This book is a comprehensive introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. It is suitable for students and research workers whose main interest lies in finding solutions to differential equations. It therefore caters for readers primarily interested in applied mathematics and physics rather than pure mathematics.The book provides an application-orientated text that is reasonably self-contained. A large number of worked examples have been included to help readers working independently of a teacher. The advance of algebraic computation has made it possible to write programs for the tedious calculations in this research field, and thus the book also makes a survey of computer algebra packages.
As an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus, this self-contained book is ideal for both graduate and undergraduate mathematics students. The coverage includes systems of linear equations, linear differential equations, functions of matrices and the Kronecker product. Many of the problems are related to applications in areas such as group theory, Lie algebra theory and graph theory. Thus, physics and engineering students will also benefit from the book. Exercises for matrix-valued differential forms are also included.
The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 150 ready-to-run programs.The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing.
This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world. The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang -- Baxter relation, chaos, fractals, complexity, etc.
Scientific computing is a collection of tools, techniques and theories required to develop and solve mathematical models in science and engineering on a computer. This timely book provides the various skills and techniques needed in scientific computing. The topics range in difficulty from elementary to advanced, and all the latest fields in scientific computing are covered such as matrices, numerical analysis, neural networks, genetic algorithms, etc.Presented in the format of problems and detailed solutions, important concepts and techniques are introduced and developed. Many problems include software simulations. Algorithms have detailed implementations in C++ or Java. This book will prove to be invaluable not only to students and research workers in the fields of scientific computing, but also to teachers of this subject who will find this text useful as a supplement.The topics discussed in this book are part of the e-learning and distance learning courses conducted by the International School of Scientific Computing, South Africa.
This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world. The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang -- Baxter relation, chaos, fractals, complexity, etc.
The invertible point transformation is a powerful tool in the study of nonlinear differential and difference equations. This book gives a comprehensive introduction to this technique. Ordinary and partial differential equations are studied with this approach. The book also covers nonlinear difference equations. The connections with Lie symmetries, the Painlev‚ property, first integrals and the Cartan equivalence method are discussed in detail. Most of the evaluations are checked with the computer language REDUCE; the book includes 30 REDUCE programs. A short introduction to the jet bundle formalism is given.
Quantum computing and quantum information are two of the fastest-growing and most exciting research areas in physics. The possibilities of using non-local behaviour of quantum mechanics to factorize integers in random polynomial time have added to this new interest. This invaluable book provides a collection of problems in quantum computing and quantum information together with detailed solutions. It consists of two parts: in the first part finite-dimensional systems are considered, while the second part deals with finite-dimensional systems. All the important concepts and topics are included, such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gates, von Neumann entropy quantum cryptography, quantum error correction, coherent states, squeezed states, POVM measurement, beam splitter and Kerr-Hamilton operator. The topics range in difficulty from elementary o advanced. Almost all of the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn from this book important principles and strategies required for problem solving. Teachers will find it useful as a supplement, since important concepts and techniques are developed through the problems. It can also be used as a text or a supplement for linear and multilinear algebra or matrix theory.
This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlev‚ test, Painlev‚ property and integrability. Both ordinary differential equations and partial differential equations are considered.
The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 150 ready-to-run programs.The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing, University of Johannesburg.
This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.
The Carleman linearization has become a new powerful tool in the study of nonlinear dynamical systems. Nevertheless, there is the general lack of familiarity with the Carleman embedding technique among those working in the field of nonlinear models. This book provides a systematic presentation of the Carleman linearization, its generalizations and applications. It also includes a review of existing alternative methods for linearization of nonlinear dynamical systems. There are probably no books covering such a wide spectrum of linearization algorithms. This book also gives a comprehensive introduction to the Kronecker product of matrices, whereas most books deal with it only superficially. The Kronecker product of matrices plays an important role in mathematics and in applications found in theoretical physics.
