Applied Complex Variables

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

Power is an unavoidable issue in social work. This important text explores these complex issues, both at a conceptual and applied level, in order to give students a clear understanding of the theoreti

Monitoring Ecological Impacts provides the tools needed by professional ecologists, scientists, engineers, planners and managers to design assessment programs that can reliably monitor, detect and allow management of human impacts on the natural environment. The procedures described are well grounded in inferential logic, and the statistical models needed to analyse complex data are given. Step-by-step guidelines and flow diagrams provide the reader with clear and useable protocols, which can be applied in any region of the world and to a wide range of human impacts. In addition, real examples are used to show how the theory can be put into practice. Although the context of this book is flowing water environments, especially rivers and streams, the advice for designing assessment programs can be applied to any ecosystem.

From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.

Detailing the main methods in the theory of involutive systems of complex vector fields this book examines the major results from the last twenty five years in the subject. One of the key tools of the subject - the Baouendi-Treves approximation theorem - is proved for many function spaces. This in turn is applied to questions in partial differential equations and several complex variables. Many basic problems such as regularity, unique continuation and boundary behaviour of the solutions are explored. The local solvability of systems of partial differential equations is studied in some detail. The book provides a solid background for others new to the field and also contains a treatment of many recent results which will be of interest to researchers in the subject.

The study of translation is constantly expanding in a world that is experiencing a flourish of translated texts unparalleled in human history. Courses on translation, theory of translation and translation studies are being introduced at university level all over the world. This book provides a panorama of the many ways in which the complex phenomenon of translation is analysed. The contributions to this volume, by a group of leading international scholars, include traditional and new approaches in an interdisciplinary perspective and are representative of the multiplicity of approaches to translation studies, from the literary, to the linguistic, from the cognitive to the cross-cultural, from the descriptive to the applied and to the psychoanalytical. The range of topics covered and the exhaustive bibliography make this book a useful introduction but also provide new and stimulating readings for those already acquainted with the discipline.

In this volume, the author covers the mathematical methods appropriate to both linear-systems theory and signal processing. The text deals with a number of topics usually found in introductory linear-systems courses, such as complex numbers and Laplace transforms, and addresses additional topics such as complex variable theory and Fourier series and transforms. Although the discussion is mathematically self-contained, it assumes that the reader has a firm background in calculus and differential equations. Each chapter contains a number of worked examples plus exercises designed to allow the student to put concepts into practice. The author writes in a mathematically elegant yet relaxed and readable style, and provides interesting historical notes along the way. Undergraduate students of electrical engineering, applied mathematics, and related disciplines - and their teachers - will welcome this book.

This book shows that Holocene human ecosystems are complex adaptive systems in which humans interacted with their environment in a nested series of spatial and temporal scales. Using panarchy theory, it integrates paleoecological and archaeological research from the Eastern Woodlands of North America providing a paradigm to help resolve long-standing disagreements between ecologists and archaeologists about the importance of prehistoric Native Americans as agents for ecological change. The authors present the concept of a panarchy of complex adaptive cycles as applied to the development of increasingly complex human ecosystems through time. They explore examples of ecological interactions at the level of gene, population, community, landscape and regional hierarchical scales, emphasizing the ecological pattern and process involving the development of human ecosystems. Finally, they offer a perspective on the implications of the legacy of Native Americans as agents of change for conserv

Control of office has long been regarded as the key element in understanding power and policy in the Soviet system. What, however, accounts for the control of office and how are individuals recruited into positions of power and responsibility? In An Algebra of Soviet Power, Michael Urban adopts a fresh approach and introduces into the field of political elite studies the sociological technique of vacancy chain analysis. This treats the movements of actors as sequences of complex inter-relations that are structured by the properties and powers of the personnel system rather than by the consequences of individual intentions or characteristics. This algebraic method is applied to a large body of career data of officials from the Soviet Republic of Belorussia for the period 1966–86. The author documents how, despite the formal systems of nomenklatura - central control over personnel placement - the flow of individuals through the hierarchy of offices in Belorussia has not been influenced b

Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to co

Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometric

Sensory scientists are often faced with making business decisions based on the results of complex sensory tests involving a multitude of variables. Multivariate and Probabilistic Analyses of Sensory S

This book describes the analysis and behaviour of internal flows encountered in propulsion systems, fluid machinery (compressors, turbines and pumps) and ducts (diffusers, nozzles and combustion chambers). The focus is on phenomena that are important in setting the performance of a broad range of fluid devices. The authors show that even for complex processes one can learn a great deal about the behaviour of such devices from a clear understanding and rigorous use of basic principles. Throughout the book they illustrate theoretical principles by reference to technological applications. The strong emphasis on fundamentals, however, means that the ideas presented can be applied beyond internal flow to other types of fluid motion. The book equips students and practising engineers with a range of new analytical tools. These tools offer enhanced interpretation and application of both experimental measurements and the computational procedures that characterize modern fluids engineering.

