Methods of Nonlinear Analysis

Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780

It is now widely recognized that the climate system is governed by nonlinear, multi-scale processes, whereby memory effects and stochastic forcing by fast processes, such as weather and convective systems, can induce regime behavior. Motivated by present difficulties in understanding the climate system and to aid the improvement of numerical weather and climate models, this book gathers contributions from mathematics, physics and climate science to highlight the latest developments and current research questions in nonlinear and stochastic climate dynamics. Leading researchers discuss some of the most challenging and exciting areas of research in the mathematical geosciences, such as the theory of tipping points and of extreme events including spatial extremes, climate networks, data assimilation and dynamical systems. This book provides graduate students and researchers with a broad overview of the physical climate system and introduces powerful data analysis and modeling methods for

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in th

Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The

This is the first textbook on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for opti

An adaptive system for linear systems with unknown parameters is a nonlinear system. The analysis of such adaptive systems requires similar techniques to analysis for nonlinear systems. Therefore it i

The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically l

Describes the properties of nonlinear microwave and radio frequency circuits and the analytical methods necessary to understand them quantitatively. Topics include solid state device modeling, harmon

This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicl

The second edition of this book provides a conceptual understanding of analysis of variance. It outlines methods for analysing variance that are used to study the effect of one or more nominal variabl

Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback

Using phase–plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems

* Explains the physical meaning of linear and nonlinear structural mechanics. * Shows how to perform nonlinear structural analysis. * Points out important nonlinear structural dynamics behaviors. * Pr

The second edition of An Introduction to Nonlinear Finite Element Analysis has the same objective as the first edition, namely, to facilitate an easy and thorough understanding of the details that are

Of related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts ".an extraordinary presentation of concepts and methods concerning the use and analysis of

An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are

Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory. This broad coverage, the authors' clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their s

This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorith

One of the first books in this area, this text focuses on important aspects of the system operation, analysis and performance evaluation of selected chaos-based digital communications systems – a hot

The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of s

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tens

Governments and road safety agencies around the world have either introduced or are considering 'safe system' strategies, a long overdue acknowledgement that different elements of the road system cont

Governments and road safety agencies around the world have either introduced or are considering 'safe system' strategies, a long overdue acknowledgement that different elements of the road system cont

This practical guide covers the most essential statistics-related tasks and problems encountered in high-energy physics data analyses. It addresses both advanced students entering the field of particl

A one-stop reference to themajor techniques for analyzingmicrowave planar transmission line structuresThe last two decades have seen important progress in the development of methods for the analysis o

This volume describes the new boundary element method (BEM) based on two fundamental solutions and new analyses and results for the fracture mechanics of layered and functionally graded materials, mea

The author applies methods of nonlinear elasticity to investigate the defects in the crystal structure of solids such as dislocations and disclinations that characterize the plastic and strength prope

Modelling and Forecasting Financial Data brings together a coherent and accessible set of chapters on recent research results on this topic. To make such methods readily useful in practice, the contri

This monograph is devoted to methods of reduction of nonlinear control systems to a simpler form: for example, decomposition into systems of lesser dimension. The approach centres on the immersion o

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second

This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Exampl

Responding to the developments of the past twenty years, Les Kirkup has thoroughly updated his popular book on experimental methods, while retaining the extensive coverage and practical advice from the first edition. Many topics from that edition remain, including keeping a record of work, how to deal with measurement uncertainties, understanding the statistical basis of data analysis and reporting the results of experiments. However, with new technologies influencing how experiments are devised, carried out, analyzed, presented and reported, this new edition reflects the digital changes which have taken place and the increased emphasis on the importance of communication skills in reporting results. Bringing together key elements of experimental methods into one coherent book, it is perfect for students seeking guidance with their experimental work, including how to acquire, analyse and present data. Exercises, worked examples and end-of-chapter problems are provided throughout the boo