Methods

Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course that the author has developed over twenty years, the text is split into three parts. The quick introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, the representation of surfaces, the boundary integral method, the multigrid method,

The techniques used in the welding of thin sheet metal as used on vehicle bodies are vastly different to those used in welding heavier structures. This book covers the various methods of welding used to make and repair sheet metal body panels. Whereas some forms of welding are straightforward, others require a significant amount of skill.The important thing for anyone wanting to achieve a good finish to body repair work is to start with the correct techniques: skill then comes with practice. When restoring a classic car of some value, it is worth putting the time and effort into becoming skilled in the use of all the techniques covered in this book in order to achieve a professional finish to your work. With nearly 200 colour photographs and illustrations, this book lists the equipment and materials required to achieve a successful outcome.It describes the different methods of welding and how to choose the correct method for the job and provides step-by-step practical guidance to achie

Semiconducting nanostructures such as nanowires (NWs) have been used as building blocks for various types of sensors, energy storage and generation devices, electronic devices and for new manufacturing methods involving printed NWs. The response of these sensing/energy/electronic components and the new fabrication methods depends very much on the quality of NWs and for this reason it is important to understand the growth mechanism of 1D semiconducting nanostructures. This is also important to understand the compatibility of NW growth steps and tools used in the process with these unconventional substrates such as plastic that are used in flexible and large area electronics. Therefore, this Element presents at length discussion about the growth mechanisms, growth conditions and the tools used for the synthesis of NWs. Although NWs from Si, ZnO and carbon nanotubes (CNTs) are included, the discussion is generic and relevant to several other types of NWs as well as heterostructures.

This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze

Although American scholars sometimes consider European legal scholarship as old-fashioned and inward-looking and Europeans often perceive American legal scholarship as amateur social science, both traditions share a joint challenge. If legal scholarship becomes too much separated from practice, legal scholars will ultimately make themselves superfluous. If legal scholars, on the other hand, cannot explain to other disciplines what is academic about their research, which methodologies are typical, and what separates proper research from mediocre or poor research, they will probably end up in a similar situation. Therefore we need a debate on what unites legal academics on both sides of the Atlantic. Should legal scholarship aspire to the status of a science and gradually adopt more and more of the methods, (quality) standards, and practices of other (social) sciences? What sort of methods do we need to study law in its social context and how should legal scholarship deal with the challe

A key aspect of robotics today is estimating the state, such as position and orientation, of a robot as it moves through the world. Most robots and autonomous vehicles depend on noisy data from sensors such as cameras or laser rangefinders to navigate in a three-dimensional world. This book presents common sensor models and practical advice on how to carry out state estimation for rotations and other state variables. It covers both classical state estimation methods such as the Kalman filter, as well as important modern topics such as batch estimation, the Bayes filter, sigmapoint and particle filters, robust estimation for outlier rejection, and continuous-time trajectory estimation and its connection to Gaussian-process regression. The methods are demonstrated in the context of important applications such as point-cloud alignment, pose-graph relaxation, bundle adjustment, and simultaneous localization and mapping. Students and practitioners of robotics alike will find this a valuable

Although American scholars sometimes consider European legal scholarship as old-fashioned and inward-looking and Europeans often perceive American legal scholarship as amateur social science, both traditions share a joint challenge. If legal scholarship becomes too much separated from practice, legal scholars will ultimately make themselves superfluous. If legal scholars, on the other hand, cannot explain to other disciplines what is academic about their research, which methodologies are typical, and what separates proper research from mediocre or poor research, they will probably end up in a similar situation. Therefore we need a debate on what unites legal academics on both sides of the Atlantic. Should legal scholarship aspire to the status of a science and gradually adopt more and more of the methods, (quality) standards, and practices of other (social) sciences? What sort of methods do we need to study law in its social context and how should legal scholarship deal with the challe

The financial statements of banks differ very much from those of non-banks. The assets and liabilities are mostly financial based, and the equity ratio is far lower than the equity ratios of industrial companies. Banking supervision has a big influence on the financial statements too. Recent years have shown the risks which can evolve from banks, but normal instruments of financial statement analysis are not sufficient to analyse banks and locate these risks: different methods are needed.This book, by experienced bank analyst Thomas Padberg, provides analysts and investors with the tools to analyse bank financial statements, find problems in bank finances, and assess the risks of banks. Examples with real bank financial data are used to show readers the step-by-step methods to follow when looking at bank financial statements.The book covers:- The specific accounting rules that apply to banks- How to analyse bank segment reporting- The ratios to use when analysing bank financial stateme

