Introduction to Nonlinear Differential and Integral Equations

Author: Harold Thayer Davis

Publisher: Courier Corporation

ISBN: 9780486609713

Category: Mathematics

Page: 566

View: 5787

Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

Adaptive Nonlinear System Identification

The Volterra and Wiener Model Approaches

Author: Tokunbo Ogunfunmi

Publisher: Springer Science & Business Media

ISBN: 0387686304

Category: Science

Page: 232

View: 7319

Focuses on System Identification applications of the adaptive methods presented. but which can also be applied to other applications of adaptive nonlinear processes. Covers recent research results in the area of adaptive nonlinear system identification from the authors and other researchers in the field.

Introduction to Non-linear Systems

Author: J. Berry,John Stephen Berry

Publisher: Hodder Education

ISBN: 9780340677001

Category: Automatic control

Page: 212

View: 4583

Since the popularization of chaos theory, great interest has been generated in non-linear dynamical systems. This text presents an introduction to the basic mathematical concepts and techniques needed to describe and analyze these, aimed at students who have taken a first course in calculus. After reviewing the basic ideas of differential equations, matrix algebra and iteration methods, first and second order continuous systems are discussed. Chapter Four investigates discrete systems and the final chapter is a collection of investigations that can be explored as more open ended tasks.

Nonlinear System Analysis

Author: Austin Blaquiere

Publisher: Elsevier

ISBN: 0323151663

Category: Technology & Engineering

Page: 408

View: 5101

Nonlinear System Analysis focuses on the study of systems whose behavior is governed by nonlinear differential equations. This book is composed of nine chapters that cover some problems that play a major role in engineering and physics. The opening chapter briefly introduces the difference between linear and nonlinear systems. Considerable chapters are devoted to engineering and physics related problems and their applications to particle accelerators, frequency measurements, and masers. Included in these chapters are important practical problems, such as synchronization, stability of systems with periodic coefficients, and effect of random disturbances. The remaining chapters examine random fluctuations of the motion and self-oscillators. This book is intended primarily for engineers and physicists.

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Author: Stephen Wiggins

Publisher: Springer Science & Business Media

ISBN: 1475740670

Category: Mathematics

Page: 672

View: 5299

This volume is an introduction to applied nonlinear dynamics and chaos. The emphasis is on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains an extensive bibliography and a detailed glossary of terms.

Instabilities, Chaos and Turbulence

An Introduction to Nonlinear Dynamics and Complex Systems

Author: Paul Manneville

Publisher: Imperial College Press

ISBN: 9781860944918

Category: Science

Page: 391

View: 3651

This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.

Introduction to Nonlinear Dynamics for Physicists

Author: H. D. I. Abarbanel,M. I. Rabinovich,Mikhael M. Sushchik

Publisher: World Scientific

ISBN: 9789810214104

Category: Science

Page: 158

View: 601

This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.

Systems & Control

An Introduction to Linear, Sampled & Non-linear Systems

Author: T. Dougherty

Publisher: World Scientific

ISBN: 9789810223465

Category: Technology & Engineering

Page: 640

View: 9997

The primary function of this book is to serve as a textbook on linear systems and control. It is aimed principally at undergraduates taking courses in Electrical Engineering, Electronics or Mechanical Engineering who are in the penultimate and final years of an Honours degree. Because the text is closely integrated with the use of a widely available software package, it will also be of interest and use to a more expert audience with a control background, but who may not be familiar with these invaluable tools. Finally, it may be of use to others who may not be control specialists, but who need to acquire a background of control for other purposes. Some of the material has been used successfully for such a purpose with an M.Sc programme for Power Engineering students.

Nonlinear Systems

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN: 9780521406680

Category: Mathematics

Page: 317

View: 8402

A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.

An Introduction to Nonlinear Partial Differential Equations

Author: J. David Logan

Publisher: John Wiley & Sons

ISBN: 0470225955

Category: Mathematics

Page: 397

View: 880

An Introduction to Nonlinear Partial Differential Equations is a textbook on nonlinear partial differential equations. It is technique oriented with an emphasis on applications and is designed to build a foundation for studying advanced treatises in the field. The Second Edition features an updated bibliography as well as an increase in the number of exercises. All software references have been updated with the latest version of [email protected], the corresponding graphics have also been updated using [email protected] An increased focus on hydrogeology...

