Method

Polynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasising computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate

Teacher's Materials contains teacher's materials and answer keys for Familia Romana (Lingua Latina Pars I) and Roma Aeterna (Lingua Latina Pars II) and answer keys for Exercitia Latina I and II.Hans Orberg’s Lingua Latina per se illustrata is the world’s premiere series for learning Latin via the Natural Method. Students learn grammar and vocabulary intuitively through extended contextual reading and an innovative system of marginal notes, giving students the opportunity to learn Latin without resorting to translation. Further information on Roma Aeterna and all titles in this widely adopted series can be be found at www.pullins.com.

Despite the profound influence exerted by August Strindberg on the development of modernist theatre and drama, the myth persisted that his plays - particularly such later works as A Dream Play, To Damascus, and The Ghost Sonata - are somehow 'unperformable'. Nothing could be farther from the truth, as this book sets out to demonstrate by providing a detailed performance analysis of the major works created after the period of personal crisis which Strindberg called his Inferno. Ranging from the early productions of Max Reinhardt and Olof Molander to the reinterpretations of Robert Lepage, Robert Wilson and Ingmar Bergman in our own day, this study explores the crucial impact that this writer's allusive (and elusive) method of playwriting has had on the changing nature of the theatrical experience. Each chapter ends with a section devoted to innovative Strindberg performances on the contemporary stage.

Comparison of the grammars of human languages reveals systematic patterns of variation. Typology and universals research uncovers those patterns to formulate universal constraints on language and seek their exploration. In this essential textbook, William Croft presents a comprehensive introduction to the method and theory used in studying typology and universals. The theoretical issues discussed range from the most fundamental to the most abstract. The book provides students and researchers with extensive examples of language universals in phonology, morphology, syntax and semantics. This second edition has been thoroughly rewritten and updated to reflect advances in typology and universals in the past decade, including: new methodologies such as the semantic map model and questions of syntactic argumentation; discussion of current debates over deeper explanations for specific classes of universals; and comparison of the typological and generative approaches to language.

Tycho Brahe (1546–1601), the premier patron-practitioner of science in sixteenth-century Europe, established a new role of scientist as administrator, active reformer, and natural philosopher. This book explores Brahe's wide range of activities which encompass much more than his reputed role of astronomer, portraying Brahe as Platonic philosopher, Paracelsian chemist, Ovidian poet, and devoted family man. From his private island in Denmark, Brahe used patronage, printing, friendship, and marriage to incorporate men and women skilled in science, technology, and the fine arts into his program of cosmic reform. This pioneering study includes capsule biographies of over a hundred men and women, including Johannes Kepler, Willebrord Snel, Willem Blaeu, several bishops and numerous technical specialists all of whom helped shape the culture of the Scientific Revolution. Under Tycho Brahe's leadership, their teamwork achieved breakthroughs in astronomy, scientific method, and research organiza

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for al

Scientists and 'anti-scientists' alike need a more realistic image of science. The traditional mode of research, academic science, is not just a 'method': it is a distinctive culture, whose members win esteem and employment by making public their findings. Fierce competition for credibility is strictly regulated by established practices such as peer review. Highly specialized international communities of independent experts form spontaneously and generate the type of knowledge we call 'scientific' - systematic, theoretical, empirically-tested, quantitative, and so on. Ziman shows that these familiar 'philosophical' features of scientific knowledge are inseparable from the ordinary cognitive capabilities and peculiar social relationships of its producers. This wide-angled close-up of the natural and human sciences recognizes their unique value, whilst revealing the limits of their rationality, reliability, and universal applicability. It also shows how, for better or worse, the new 'po

Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.

The only method of circuit analysis known to most engineers and students is nodal or loop analysis. Although this works well for obtaining numerical solutions, it is almost useless for obtaining analytical solutions in all but the simplest cases. In this unusual 2002 book, Vorpérian describes remarkable alternative techniques to solve, almost by inspection, complicated linear circuits in symbolic form and obtain meaningful analytical answers for any transfer function or impedance. Although not intended to replace traditional computer-based methods, these techniques provide engineers with a powerful set of tools for tackling circuit design problems. They also have great value in enhancing students' understanding of circuit operation, making this an ideal course book, and numerous problems and worked examples are included. Originally developed by Professor David Middlebrook and others at Caltech (California Institute of Technology), the techniques described here are now widely taught at