Is there more to qualitative data collection than face-to-face interviews? Answering with a resounding 'yes', this book introduces the reader to a wide array of exciting and novel techniques for collecting qualitative data in the social and health sciences. Collecting Qualitative Data offers a practical and accessible guide to textual, media and virtual methods currently under-utilised within qualitative research. Contributors from a range of disciplines share their experiences of implementing a particular technique, provide step-by-step guidance to using that approach, and highlight both the potential and pitfalls. From gathering blog data to the story completion method to conducting focus groups online, the methods and data types featured in this book are ideally suited to student projects and other time- and resource-limited research. In presenting several innovative ways that data can be collected, new modes of scholarship and new research orientations are opened up to student rese

Written by two leading experts, this is a compact guide to the key tools and methods necessary to carry out cost-benefit analysis (CBA). The authors use modern economic tools to obtain general equilibrium cost-benefit rules that can be used to evaluate small projects, as well as large and even mega projects. Intertemporal issues like discounting, the shadow price of capital, and the treatment of risk are covered, and a state-of-the-art summary of available methods for the valuation of unpriced commodities is also included. In addition, the book provides detailed expositions of the marginal cost of public goods (MCPF), the marginal excess burden of taxes (MEB), and second-best evaluation rules, and shows how these concepts are interrelated. The importance of undertaking due diligence in evaluations is highlighted. This is an excellent toolkit for graduate students learning about the principles of CBA, and is a useful guide for government officials and policymakers.

Written by two leading experts, this is a compact guide to the key tools and methods necessary to carry out cost-benefit analysis (CBA). The authors use modern economic tools to obtain general equilibrium cost-benefit rules that can be used to evaluate small projects, as well as large and even mega projects. Intertemporal issues like discounting, the shadow price of capital, and the treatment of risk are covered, and a state-of-the-art summary of available methods for the valuation of unpriced commodities is also included. In addition, the book provides detailed expositions of the marginal cost of public goods (MCPF), the marginal excess burden of taxes (MEB), and second-best evaluation rules, and shows how these concepts are interrelated. The importance of undertaking due diligence in evaluations is highlighted. This is an excellent toolkit for graduate students learning about the principles of CBA, and is a useful guide for government officials and policymakers.

This sophisticated package of statistical methods is for advanced master's (MPH) and PhD students in public health and epidemiology who are involved in the analysis of data. It makes the link from statistical theory to data analysis, focusing on the methods and data types most common in public health and related fields. Like most toolboxes, the statistical tools in this book are organized into sections with similar objectives. Unlike most toolboxes, however, these tools are accompanied by complete instructions, explanations, detailed examples, and advice on relevant issues and potential pitfalls - conveying skills, intuition, and experience. The only prerequisite is a first-year statistics course and familiarity with a computing package such as R, Stata, SPSS, or SAS. Though the book is not tied to a particular computing language, its figures and analyses were all created using R. Relevant R code, data sets, and links to public data sets are available from www.cambridge.org/97811071130

It has been more than thirty-five years since the first commercial recordings of hip-hop music were made. This Companion, written by renowned scholars and industry professionals reflects the passion and scholarly activity occurring in the new generation of hip-hop studies. It covers a diverse range of case studies from Nerdcore hip-hop to instrumental hip-hop to the role of rappers in the Obama campaign and from countries including Senegal, Japan, Germany, Cuba, and the UK. Chapters provide an overview of the 'four elements' of hip-hop - MCing, DJing, break dancing (or breakin'), and graffiti - in addition to key topics such as religion, theatre, film, gender, and politics. Intended for students, scholars, and the most serious of 'hip-hop heads', this collection incorporates methods in studying hip-hop flow, as well as the music analysis of hip-hop and methods from linguistics, political science, gender and film studies to provide exciting new perspectives on this rapidly developing fi

It has been more than thirty-five years since the first commercial recordings of hip-hop music were made. This Companion, written by renowned scholars and industry professionals reflects the passion and scholarly activity occurring in the new generation of hip-hop studies. It covers a diverse range of case studies from Nerdcore hip-hop to instrumental hip-hop to the role of rappers in the Obama campaign and from countries including Senegal, Japan, Germany, Cuba, and the UK. Chapters provide an overview of the 'four elements' of hip-hop - MCing, DJing, break dancing (or breakin'), and graffiti - in addition to key topics such as religion, theatre, film, gender, and politics. Intended for students, scholars, and the most serious of 'hip-hop heads', this collection incorporates methods in studying hip-hop flow, as well as the music analysis of hip-hop and methods from linguistics, political science, gender and film studies to provide exciting new perspectives on this rapidly developing fi