Quantum mesoscopic physics covers a whole class in interference effects related to the propagation of waves in complex and random media. These effects are ubiquitous in physics, from the behaviour of electrons in metals and semiconductors to the propagation of electromagnetic waves in suspensions such as colloids, and quantum systems like cold atomic gases. A solid introduction to quantum mesoscopic physics, this book is a modern account of the problem of coherent wave propagation in random media. It provides a unified account of the basic theoretical tools and methods, highlighting the common aspects of the various optical and electronic phenomena involved and presenting a large number of experimental results. With over 200 figures, and exercises throughout, the book was originally published in 2007 and is ideal for graduate students in physics, electrical engineering, applied physics, acoustics and astrophysics. It will also be an interesting reference for researchers.

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title,

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

Data Analysis Using Regression and Multilevel/Hierarchical Models, first published in 2007, is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout.

Data Analysis Using Regression and Multilevel/Hierarchical Models, first published in 2007, is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout.

Tropical glaciers are both highly sensitive indicators of global climate and fresh water reservoirs in some fast developing regions. This book gives a theoretical and practical analysis of tropical glaciology including a useful definition of tropical glacier-climate regimes and the analysis of the main glaciological key variables. The Rwenzori and the Cordillera Blanca are investigated as examples of tropical glacierized mountains. The fluctuations of their glaciers since the end of the Little Ice Age are reconstructed and the probable climatic reasons are discussed. The evidence of great expansions of mountain glaciers throughout the tropics on several occasions during the Quaternary are summarised, examined and then applied and contrasted. The accompanying map of the Rwenzori Mountains National Park at a scale of 1:100,000 shows the spectacular retreat of the glaciers during the last century, and their extensions over half the area of the Park in the last 300,000 years.

Feeding Ecology in Apes and Other Primates focuses on evolutionary perspectives of the complex interactions between the environment, food sources, physiology and behaviour in primates. This highly interdisciplinary volume provides a benchmark to assess dietary alterations that affected human evolution by putting the focus on the diet of hominid primates. It also offers a fresh perspective on the behavioural ecology of the last common ancestor by integrating corresponding information from both human and non-human primates. The potential of innovations of applied biotechnology are also explored to set new standards for future research on feeding ecology, and new information on feeding ecology in humans, apes and other primates is synthesized to help refine or modify current models of socioecology. By taking a comparative view, this book will be interesting to primatologists, anthropologists, behavioural ecologists and evolutionary biologists who want to understand better non-human primat

Advanced Dynamics is a broad and detailed description of the analytical tools of dynamics as used in mechanical and aerospace engineering. The strengths and weaknesses of various approaches are discussed, and particular emphasis is placed on learning through problem solving. The book begins with a thorough review of vectorial dynamics and goes on to cover Lagrange's and Hamilton's equations as well as less familiar topics such as impulse response, and differential forms and integrability. Techniques are described that provide a considerable improvement in computational efficiency over the standard classical methods, especially when applied to complex dynamical systems. The treatment of numerical analysis includes discussions of numerical stability and constraint stabilization. Many worked examples and homework problems are provided. The book is intended for use on graduate courses on dynamics, and will also appeal to researchers in mechanical and aerospace engineering.

SuperFractals, first published in 2006, is the successor to Fractals Everywhere, in which the power and beauty of Iterated Function Systems were introduced and applied to producing startling and original images that reflect complex structures found for example in nature. This provoked the question of whether there is a deeper connection between topology, geometry, IFS and codes on the one hand and biology, DNA and protein development on the other. Now, 20 years later, Barnsley explains how IFS have developed in order to address this issue. Ideas such as fractal tops and superIFS are introduced, and the classical deterministic approach is combined with probabilistic ideas to produce new mathematics and algorithms that open a whole theory that could have applications in computer graphics, bioinformatics, economics, signal processing and beyond. For the first time these ideas are explained in book form, and illustrated with breathtaking pictures.

Free Probability Theory studies a special class of 'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This 2006 book gives a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.

This set consists of the third edition of this highly acclaimed undergraduate textbook and its solutions manual containing complete worked solutions to half of the problems. Suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences, the text provides lucid descriptions of all the topics, many worked examples, and over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, the remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further re

The general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot. The book is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.

This study of reduplication in Afrikaans provides a unified and principled analysis of an unusual and highly complex word formation process, shedding new light on the scope and content of various fundamental lexicalist principles of word formation. Surprisingly, Rudolf Botha concludes that the principles involved in Afrikaans reduplication are not unique to Afrikaans, as has often been thought, and are used by many other languages. Moreover, the interpretation of Afrikaans reduplications depends on principles of conceptual structure that are restricted neither to Afrikaans nor to the interpretation of reduplications, thus supporting recent work on cognition and meaning undertaken by Ray Jackendoff and other scholars. In analysing the data, Professor Botha has also provided a concrete illustration of how the Galilean style of linguistic inquiry can fruitfully be applied in the study of word formation and meaning. The study thus represents an important theoretical and methodological adva

Mathematical Methods for Physics and Engineering, Third Edition is a highly acclaimed undergraduate textbook that teaches all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. This solutions manual accompanies the third edition of Mathematical Methods for Physics and Engineering. It contains complete worked solutions to over 400 exercises in the main textbook, the odd-numbered exercises, that are provided with hints and answers. The even-numbered exercises have no hints, answers or worked solutions and are intended for unaided homework problems; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9

The discipline of nonlinear dynamics has developed explosively in all areas of physics. This comprehensive primer summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Regev demonstrates the possible application of ideas including strange attractors, Poincaré sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems. This self-contained text will appeal to a broad audience of astrophysicists and astronomers who wish to understand and apply modern dynamical approaches to the problems they are working on. It provides researchers and graduate students with the investigative tools they need to fully explore chaotic and complex phenomena.

