Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures

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Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures

Gardini Laura,Avrutin Viktor,Sushko Iryna,Tramontana Fabio
Continuous And Discontinuous Piecewise smooth One dimensional Maps Invariant Sets And Bifurcation Structures Book PDF

Author : Gardini Laura,Avrutin Viktor,Sushko Iryna,Tramontana Fabio
Publisher : World Scientific
Page : 648 pages
File Size : 52,8 Mb
Release : 2019-05-28
Category : Mathematics
ISBN : 9789811204715

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Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures by Gardini Laura,Avrutin Viktor,Sushko Iryna,Tramontana Fabio Pdf

The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Advances in Discrete Dynamical Systems, Difference Equations and Applications

Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić
Advances in Discrete Dynamical Systems Difference Equations and Applications Book PDF

Author : Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić
Publisher : Springer Nature
Page : 534 pages
File Size : 41,8 Mb
Release : 2023-03-25
Category : Mathematics
ISBN : 9783031252259

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Advances in Discrete Dynamical Systems, Difference Equations and Applications by Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić Pdf

​This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

Nonlinear Economic Dynamics and Financial Modelling

Roberto Dieci,Xue-Zhong He,Cars Hommes
Nonlinear Economic Dynamics and Financial Modelling Book PDF

Author : Roberto Dieci,Xue-Zhong He,Cars Hommes
Publisher : Springer
Page : 389 pages
File Size : 42,8 Mb
Release : 2014-07-26
Category : Business & Economics
ISBN : 9783319074702

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Nonlinear Economic Dynamics and Financial Modelling by Roberto Dieci,Xue-Zhong He,Cars Hommes Pdf

This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly rational heterogeneous agents to estimation, time series modelling and empirical analysis and from risk management of interest-rate products, futures price volatility and American option pricing with stochastic volatility to evaluation of risk and derivatives of electricity market. The book illustrates some of the most recent research tools in these areas and will be of interest to economists working in economic dynamics and financial market modelling, to mathematicians who are interested in applying complexity theory to economics and finance and to market practitioners and researchers in quantitative finance interested in limit order, futures and electricity market modelling, derivative pricing and risk management.

Cycles, Growth and the Great Recession

Annalisa Cristini,Stephen Fazzari,Edward Greenberg,Riccardo Leoni
Cycles Growth and the Great Recession Book PDF

Author : Annalisa Cristini,Stephen Fazzari,Edward Greenberg,Riccardo Leoni
Publisher : Routledge
Page : 261 pages
File Size : 49,9 Mb
Release : 2014-11-13
Category : Business & Economics
ISBN : 9781317751137

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Cycles, Growth and the Great Recession by Annalisa Cristini,Stephen Fazzari,Edward Greenberg,Riccardo Leoni Pdf

Cycles, Growth and the Great Recession is a collection of papers that assess the nature and role of the business cycle in contemporary economies. These assessments are made in the context of the financial market instability that distinguishes the Great Recession from previous post-war slowdowns. Theorists and applied scholars in the fields of economics and mathematical economics discuss various approaches to understanding cycles and growth, and present mathematical and applied macro models to show how uncertainty shapes cycles by affecting the economic agent choice. Also included is an empirical section that investigates how the Great Recession affected households’ housing wealth, labour productivity and migration decisions. This book aims to: Propose a novel understanding of the business cycle by comparing the approaches of various scholars, starting from Hyman Minsky and Piero Ferri. Show that uncertainty is a main feature of the business cycle that affects decision-making and economic behaviour in general. Explain with mathematical models how the behaviour of economic agents can lead to cyclical paths for modern developed economies. Augment theory with empirical analysis of some central issues related to the Great Recession. This book comprises an original view of such widely discussed subjects as business cycles, uncertainty, economic growth and the Great Recession, constructed around theory, models and applications.