In this groundbreaking book, David H. Rosen, M.D., offers depressed individuals, their families, and therapists a lifesaving course in healing the soul through creativity. This is a book about transforming depression and its powerful pull toward suicide into a meaningful alternative.In Transforming Depression, Dr. Rosen applies Carl Jung's method of active imagination to treating depressed and suicidal individuals. Having dealt with depression in his own life and the suicides of loved ones, Dr. Rosen shows that when people learn to confront the rich images and symbols that emerge from their struggles, they can turn their despair into a fountain of creative energy. He details the paths of four patients whose work in painting, pottery, and dance -- in conjunction with psychotherapy -- led them from depression to a more meaningful life. Their dramatic paintings illustrate the text.Part One presents an overview of the biological, psychological, sociological, and spiritual factors involved

This is the second volume in a two-volume set, which provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. The second volume contains a study of the representations of the geometries under consideration in GF(2)-vector spaces as well as in some non-abelian groups. The central part is the classification of the amalgam of maximal parabolics, associated with a flag transitive action on a Petersen or tilde geometry. The classification is based on the method of group amalgam, the most promising tool in modern finite group theory. Via their systematic treatment of group amalgams, the authors establish a deep and important mathematical result. This book will be of great interest to researchers in finite group theory, finite geometries and algebraic combinatorics.

This graduate-level textbook on thermal physics covers classical thermodynamics, statistical mechanics and its applications. It describes theoretical methods to calculate thermodynamic properties, such as the equation of state, specific heat, Helmholtz free energy, magnetic susceptibility and phase transitions of macroscopic systems. In addition to the more standard material covered, this book also describes powerful techniques, which are not found elsewhere, to determine the correlation effects on which the thermodynamic properties are based. Particular emphasis is given to the cluster variation method and a novel formulation is developed for its expression in terms of correlation functions. Although a basic knowledge of quantum mechanics is required, the mathematical formulations are accessible and entirely self-contained. The book will therefore constitute an ideal companion text for graduate students studying courses on the theory of complex analysis, classical mechanics, classical

This graduate-level textbook on thermal physics covers classical thermodynamics, statistical mechanics and its applications. It describes theoretical methods to calculate thermodynamic properties, such as the equation of state, specific heat, Helmholtz free energy, magnetic susceptibility and phase transitions of macroscopic systems. In addition to the more standard material covered, this book also describes powerful techniques, which are not found elsewhere, to determine the correlation effects on which the thermodynamic properties are based. Particular emphasis is given to the cluster variation method and a novel formulation is developed for its expression in terms of correlation functions. Although a basic knowledge of quantum mechanics is required, the mathematical formulations are accessible and entirely self-contained. The book will therefore constitute an ideal companion text for graduate students studying courses on the theory of complex analysis, classical mechanics, classical

Stanley J. Tambiah discusses the life of Edmund Leach (1910–1989), one of Britain's foremost social and cultural anthropologists, and a man of extraordinary versatility, originality and intellectual breadth. His substantial contributions to anthropology deal with topics including kinship and social organization, hill tribes and valley peoples, tenure and peasant economy, aesthetics, British structural-functional methodology, the structuralism of Levi-Strauss, biblical narratives and the myths of Classical Greece. Leach was not wedded to any settled orthodoxy: what makes his work exciting is his experimentation with new ideas, and his expansions of the horizons of the discipline. His distinctive view of the comparative method allows him to transcend the stale dichotomy between 'them primitives' and 'us moderns', finding instead a dialectic between 'us' and 'them' which opens up the possibility for illuminating common human propensities and capacities.

This is a systematic and comprehensive introduction both to compositional proof methods for the state-based verification of concurrent programs, such as the assumption-commitment and rely-guarantee paradigms, and to noncompositional methods, whose presentation culminates in an exposition of the communication-closed-layers (CCL) paradigm for verifying network protocols. Compositional concurrency verification methods reduce the verification of a concurrent program to the independent verification of its parts. If those parts are tightly coupled, one additionally needs verification methods based on the causal order between events. These are presented using CCL. The semantic approach followed here allows a systematic presentation of all these concepts in a unified framework which highlights essential concepts. This 2001 book is self-contained, guiding the reader from advanced undergraduate level. Every method is illustrated by examples, and a picture gallery of some of the subject's key fig

