It's a Nonlinear World

ISBN-13: 9780387753386 / Angielski / Twarda / 2010 / 384 str.

Richard H Enns

Opis

Drawing examplesfrom mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations.After an introductorychapter that explores what it means to be nonlinear, the book covers the mathematical conceptssuch as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations.No prior knowledge of Maple is assumed.The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world," or for self-study by practicing scientists and engineers."

Recenzje

From the reviews:

"The text is filled with examples from all areas the obvious, like physics, engineering, and chemistry, the likely, such as biology and economics, and the more unusual, like politics and sports. ... Practicing scientists and engineers who would like a detailed exposure to dynamical systems (colloquially known as chaos theory) might use the volume as a desk reference or for self-study. Summing Up: Recommended. Upper-division undergraduates and above." (M. D. Sanford, Choice, Vol. 48 (10), June, 2011)

"It's a Nonlinear World is a fascinating collection of problems from many different areas ... and much more where mathematics can be used to provide illuminating solutions. This book very clearly indicates the role of nonlinearity in problems occurring in the real contemporary world. ... Every chapter is followed by an exercise section where there are multiple problems which extend some of the ideas discussed in the chapters. ... This book can be used for an advanced undergraduate or a graduate course on applied mathematics." (Lakshmi Chandrasekaran, The Mathematical Association of America, February, 2011)

"It is useful to have many applications listed in one place, with references to sources: The primary beneficiaries will probably be instructors of undergraduate ODE courses seeking to supplement their teaching with more applications or to supply their students with projects." (Mark Levi, Mathematical Reviews, Issue 2012 a)

"The book is written in a precise and lively manner, it is well illustrated, the exposition is easy to follow. ... one can use this text as a valuable source of information complementing a variety of standard college courses on ordinary and partial differential equations, mathematical modeling, applied and engineering mathematics. ... this nice text serves as an excellent appetizer designed to foster the interest to mathematical modeling and nonlinear dynamics. Highly recommended reading for a very broad audience." (Svitlana P. Rogovchenko, Zentralblatt MATH, Vol. 1214, 2011)

"This volume is a pretty good introduction for a mathematically oriented ... engineer to enter this strange world of nonlinearity and understand some fundamentals of how chaotic dynamics, limit cycles, and so on emerge from simple nonlinear systems. ... the book includes illustrated examples and hints on how to program them in Maple or Mathematica. ... Students or practicing engineers wanting to extend the horizon of their knowledge ... will find this book quite enlightening and useful." (Sandeep Shukla, ACM Computing Reviews, March, 2012)

Spis treści

Preface.- Part I. World of Mathematics.- 1. World of Nonlinear Systems.- 2. World of Nonlinear ODEs.-  3. World of Nonlinear Maps.-  4. World of Solitons.- Part II. Our Nonlinear World.- 5. World of Motion.- 6. World of Sports.- 7. World of Electromagnetism.- 8. World of Weather Prediction.- 9. World of Chemistry.- 10. World of Disease.- 11. World of War.-  Bibliography.- Index.

Blurb

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the remainder of Part I covers nonlinear mathematical concepts such as fixed points, limit cycles, fractals, chaos, bifurcations, and solitons, and nonlinear diagnostic tools such as fixed point analysis, bifurcation diagrams, and Lyapunov exponents, to name a few. Part II of the text presents illustrative examples of nonlinear dynamics that are highly relevant to the contemporary world. At the end of each chapter, a wide variety of problems are presented which extend the ideas developed in the chapter as well as allow the reader to explore other aspects of our nonlinear world. The mathematical level of the text assumes good working knowledge of basic calculus and prior exposure to ordinary differential equations and the wave and diffusion equations. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world" or for self-study by practicing scientists and engineers. The more casual reader can simply read the book for intellectual enjoyment.