarded in even years to outstanding young researchers in nonlinear science. He was a founding director (1981-1985) of the Center for Nonlinear Science in New Mexico.

Product Details

• Hardcover: 504 pages
• Publisher: Oxford University Press, USA; 2 edition (December 4, 2003)
• Language: English
• ISBN-10: 0198528523
• ISBN-13: 978-0198528524
• Product Dimensions: 9.3 x 6.2 x 1.2 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,066,621 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

4.0 out of 5 stars Very Well Written, April 11, 2001

By 

"tjhenn" (Madison, WI USA) - See all my reviews

This review is from: Nonlinear Science: Emergence and Dynamics of Coherent Structures (Oxford Applied and Engineering Mathematics, 1) (Hardcover)

I am currently taking a couse based on this book and am fairly impressed. The book is very interesting to read and Scott occasionally adds some humourous bits or interesting facts that help out alot. However on the mathematics side alot of steps are skipped which makes it difficult to follow at times. However there are a load of references given for each chapter, so if you do get stuck you can go to the source. Overall an interesting book, but not the best for an introduction to the material.

4 of 4 people found the following review helpful:

5.0 out of 5 stars Every Student in Science and Engineering should read this, April 1, 2004

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"shohet2" (Madison, WI United States) - See all my reviews

This review is from: Nonlinear Science: Emergence and Dynamics of Coherent Structures (Oxford Texts in Applied and Engineering Mathematics 8) (Hardcover)

This book has a very important mission. It is to break through the conventional approach to science and engineering in which mathematical representations of systems are almost always linearized. When faced with a nonlinear equation today, most students immediately race to solve the problem with a computer, thereby missing the opportunity to ever observe new qualitative structures that emerge from the nonlinear mathematics. To go past this bottleneck, the author starts with a historical review of the experimental and theoretical developments in nonlinear science which often amazes the students of today since many discoveries were made more than 2 centuries ago! The student is then guided through the relevant linear theory and gently introduced to the classical nonlinear equations that have produced soliton waves which have even made their way into Star Trek! The notion that a wave equation is not necessary to produce traveling wave solutions in is another striking development, which is a critical approach to the propagation of impulses in nerve fibers, for example. Yet the concept itself is introduced by examining the behavior of a candle!
The skills needed for the Backlund transformation, inverse scattering and perturbation methods are introduced, but there are always numbers of well-thought-out problems that cover the basics as well as the more detailed concepts in each chapter.
What is particularly impressive about this book is the wide range of nonlinear phenomena in an incredible number of disciplines that exhibit similar nonlinear behavior. For those who search for cross-disciplinary applications, this book is a marvelous compendium of information.
This text is extremely well written. It can easily be used as a text in a seminar-style class, where one can sense the author's presence as the guiding hand behind the material.