Overview

Philosophy of the Text This text presents an introductory survey of the basic concepts and applied mathematical methods of nonlinear science as well as an introduction to some simple related nonlinear experimental activities. Students in engineering, phys ics, chemistry, mathematics, computing science, and biology should be able to successfully use this book. In an effort to provide the reader with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of the Maple software sys tem applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The CD-ROM provided with this book gives a wide variety of illustrative non linear examples solved with Maple. In addition, numerous annotated examples are sprinkled throughout the text and also placed on the CD. An accompanying set of experimental activities keyed to the theory developed in Part I of the book is given in Part II. These activities allow the student the option of hands on experience in exploring nonlinear phenomena in the REAL world. Although the experiments are easy to perform, they give rise to experimental and theoretical complexities which are not to be underestimated.

Full Product Details

Author:   Richard H. Enns ,  George McGuire
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2nd Revised edition
ISBN:  

9783764341190

ISBN 10:   376434119
Pages:   656
Publication Date:   January 2000
Audience:   College/higher education ,  Undergraduate ,  Postgraduate, Research & Scholarly
Replaced By:   9780817641191
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Part 1 Theory: introduction; non-linear systems - part I; non-linear systems - part II; topological analysis; analytic methods; the numerical approach; limit cycles; forced oscillators; non-linear maps; non-linear PDE phenomena; numerical simulation; inverse scattering method. Part 2 Experimental activities: introduction to non-linear experiments - spin toy pendulum; driven eardrum; non-linear damping; enharmonic potential; iron core inductor; non-linear LRC circuit; tunnel diode negative resistance curve; tunnel diode self-excited oscillator; forced Duffing equation; focal point instability; compound pendulum; stable limit cycle; Van der Pol limit cycle relaxation oscillations - neon bulb; relaxation oscillations - drinking bird; relaxation oscillations - tunnel diode; hard spring; non-linear resonance curve - mechanical; non-linear resonance curve - electrical; non-linear resonance curve - magnetic; sub-harmonic response - period doubling; diode - period doubling; five-well magnetic potential; power spectrum; entrainment and quasiperiodicity; quasiperiodicity; Chua's butterfly; route to chaos; driven spin toy; mapping.

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