This Companion takes as its starting point the realization that Jesus of Nazareth cannot be studied purely as a subject of ancient history, 'a man like any other man'. History, literature, theology and the dynamic of a living, worldwide religious reality, all appropriately impinge on the study of Jesus. The two parts of the book roughly correspond to the interdependent tasks of historical description and critical and theological reflection. It incorporates the most up-to-date historical work on Jesus the Jew with the 'bigger issues' of critical method, the story of Christian faith and study, and Jesus in a global church and in the encounter with Judaism and Islam. Written by seventeen leading international scholars, the book encourages students of the historical Jesus to discover the vital contribution of theology, and students of doctrine to engage the Christ of faith as Jesus the first-century Jew.

This Companion takes as its starting point the realization that Jesus of Nazareth cannot be studied purely as a subject of ancient history, 'a man like any other man'. History, literature, theology and the dynamic of a living, worldwide religious reality, all appropriately impinge on the study of Jesus. The two parts of the book roughly correspond to the interdependent tasks of historical description and critical and theological reflection. It incorporates the most up-to-date historical work on Jesus the Jew with the 'bigger issues' of critical method, the story of Christian faith and study, and Jesus in a global church and in the encounter with Judaism and Islam. Written by seventeen leading international scholars, the book encourages students of the historical Jesus to discover the vital contribution of theology, and students of doctrine to engage the Christ of faith as Jesus the first-century Jew.

What do we do if different studies appear to give different answers? When applying research to questions for individual patients or for health policy, one of the challenges is interpreting such apparently conflicting research. A systematic review is a method to systematically identify relevant research, appraise its quality, and synthesize the results. The last two decades have seen increasing interest and developments in methods for doing high quality systematic reviews. Part I of this book provides a clear introduction to the concepts of reviewing, and lucidly describes the difficulties and traps to avoid. A unique feature of the book is its description, in Part II, of the different methods needed for different types of health care questions: frequency of disease, prognosis, diagnosis, risk, and management. As well as illustrative examples, there are exercises for each of the sections. This is essential reading for those interested in synthesizing health care research.

Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

This is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory, it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories, both at the classical and quantum levels. Furthermore, they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely the N=3 supersymmetric Yang-Mills theory. Harmonic Superspace makes manifest many remarkable geometric properties of the N=2 theories, for example, the one-to-one correspondence between N=2 supersymmetric matter, and hyper-Kähler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory, string theory and complex g

本書分析電腦軟體，以及網際網路與電子商務相關專利之發展，特別是有關商業方法(business method)之專利，以及由此而生之法律與科技策略；其中包含了軟體之著作權與專利權的保護演進，電子商務專利之興起與發展，商業方法專利的分析、創新與迴避設計，以及因應新興之專利趨勢我們可以採行之策略。與其他探討智慧財產權法律書籍不同之處，在於本書強調了科技、法律與管理的整合。除了將法律的內涵，例如軟體專利與

In this 2001 book Jonathan Price attempts to demonstrate that Thucydides consciously viewed and presented the Peloponnesian War in terms of a condition of civil strife - stasis, in Greek. Thucydides defines stasis as a set of symptoms indicating an internal disturbance in both individuals and states. This diagnostic method, in contrast to all other approaches in antiquity, allows an observer to identify stasis even when the combatants do not or cannot openly acknowledge the nature of their conflict. The words and actions which Thucydides chooses for his narrative meet his criteria for stasis: the speeches in the History represent the breakdown of language and communication characteristic of internal conflict, and the zeal for victory led to acts of unusual brutality and cruelty, and overall disregard for genuinely Hellenic customs, codes of morality and civic loyalty. Viewing the Peloponnesian War as a destructive internal war had profound consequences for Thucydides' historical vision

This 2001 handbook surveys the state of practice, method and understanding in the field of mathematical finance. Every chapter has been written by leading researchers and each starts by briefly surveying the existing results for a given topic, then discusses more recent results and, finally, points out open problems with an indication of what needs to be done in order to solve them. The primary audiences for the book are doctoral students, researchers and practitioners who already have some basic knowledge of mathematical finance. In sum, this is a comprehensive reference work for mathematical finance and will be indispensable to readers who need to find a quick introduction or reference to a specific topic, leading all the way to cutting edge material.