Advances in qualitative methods and recent developments in the philosophy of science have led to an emphasis on explanation via reference to causal mechanisms. This book argues that the method known as process tracing is particularly well suited to developing and assessing theories about such mechanisms. The editors begin by establishing a philosophical basis for process tracing - one that captures mainstream uses while simultaneously being open to applications by interpretive scholars. Equally important, they go on to establish best practices for individual process-tracing accounts - how micro to go, when to start (and stop), and how to deal with the problem of equifinality. The contributors then explore the application of process tracing across a range of subfields and theories in political science. This is an applied methods book which seeks to shrink the gap between the broad assertion that 'process tracing is good' and the precise claim 'this is an instance of good process tracing

Advances in qualitative methods and recent developments in the philosophy of science have led to an emphasis on explanation via reference to causal mechanisms. This book argues that the method known as process tracing is particularly well suited to developing and assessing theories about such mechanisms. The editors begin by establishing a philosophical basis for process tracing - one that captures mainstream uses while simultaneously being open to applications by interpretive scholars. Equally important, they go on to establish best practices for individual process-tracing accounts - how micro to go, when to start (and stop), and how to deal with the problem of equifinality. The contributors then explore the application of process tracing across a range of subfields and theories in political science. This is an applied methods book which seeks to shrink the gap between the broad assertion that 'process tracing is good' and the precise claim 'this is an instance of good process tracing

In the political fight over copyright, Internet advocacy has reshaped the playing field. This was shown in the 2012 'SOPA blackout', when the largest online protest in history stopped two copyright bills in their tracks. This protest was the culmination of an intellectual and political evolution more than a decade in the making. This book examines the debate over digital copyright, from the late 1980s through early 2012, and the new tools of political communication involved in the advocacy around the issue. Drawing on methods from legal studies, political science and communications, it explores the rise of a coalition seeking more limited copyright, as well as how these early-adopting, technology-savvy policy advocates used online communication to shock the world. It compares key bills, congressional debates, and offline and online media coverage using quantitative and qualitative methods to create a rigorous study for researchers that is also accessible to a general audience.

Knowing an astrophysical object's distance is key to understanding it. IAU Symposium 289 brought together experts on distance determinations and, importantly, the underlying physics enabling it, covering scales from the solar neighbourhood to the edge of the Universe. It explores how various methods are employed to define the milestones deeper into space, from trigonometry to applications based on general relativistic effects and even more exotic techniques. The contributors to this volume emphasise the physical bases of the methods and recent advances made to further our physical insights. The volume provides a snapshot of the field of distance measurement, offering not only up-to-date results and a cutting-edge account of recent progress, but also full discussion of the pitfalls encountered and the uncertainties that remain. This Symposium is especially timely, as we look forward to the era of high-precision astrometry data from Gaia and very long baseline interferometers on the grou

In the political fight over copyright, Internet advocacy has reshaped the playing field. This was shown in the 2012 'SOPA blackout', when the largest online protest in history stopped two copyright bills in their tracks. This protest was the culmination of an intellectual and political evolution more than a decade in the making. This book examines the debate over digital copyright, from the late 1980s through early 2012, and the new tools of political communication involved in the advocacy around the issue. Drawing on methods from legal studies, political science and communications, it explores the rise of a coalition seeking more limited copyright, as well as how these early-adopting, technology-savvy policy advocates used online communication to shock the world. It compares key bills, congressional debates, and offline and online media coverage using quantitative and qualitative methods to create a rigorous study for researchers that is also accessible to a general audience.

