Overview

Much mathematical modelling 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, covers several important areas of nonlinear science, and 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.This is the latest title in the Oxford Texts in Applied and Engineering Mathematics, which includes a range of texts from the undergraduate through to the graduate level. Most titles should be based on taught courses which explain the mathematical or computational techniques required for the resolution of fundamental applied problems. Other books in the series include: D. W. Jordan and P. Smith: Nonlinear ordinary differential equations: an introduction to dynamical systems 3rd Edition; I. J. Sobey: Introduction to interactive boundary layer theory; A. B. Tayler: Mathematical Models in Applied Mechanics (reissue); Ramdas Ram-Mohan: Finite Element and Boundary Element Applications in Quantum Mechanics; Lapeyre et al: Introduction to Monte-Carlo Methods for Transport and Diffusion Equations; Isaac Elishakoff & Yong Jin Ren: Finite Element Methods for Structures with Large Stochastic Variations

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9780198528524

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Reviews

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

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

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

Author Information

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.

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