This 2001 book gives a self-contained exposition of the theory of gravitational solitons and provides a comprehensive review of exact soliton solutions to Einstein's equations. The text begins with a detailed discussion of the extension of the Inverse Scattering Method to the theory of gravitation, starting with pure gravity and then extending it to the coupling of gravity with the electromagnetic field. There follows a systematic review of the gravitational soliton solutions based on their symmetries. These solutions include some of the most interesting in gravitational physics such as those describing inhomogeneous cosmological models, cylindrical waves, the collision of exact gravity waves, and the Schwarzschild and Kerr black holes. A valuable reference for researchers and graduate students in the fields of general relativity, string theory and cosmology, this book will also be of interest to mathematical physicists in general.

The shift from state-led to market-oriented, neoliberal economic policies has been one of the most important changes in the developing world during the last two decades. Although much existing research has focused on why countries choose these neoliberal policy reforms and how they implement them, Richard Snyder's study offers an analysis of politics after neoliberalism. The book proposes a framework that explains how neoliberal reforms, rather than unleashing market forces, actually trigger 're-regulation' processes involving strategic interactions between political entrepreneurs and societal groups. Depending on the strengths and strategies of politicians and societal groups, reregulation results in different types of new institutions for market governance with contrasting consequences for economic efficiency and social justice. This framework is used in conjunction with an innovative subnational comparative method to analyze evidence from four Mexican states about the politics of re

This book examines emancipation after the Emancipation Proclamation of 1863. Focusing on the making and meaning of the Thirteenth Amendment, Final Freedom looks at the struggle among legal thinkers, politicians, and ordinary Americans in the North and the border states to find a way to abolish slavery that would overcome the inadequacies of the Emancipation Proclamation. The book tells the dramatic story of the creation of a constitutional amendment and reveals an unprecedented transformation in American race relations, politics, and constitutional thought. Using a wide array of archival and published sources, Professor Vorenberg argues that the crucial consideration of emancipation occurred after, not before, the Emancipation Proclamation; that the debate over final freedom was shaped by a level of volatility in party politics underestimated by prior historians; and that the abolition of slavery by constitutional amendment represented a novel method of reform that transformed attitude

The introduction of numerical methods, particularly finite element (FE) analysis, represents a significant advance in metal forming operations. Numerical methods are used increasingly to optimize product design and deal with problems in metal forging, rolling, and extrusion processes. Metal Forming Analysis, first published in 2001, describes the most important numerical techniques for simulating metal forming operations. The first part of the book describes principles and procedures and includes numerous examples and worked problems. The remaining chapters focus on applications of numerical analysis to specific forming operations. Most of these results are drawn from the authors' research in the areas of metal testing, sheet metal forming, forging, extrusion, and similar operations. Sufficient information is presented so that readers can understand the nonlinear finite element method as applied to forming problems without a prior background in structural finite element analysis. Gradu

The power of an anthropological approach to long-term history lies in its unique ability to combine diverse evidence, from archaeological artifacts to ethnographic texts and comparative word lists. In this innovative book, Kirch and Green explicitly develop the theoretical underpinnings, as well as the particular methods, for such a historical anthropology. Drawing upon and integrating the approaches of archaeology, comparative ethnography, and historical linguistics, they advance a phylogenetic model for cultural diversification, and apply a triangulation method for historical reconstruction. They illustrate their approach through meticulous application to the history of the Polynesian cultures, and for the first time reconstruct in extensive detail the Ancestral Polynesian culture that flourished in the Polynesian homeland - Hawaiki - some 2,500 years ago. Of great significance for Oceanic studies, Kirch and Green's book will be essential reading for any anthropologist, prehistorian,

Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.