Introduction to Nonlinear Science

Author: G. Nicolis

Publisher: Cambridge University Press

ISBN: 9780521467827

Category: Mathematics

Page: 254

View: 2182

One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministic phase space descriptions. This book is suitable for senior undergraduate and graduate students taking nonlinear courses from many different perspectives including physics, chemistry, biology, and engineering.

An Introduction to Complex Systems

Society, Ecology, and Nonlinear Dynamics

Author: Paul Fieguth

Publisher: Springer

ISBN: 3319446061

Category: Science

Page: 346

View: 5427

This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or perspective. Instead, the book seeks to emphasize understanding, concepts, and ideas, in a way that is mathematically rigorous, so that the concepts do not feel vague, but not so technical that the mathematics get in the way. The book is intended for undergraduate students in a technical domain such as engineering, computer science, physics, mathematics, and environmental studies.

Nonlinear Systems in Heat Transfer

Mathematical Modeling and Analytical Methods

Author: Davood Domairry Ganji,Yaser Sabzehmeidani,Amin Sedighiamiri

Publisher: Elsevier

ISBN: 0128120207

Category: Science

Page: 288

View: 1193

Nonlinear Heat Transfer: Mathematical Modeling and Analytical Methods addresses recent progress and original research in nonlinear science and its application in the area of heat transfer, with a particular focus on the most important advances and challenging applications. The importance of understanding analytical methods for solving linear and nonlinear constitutive equations is essential in studying engineering problems. This book provides a comprehensive range of (partial) differential equations, applied in the field of heat transfer, tackling a comprehensive range of nonlinear mathematical problems in heat radiation, heat conduction, heat convection, heat diffusion and non-Newtonian fluid systems. Providing various innovative analytical techniques and their practical application in nonlinear engineering problems is the unique point of this book. Drawing a balance between theory and practice, the different chapters of the book focus not only on the broader linear and nonlinear problems, but also applied examples of practical solutions by the outlined methodologies. Demonstrates applied mathematical techniques in the engineering applications, especially in nonlinear phenomena Exhibits a complete understanding of analytical methods and nonlinear differential equations in heat transfer Provides the tools to model and interpret applicable methods in heat transfer processes or systems to solve related complexities

Nonlinear Ordinary Differential Equations

An Introduction for Scientists and Engineers

Author: Dominic Jordan,Peter Smith

Publisher: Oxford University Press on Demand

ISBN: 0199208247

Category: Mathematics

Page: 531

View: 8626

Thoroughly updated and expanded 4th edition of the classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences it is published alongside a separate Problems and Solutions Sourcebook containing over 500 problems and fully-worked solutions.

Nonlinear Control Systems

Author: Alberto Isidori

Publisher: Springer Science & Business Media

ISBN: 9783540199168

Category: Technology & Engineering

Page: 549

View: 6844

The purpose of this book is to present a self-contained description of the fun damentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as weil as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teach ing at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl-Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985.

Linear, Time-varying Approximations to Nonlinear Dynamical Systems

with Applications in Control and Optimization

Author: Maria Tomas-Rodriguez,Stephen P. Banks

Publisher: Springer Science & Business Media

ISBN: 184996100X

Category: Mathematics

Page: 300

View: 6195

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Nonlinear Systems Analysis

Second Edition

Author: M. Vidyasagar

Publisher: SIAM

ISBN: 9780898719185

Category: Differential equations, Nonlinear

Page: 498

View: 1877

When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.

Applied Mathematics in Hydraulic Engineering

An Introduction to Nonlinear Differential Equations

Author: Kazumasa Mizumura

Publisher: World Scientific

ISBN: 9814299553

Category: Technology & Engineering

Page: 424

View: 5237

This is a teaching guide and reference to treating nonlinear mathematical problems in hydraulic, hydrologic and coastal engineering--