Frequency-domain Approach To Hopf Bifurcation Analysis: Continuous Time-delayed Systems

Franco Sebastian Gentile,Jorge Luis Moiola,Guanrong Chen
Frequency domain Approach To Hopf Bifurcation Analysis Continuous Time delayed Systems Book PDF

Author : Franco Sebastian Gentile,Jorge Luis Moiola,Guanrong Chen
Publisher : World Scientific
Page : 393 pages
File Size : 46,5 Mb
Release : 2019-10-07
Category : Technology & Engineering
ISBN : 9789811205484

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Frequency-domain Approach To Hopf Bifurcation Analysis: Continuous Time-delayed Systems by Franco Sebastian Gentile,Jorge Luis Moiola,Guanrong Chen Pdf

This book is devoted to the study of an effective frequency-domain approach, based on systems control theory, to compute and analyze several types of standard bifurcation conditions for general continuous-time nonlinear dynamical systems. A very rich pictorial gallery of local bifurcation diagrams for such nonlinear systems under simultaneous variations of several system parameters is presented. Some higher-order harmonic balance approximation formulas are derived for analyzing the oscillatory dynamics in small neighborhoods of certain types of Hopf and degenerate Hopf bifurcations.The frequency-domain approach is then extended to the large class of delay-differential equations, where the time delays can be either discrete or distributed. For the case of discrete delays, two alternatives are presented, depending on the structure of the underlying dynamical system, where the more general setting is then extended to the case of distributed time-delayed systems. Some representative examples in engineering and biology are discussed.

Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Ii. Memristors And Cnn: The Right Stuff For Ai And Brain-like Computers

Leon O Chua
Chua Lectures The From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos Volume Ii Memristors And Cnn The Right Stuff For Ai And Brain like Computers Book PDF

Author : Leon O Chua
Publisher : World Scientific
Page : 248 pages
File Size : 54,9 Mb
Release : 2020-08-19
Category : Technology & Engineering
ISBN : 9789811215902

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Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Ii. Memristors And Cnn: The Right Stuff For Ai And Brain-like Computers by Leon O Chua Pdf

This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume II — shows that memristors can be either volatile or non-volatile, and effectively proving that synapses are non-volatile memristors, while action potentials are generated by locally-active memristors.

Toward General Theory Of Differential-operator And Kinetic Models

Nikolay Sidorov,Denis Sidorov,Alexander V Sinitsyn
Toward General Theory Of Differential operator And Kinetic Models Book PDF

Author : Nikolay Sidorov,Denis Sidorov,Alexander V Sinitsyn
Publisher : World Scientific
Page : 495 pages
File Size : 47,7 Mb
Release : 2020-03-13
Category : Science
ISBN : 9789811213762

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Toward General Theory Of Differential-operator And Kinetic Models by Nikolay Sidorov,Denis Sidorov,Alexander V Sinitsyn Pdf

This volume provides a comprehensive introduction to the modern theory of differential-operator and kinetic models including Vlasov-Maxwell, Fredholm, Lyapunov-Schmidt branching equations to name a few. This book will bridge the gap in the considerable body of existing academic literature on the analytical methods used in studies of complex behavior of differential-operator equations and kinetic models. This monograph will be of interest to mathematicians, physicists and engineers interested in the theory of such non-standard systems.

Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos (In 4 Volumes)

Leon O Chua
Chua Lectures The From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos In 4 Volumes Book PDF

Author : Leon O Chua
Publisher : World Scientific
Page : 1008 pages
File Size : 54,6 Mb
Release : 2020-08-19
Category : Technology & Engineering
ISBN : 9789811228933

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Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos (In 4 Volumes) by Leon O Chua Pdf