In this vital new study, Andrew Abbott presents a fresh and daring analysis of the evolution and development of the social sciences. Chaos of Disciplines reconsiders how knowledge actually changes and advances. Challenging the accepted belief that social sciences are in a perpetual state of progress, Abbott contends that disciplines instead cycle around an inevitable pattern of core principles. New schools of thought, then, are less a reaction to an established order than they are a reinvention of fundamental concepts.Chaos of Disciplines uses fractals to explain the patterns of disciplines, and then applies them to key debates that surround the social sciences. Abbott argues that knowledge in different disciplines is organized by common oppositions that function at any level of theoretical or methodological scale. Opposing perspectives of thought and method, then, in fields ranging from history, sociology, and literature, are to the contrary, radically similar; much like fractals, the

Computerized data acquisition systems are often the principle method of recording experimental results. This book takes the reader step-by-step through the process of data acquisition and analysis, explaining how to set up the systems and then obtain useful information from the data recorded. In an easy-to-read style, it guides researchers through the basics of data acquisition systems, explains the important underlying concepts, and gives numerous examples of how to analyze the recorded information. While aimed at researchers in the life sciences, the topics covered are general and will be valuable to anyone interested in learning to use data acquisition systems. The principles can be applied to the collection of data from respiratory apparatus to behavioral science experiments, and a host of other situations. Many illustrations and worked examples accompany the text, and the mathematics are kept simple. This book is an invaluable tool for the non-engineer who is collecting and analyz

Computerized data acquisition systems are often the principle method of recording experimental results. This book takes the reader step-by-step through the process of data acquisition and analysis, explaining how to set up the systems and then obtain useful information from the data recorded. In an easy-to-read style, it guides researchers through the basics of data acquisition systems, explains the important underlying concepts, and gives numerous examples of how to analyze the recorded information. While aimed at researchers in the life sciences, the topics covered are general and will be valuable to anyone interested in learning to use data acquisition systems. The principles can be applied to the collection of data from respiratory apparatus to behavioral science experiments, and a host of other situations. Many illustrations and worked examples accompany the text, and the mathematics are kept simple. This book is an invaluable tool for the non-engineer who is collecting and analyz

In Genders, Races and Religious Cultures in Modern American Poetries, Rachel Blau Duplessis shows how, through poetic language, modernist writers represented the debates and ideologies concerning New Woman, New Negro and New Jew in the early twentieth century. From the poetic text emerge such social issues of modernity as debates on suffrage, sexuality, manhood, and African-American and Jewish subjectivities. By a reading method she calls 'social philology' - a form of close reading inflected with the approaches of cultural studies - Duplessis engages with the work of such canonical poets as Wallace Stevens, Ezra Pound, T. S. Eliot, William Carlos Williams, Gertrude Stein, Marianne Moore and H. D., as well as Mina Loy, Countee Cullen, Alfred Kreymborg and Langston Hughes, writers, she claims, still marginalized by existing constructions of modernism. This book is an ambitious attempt to remap our understanding of modern poetries and poetics, and the relationship between early twentieth

This volume collects some of the seminal essays on Descartes by Daniel Garber, one of the pre-eminent scholars of early-modern philosophy. A central theme unifying the volume is the interconnection between Descartes' philosophical and scientific interests, and the extent to which these two sides of the Cartesian program illuminate each other, a question rarely treated in the existing literature. Amongst the specific topics discussed in the essays are Descartes' celebrated method, his demand for certainty in the sciences, his account of the relation of mind and body, and his conception of God's activity on the physical world. This collection will be a mandatory purchase for any serious student of or professional working in seventeenth-century philosophy, history of science, or history of ideas.

This volume collects some of the seminal essays on Descartes by Daniel Garber, one of the pre-eminent scholars of early-modern philosophy. A central theme unifying the volume is the interconnection between Descartes' philosophical and scientific interests, and the extent to which these two sides of the Cartesian program illuminate each other, a question rarely treated in the existing literature. Amongst the specific topics discussed in the essays are Descartes' celebrated method, his demand for certainty in the sciences, his account of the relation of mind and body, and his conception of God's activity on the physical world. This collection will be a mandatory purchase for any serious student of or professional working in seventeenth-century philosophy, history of science, or history of ideas.

The study of biofilm considers the close association of micro-organisms with each other at interfaces and the consequent physiological adaptation to the proximity of other cells and surfaces. As such it is relevant to a variety of disciplines, including medicine, dentistry, bioremediation, biofouling, water technology, engineering and food science. Although the habitats studied, and their associated cellular communities, differ widely, some common elements exist such as method of attachment, coadhesion, regulation of biofilm phenotype and biofilm architecture. This book aims to distil the common principles of biofilm physiology and growth for all interested disciplines. It will appeal to the specialist biofilm researcher as well as to students wishing to introduce themselves to the topic.

Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. In this volume the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves are discussed with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases which have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.