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough present

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough present

Structure-based (SBDD) and ligand-based (LBDD) drug design are extremely important and active areas of research in both the academic and commercial realms. This book provides a complete snapshot of the field of computer-aided drug design and associated experimental approaches. Topics covered include X-ray crystallography, NMR, fragment-based drug design, free energy methods, docking and scoring, linear-scaling quantum calculations, QSAR, pharmacophore methods, computational ADME-Tox, and drug discovery case studies. A variety of authors from academic and commercial institutions all over the world have contributed to this book, which is illustrated with more than 200 images. This is the only book to cover the subject of structure and ligand-based drug design, and it provides the most up-to-date information on a wide range of topics for the practising computational chemist, medicinal chemist, or structural biologist. Professor Kenneth Merz has been selected as the recipient of the 2010 A

In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on the complex plane. In the development of the theory the main emphasis is on asymptotic behaviour and the distribution of zeros. In the following chapters, the author explores the exact upper and lower bounds are given for the orthonormal polynomials and for the location of their zeros; regular n-th root asymptotic behaviour; and applications of the theory, including exact rates for convergence of rational interpolants, best rational approximants and non-diagonal Pade approximants to Markov functions (Cauchy transforms of measures). The results are based on potential theoretic methods, so both the methods and the results can be extended to extremal polynomials in norms other than L2 norms. A sketch of the theory of logarithmic potentials

This book covers the fundamental principles of space-time coding for wireless communications over multiple-input multiple-output (MIMO) channels, and sets out practical coding methods for achieving the performance improvements predicted by the theory. Starting with background material on wireless communications and the capacity of MIMO channels, the book then reviews design criteria for space-time codes. A detailed treatment of the theory behind space-time block codes then leads on to an in-depth discussion of space-time trellis codes. The book continues with discussion of differential space-time modulation, BLAST and some other space-time processing methods and the final chapter addresses additional topics in space-time coding. The theory and practice sections can be used independently of each other. Written by one of the inventors of space-time block coding, this book is ideal for a graduate student familiar with the basics of digital communications, and for engineers implementing th

The book presents a series of studies that probe young children's knowledge of a relatively well-defined, abstract semantic realm, that of definite and indefinite reference. Topics investigated include children's knowledge of the difference between referring to particular objects (e.g. I have a dog, which refers to a particular dog) and no particular objects at all (e.g. I don't have a dog, which makes reference to no particular dog) and their knowledge of how to account for the knowledge of their listeners in situations, e.g. in which they have in mind a particular reference but their listen does not. Because overlapping problems are investigated by a wide variety of methods, it is possible to verify more certainly the true level of children's performance. At the same time, the investigation by many methods illustrates how methodological problems may systematically affect and at times even distort our picture of development if not carefully allowed for.

The new farming methods that so radically changed English agriculture in the eighteenth and early nineteenth centuries were not adopted immediately by all farmers. The rate of improvement was uneven, not only between one farmer and another, but between different farming regions. This book suggests an approach to the problem of regional agricultural change and the factors which determined the different rates of change. Dr Grigg begins by describing the differences between the agricultural regions of South Lincolnshire - that is the two parts of Kesteven and Holland, an area fairly typical of eastern England - at the end of the eighteenth century. These were differences not only of land use and soil type but of landownership and farm size, productivity and location. The diffusion and adoption of new methods in each region is considered against the general economic background of the late eighteenth century and the boom conditions of the period of the Napoleonic Wars. The later part of the

Fishes is a practical introduction to the study of fish remains from archaeological sites, designed for archaeologists and archaezoologists working in the field and in the laboratory. It provides clear guidelines for the identification of remains and how to interpret them. The identification and analysis of fish remains unearthed in archaeological excavations are invaluable factors in the reconstruction of climate, economic strategy, diet and trade. In this manual the authors discuss the importance of fishes in past economies and in archaeological research. They describe methods of extraction, fish anatomy and classification with the aid of numerous line drawings. The book also includes a survey of fishes most likely to be represented in archaeological sites and describes the biology of fishes in order to help archaeozoologists make informed judgements about methods of exploitation, size of fish caught and meat yield. This study is unique in making a realistic assessment of both the po

The second edition of this standard text guides biomedical researchers in the selection and use of advanced statistical methods and the presentation of results to clinical colleagues. It assumes no knowledge of mathematics beyond high school level and is accessible to anyone with an introductory background in statistics. The Stata statistical software package is again used to perform the analyses, this time employing the much improved version 10 with its intuitive point and click as well as character-based commands. Topics covered include linear, logistic and Poisson regression, survival analysis, fixed-effects analysis of variance, and repeated-measure analysis of variance. Restricted cubic splines are used to model non-linear relationships. Each method is introduced in its simplest form and then extended to cover more complex situations. An appendix will help the reader select the most appropriate statistical methods for their data. The text makes extensive use of real data sets avai