This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume I — covers everything that a researcher may want to know about memristors but is too afraid to ask.Volume II — shows that memristors can be either volatile or non-volatile, and effectively proving that synapses are non-volatile memristors, while action potentials are generated by locally-active memristors.Volume III — presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and sound of chaos from the Chua Circuit, invented in 1984 by Leon Chua, and has now become the standard textbook example of chaos exhibited by a real nonlinear electronic circuit, and not by computer simulations.Volume IV — surprises the audience with a new law of nature — dubbed the local activity principle, as discovered and proved mathematically in 1996 by Leon Chua. In particular, a Corollary of Chua's local activity theorem, dubbed the edge of chaos, is shown via insightful examples to be the originator of most complex phenomena, including intelligence, creativity, and deep learning. The edge of chaos is Mother Nature's tool for overcoming the tyranny of the second law of thermodynamics by providing an escape hatch for entropy to decrease over time. Indeed, the local activity principle which is profusely illustrated in the final volume, is widely recognized as a new law of thermodynamics, and is identified as the sine qua non of all complex phenomena, including life itself.Exclusive Access to the accompanying Video and Audio materials comes with the purchase of this book.

Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume I. Memristors: New Circuit Element With Memory

Leon O Chua
Chua Lectures The From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos Volume I Memristors New Circuit Element With Memory Book PDF

Author : Leon O Chua
Publisher : World Scientific
Page : 216 pages
File Size : 55,9 Mb
Release : 2020-08-19
Category : Technology & Engineering
ISBN : 9789811215896

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Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume I. Memristors: New Circuit Element With Memory by Leon O Chua Pdf

This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume I — covers everything that a researcher may want to know about memristors but is too afraid to ask.

Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Iv. Local Activity Principle: Chua's Riddle, Turing Machine, And Universal Computing Rule 137

Leon O Chua
Chua Lectures The From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos Volume Iv Local Activity Principle Chua s Riddle Turing Machine And Universal Computing Rule 137 Book PDF

Author : Leon O Chua
Publisher : World Scientific
Page : 300 pages
File Size : 52,7 Mb
Release : 2020-08-19
Category : Technology & Engineering
ISBN : 9789811215926

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Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Iv. Local Activity Principle: Chua's Riddle, Turing Machine, And Universal Computing Rule 137 by Leon O Chua Pdf

This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume IV — surprises the audience with a new law of nature — dubbed the local activity principle, as discovered and proved mathematically in 1996 by Leon Chua. In particular, a Corollary of Chua's local activity theorem, dubbed the edge of chaos, is shown via insightful examples to be the originator of most complex phenomena, including intelligence, creativity, and deep learning. The edge of chaos is Mother Nature's tool for overcoming the tyranny of the second law of thermodynamics by providing an escape hatch for entropy to decrease over time. Indeed, the local activity principle which is profusely illustrated in the final volume, is widely recognized as a new law of thermodynamics, and is identified as the sine qua non of all complex phenomena, including life itself.

Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Iii. Chaos: Chua's Circuit And Complex Nonlinear Phenomena

Leon O Chua
Chua Lectures The From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos Volume Iii Chaos Chua s Circuit And Complex Nonlinear Phenomena Book PDF

Author : Leon O Chua
Publisher : World Scientific
Page : 244 pages
File Size : 51,8 Mb
Release : 2020-08-19
Category : Technology & Engineering
ISBN : 9789811215919

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Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Iii. Chaos: Chua's Circuit And Complex Nonlinear Phenomena by Leon O Chua Pdf

This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume III — presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and sound of chaos from the Chua Circuit, invented in 1984 by Leon Chua, and has now become the standard textbook example of chaos exhibited by a real nonlinear electronic circuit, and not by computer simulations.