First published in 1973 Professor Akensone(tm)s book traces the series of religious and political controversies which have battered the state schools of Northern Ireland. After the governmente(tm)s admirably intentioned, but muddled, attempt to create a non-sectarian school system in the early 1920s, the educational system was progressively manipulated by sectarianism. The way in which the author describes how children are schooled reveals a great deal about the attitudes and values of the parental generation and also helps to explain the actions of later generations.
Many dynamical systems in physics, chemistry and biology exhibit complex be haviour. The apparently random motion of a fluid is the best known example. How ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.
In recent decades, the study of signal processing has become increasingly complex, with new techniques and applications constantly being developed for the processing, transformation, and interpretation of signals. This book provides a comprehensive introduction to the traditional and modern methods used in signal processing. It is designed to impart to the reader the mathematical techniques used in modelling signals and systems, encompassing standard mathematical tools as well as newer techniques such as wavelets and neural networks. C++ and Java implementations furnish these descriptions. The book offers an excellent balance of theory and application, beginning with a complete framework of discrete-time signal processing.
Presents introductory and advanced topics in the field of computer graphics with mathematical descriptions and derivations. This book offers a balance of theory, applications, and code, and derives the underlying numerical methods and algorithms. It contains the classes in C# necessary for computer graphics, and offers an explanation of the code.
Object-oriented programming has been the most dramatic innovation in software development in the last decade. It offers a powerful way to cope with the complexity of programs. C++ is by far the most popular object-oriented language. This book gives a complete introduction to C++ and object-oriented programming. Additionally, it provides a large collection of C++ programs which are useful in finance, administration and statistics. The book contains more than 20 fully developed classes and more than 200 ready-to-run programs. The Standard Template Library is also included.
The book gives a thorough introduction into object orientated design and programming using C++. At the same time it can be used as a library of very useful programs chosen from the fields of finance, adminstration and statistics. These include programs for calculating loan periods, amortization, least squares fitting, a spelling checker, Gregorian calendar, data compression and encryption, searching and sorting. Basic C++ programming is introduced with simple introductory programs while object-oriented programming in C++ is explained as we develop useful classes. Finally we give an introduction into object orientated design and we demonstrate its power by developing a banking package.
This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world. The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang -- Baxter relation, chaos, fractals, complexity, etc.
The study of nonlinear dynamical systems has advanced tremendously in the last 15 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail. The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 100 ready-to-run programs. The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing.
The book presents examples of important techniques and theorems for Groups, Lie groups and Lie algebras. This allows the reader to gain understandings and insights through practice. Applications of these topics in physics and engineering are also provided. The book is self-contained. Each chapter gives an introduction to the topic.
Although there are many books on women in the ancient world, this is the first to explore in depth what life was like for women in the period of late antiquity (3rd to 6th centuries AD) once Christianity became the dominant religion. It is also unique in focusing on both pagan and Christian lifestyles. Dr Clark provides a fascinating and comprehensive introduction to the basic conditions of life for women: marriage, divorce, celibacy, and prostitution; legal constraints and protection;child-bearing, health care and medical theories; housing, housework, and clothes; and ancient, some still influential, theories about the nature of women. The author uses a wide range of source material - both Christian and non-Christian writings, art, and archaeology - to illustrate both what life was really like and the prevailing "discourses" of the ancient world.
The Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C]+, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked out examples and 160 ready to run programs are included. Each chapter provides a collection of interesting problems. New topics added to the 6th edition are Swarm Intelligence, Quantum Cellular Automata, Hidden Markov Model and DNA, Birkhoff's ergodic theorem and chaotic maps, Banach fixed point theorem and applications, tau-wavelets of Haar, Boolean derivatives and applications, and Cartan forms and Lagrangian.
This book provides a comprehensive collection of problems together with their detailed solutions for Bose, Spin, Fermi systems and also interacting systems. Supplementary problems are also provided. Exercises for representations of Lie groups and Lie algebras are also covered as well as computer algebra implementations. It is the only book which summarizes these topics from the quantum theory aspect in the form of exercises and solutions. The book is also self-contained. Both physicists and mathematicians will benefit from all the different techniques explained and worked out in detail.
This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explantory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages --- Mathematica and Maple --- while some problems are implemented in C++. --
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