Applications of Information Systems to Homeland Security and Defense provides an overview of complex systems techniques and presents both guidelines and specific instances of how they can be applied

The ability to navigate across town, comprehend an animated display of the functioning of the human heart, view complex multivariate data on a company's website, or to read an architectural blueprint and form a three-dimensional mental picture of a house are all tasks involving visuospatial thinking. The field of visuospatial thinking is a relatively diverse interdisciplinary research enterprise. An understanding of visuospatial thinking, and in particular, how people represent and process visual and spatial information, is relevant not only to cognitive psychology but also education, geography, architecture, medicine, design computer science/artificial intelligence, semiotics and animal cognition. The goal of this book, first published in 2005, is to present a broad overview of research on visuospatial thinking that can be used by researchers as well as students interested in this topic in both basic research and applied/naturalistic contexts.

The ability to navigate across town, comprehend an animated display of the functioning of the human heart, view complex multivariate data on a company's website, or to read an architectural blueprint and form a three-dimensional mental picture of a house are all tasks involving visuospatial thinking. The field of visuospatial thinking is a relatively diverse interdisciplinary research enterprise. An understanding of visuospatial thinking, and in particular, how people represent and process visual and spatial information, is relevant not only to cognitive psychology but also education, geography, architecture, medicine, design computer science/artificial intelligence, semiotics and animal cognition. The goal of this book, first published in 2005, is to present a broad overview of research on visuospatial thinking that can be used by researchers as well as students interested in this topic in both basic research and applied/naturalistic contexts.

Over the past two decades, no field of scientific inquiry has had a more striking impact across a wide array of disciplines–from biology to physics, computing to meteorology–than that known as chaos and complexity, the study of complex systems. Now astrophysicist John Gribbin draws on his expertise to explore, in prose that communicates not only the wonder but the substance of cutting-edge science, the principles behind chaos and complexity. He reveals the remarkable ways these two revolutionary theories have been applied over the last twenty years to explain all sorts of phenomena–from weather patterns to mass extinctions.Grounding these paradigm-shifting ideas in their historical context, Gribbin also traces their development from Newton to Darwin to Lorenz, Prigogine, and Lovelock, demonstrating how–far from overturning all that has gone before–chaos and complexity are the triumphant extensions of simple scientific laws. Ultimately, Gribbin illustrates how chaos and complexity perme

The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. It is impossible to solve the corresponding many-body problems analytically or numerically, although much insight can be gained from the analysis of simplified models. An important example is the Hubbard model, which describes interacting electrons in narrow energy bands, and which has been applied to problems as diverse as high-Tc superconductivity, band magnetism, and the metal-insulator transition. This book presents a coherent, self-contained account of the exact solution of the Hubbard model in one dimension. The early chapters will be accessible to beginning graduate students with a basic knowledge of quantum mechanics and statistical mechanics. The later chapters address more advanced topics, and are intended as a guide for researchers to some of the more topical results in the field of integrable models.

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-conta

Making the specifics of a complex concern accessible and its handling quite manageable, this fourth edition of the Project and Cost Engineers' Handbook examines the variables associated with internati

Ultrasonic wave techniques are used increasingly in areas ranging from non-destructive inspection of materials to medical diagnosis. This book brings together basic physics and modern applications. It explains the physical principles of wave propagation and then relates them to ultrasonic wave mechanics and the more recent guided wave techniques that are used to inspect and evaluate aircraft, power plants, and pipelines in chemical processing plants. Among topics covered are wave propagation in plates, rods, hollow cylinders, and multiple layers in solid and composite materials; reflection and refraction; surface and subsurface waves; and horizontal shear wave propagation. Appendices provide background information on ultrasonic non-destructive testing, elasticity theory, and complex variables, and key wave propagation experiments. The text is amplified with numerous examples, laboratory experiments, and homework exercises. Graduate students, researchers, and practising engineers will f

This book shows that Holocene human ecosystems are complex adaptive systems in which humans interacted with their environment in a nested series of spatial and temporal scales. Using panarchy theory, it integrates paleoecological and archaeological research from the Eastern Woodlands of North America providing a paradigm to help resolve long-standing disagreements between ecologists and archaeologists about the importance of prehistoric Native Americans as agents for ecological change. The authors present the concept of a panarchy of complex adaptive cycles as applied to the development of increasingly complex human ecosystems through time. They explore examples of ecological interactions at the level of gene, population, community, landscape and regional hierarchical scales, emphasizing the ecological pattern and process involving the development of human ecosystems. Finally, they offer a perspective on the implications of the legacy of Native Americans as agents of change for conserv

Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's i