The Economy as a Complex Spatial System

Pasquale Commendatore,Ingrid Kubin,Spiros Bougheas,Alan Kirman,Michael Kopel,Gian Italo Bischi
The Economy as a Complex Spatial System Book PDF

Author : Pasquale Commendatore,Ingrid Kubin,Spiros Bougheas,Alan Kirman,Michael Kopel,Gian Italo Bischi
Publisher : Springer
Page : 220 pages
File Size : 40,9 Mb
Release : 2017-09-18
Category : Science
ISBN : 9783319656274

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The Economy as a Complex Spatial System by Pasquale Commendatore,Ingrid Kubin,Spiros Bougheas,Alan Kirman,Michael Kopel,Gian Italo Bischi Pdf

This book is open access under a CC BY-NC 4.0 license. This collected volume represents the final outcome of the COST Action IS1104 “The EU in the new complex geography of economic systems: models, tools and policy evaluation”. Visualizing the EU as a complex and multi-layered network, the book is organized in three parts, each of them dealing with a different level of analysis: At the macro-level, Part I considers the interactions within large economic systems (regions or countries) involving trade, workers migration, and other factor movements. At the meso-level, Part II discusses interactions within specific but wide-ranging markets, with a focus on financial markets and banking systems. Lastly, at the micro-level, Part III explores the decision-making of single firms, especially in the context of location decisions.

Bifurcations in Piecewise-smooth Continuous Systems

David John Warwick Simpson
Bifurcations in Piecewise smooth Continuous Systems Book PDF

Author : David John Warwick Simpson
Publisher : World Scientific
Page : 255 pages
File Size : 43,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814293853

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Bifurcations in Piecewise-smooth Continuous Systems by David John Warwick Simpson Pdf

1. Fundamentals of piecewise-smooth, continuous systems. 1.1. Applications. 1.2. A framework for local behavior. 1.3. Existence of equilibria and fixed points. 1.4. The observer canonical form. 1.5. Discontinuous bifurcations. 1.6. Border-collision bifurcations. 1.7. Poincaré maps and discontinuity maps. 1.8. Period adding. 1.9. Smooth approximations -- 2. Discontinuous bifurcations in planar systems. 2.1. Periodic orbits. 2.2. The focus-focus case in detail. 2.3. Summary and classification -- 3. Codimension-two, discontinuous bifurcations. 3.1. A nonsmooth, saddle-node bifurcation. 3.2. A nonsmooth, Hopf bifurcation. 3.3. A codimension-two, discontinuous Hopf bifurcation -- 4. The growth of Saccharomyces cerevisiae. 4.1. Mathematical model. 4.2. Basic mathematical observations. 4.3. Bifurcation structure. 4.4. Simple and complicated stable oscillations -- 5. Codimension-two, border-collision bifurcations. 5.1. A nonsmooth, saddle-node bifurcation. 5.2. A nonsmooth, period-doubling bifurcation -- 6. Periodic solutions and resonance tongues. 6.1. Symbolic dynamics. 6.2. Describing and locating periodic solutions. 6.3. Resonance tongue boundaries. 6.4. Rotational symbol sequences. 6.5. Cardinality of symbol sequences. 6.6. Shrinking points. 6.7. Unfolding shrinking points -- 7. Neimark-Sacker-like bifurcations. 7.1. A two-dimensional map. 7.2. Basic dynamics. 7.3. Limiting parameter values. 7.4. Resonance tongues. 7.5. Complex phenomena relating to resonance tongues. 7.6. More complex phenomena

Global Analysis of Dynamic Models in Economics and Finance

Gian Italo Bischi,Carl Chiarella,Iryna Sushko
Global Analysis of Dynamic Models in Economics and Finance Book PDF

Author : Gian Italo Bischi,Carl Chiarella,Iryna Sushko
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 41,5 Mb
Release : 2012-08-07
Category : Business & Economics
ISBN : 9783642295034

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Global Analysis of Dynamic Models in Economics and Finance by Gian Italo Bischi,Carl Chiarella,Iryna Sushko Pdf

The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bifurcations in complementarity games, international subsidy games and issues in economic geography. A number of stochastic dynamic models are also analysed. The book is a collection of essays in honour of the 60th birthday of Laura Gardini.​

Piecewise-smooth Dynamical Systems

Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk
Piecewise smooth Dynamical Systems Book PDF

Author : Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 43,8 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9781846287084

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Piecewise-smooth Dynamical Systems by Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk Pdf

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.