The second edition of this standard text guides biomedical researchers in the selection and use of advanced statistical methods and the presentation of results to clinical colleagues. It assumes no knowledge of mathematics beyond high school level and is accessible to anyone with an introductory background in statistics. The Stata statistical software package is again used to perform the analyses, this time employing the much improved version 10 with its intuitive point and click as well as character-based commands. Topics covered include linear, logistic and Poisson regression, survival analysis, fixed-effects analysis of variance, and repeated-measure analysis of variance. Restricted cubic splines are used to model non-linear relationships. Each method is introduced in its simplest form and then extended to cover more complex situations. An appendix will help the reader select the most appropriate statistical methods for their data. The text makes extensive use of real data sets avai

The Impressionist painter Camille Pissarro's eldest son, Lucien, lived in England in 1883, then in Paris until 1890 when he finally settled in England. These travels gave rise to a substantial exchange of letters, most of which have survived. This substantial 1993 collection of the letters of Impressionist painter Camille Pissarro, published in the original French with extensive notes and illustrations, offers a unique source for anyone interested in English 'aesthetic' life towards the end of the nineteenth century. The technical discussion of the translation of drawings to woodblocks engraved by Lucien gives a unique insight into the methods employed, while intimate views on the work of their now famous friends, mainly painters, writers of anarchist theoreticians in Paris, or contemporary painters reacting to the Pre-Raphaelites in London and the Private Press movement inspired by William Morris, mingle advice on painting methods with views on current art trends, family matters, and

This book covers the fundamental principles of space-time coding for wireless communications over multiple-input multiple-output (MIMO) channels, and sets out practical coding methods for achieving the performance improvements predicted by the theory. Starting with background material on wireless communications and the capacity of MIMO channels, the book then reviews design criteria for space-time codes. A detailed treatment of the theory behind space-time block codes then leads on to an in-depth discussion of space-time trellis codes. The book continues with discussion of differential space-time modulation, BLAST and some other space-time processing methods and the final chapter addresses additional topics in space-time coding. The theory and practice sections can be used independently of each other. Written by one of the inventors of space-time block coding, this book is ideal for a graduate student familiar with the basics of digital communications, and for engineers implementing th

International agreements, such as those governing arms control or the environment, virtually always require some degree of verification of information, in order that compliance can be established. To ensure that the verification process can be regarded as efficient, effective and impartial, it is important to have a mathematical model of it. One can be derived by applying methods from statistics and the theory of non-cooperative games, developed in part by John Nash, who received a Nobel prize in 1994 for his work. The methods permit the development of rational verification strategies, as well as such fundamental concepts as guaranteed probability of detection, timeliness of inspections and the deterrence of illegal activity. In this 1996 book, the required theory is introduced gradually in the context of specific real-world examples. The only prerequisites are simple calculus and statistics, so the book should be accessible to a broad range of scientists and non-scientists, in industr

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students a

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

This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent account of the methods used to find all the solutions to certain diophantine equations, particularly those procedures which have been developed for use on a computer. The study is divided into three parts, the emphasis throughout being on examining approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, mainly focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers, with a basic knowledge of number theory, who are interested in solving diop

Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent account of the methods used to find all the solutions to certain diophantine equations, particularly those procedures which have been developed for use on a computer. The study is divided into three parts, the emphasis throughout being on examining approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, mainly focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers, with a basic knowledge of number theory, who are interested in solving diop

In the late 1960s, Berlin and Kay argued that there are commonalities of basic colour term use that extend across languages and cultures, and probably express universal features of perception and cognition. In 1992, at the Asilomar Conference Centre, visual scientists and psychologists met with linguists and anthropologists for the first time to examine how these claims have fared in the light of current knowledge. To what extent can cross-cultural regularities be explained by the operation of the human visual system? What can the study of colour categorisation tell us about concept formation? Are the Berlin-Kay results an artifact of their methods? What tools have been and should be used to probe the structure of human colour categories? In this volume, which arose from that conference but also incorporates new work, a distinguished team of contributors survey key ideas, results and techniques from the study of human colour vision, as well as field methods and theoretical interpretati

A textbook for the advanced undergraduate or graduate student beginning a serious study of X-ray crystallography. It will be of interest both to those intending to become professional crystallographers and to those physicists, chemists, biologists, geologists, metallurgists and others who will use it as a tool in their research. All major aspects of crystallography are covered - the geometry of crystals and their symmetry, theoretical and practical aspects of diffracting X-rays by crystals and how the data may be analysed to find the symmetry of the crystal and its structure. Recent advances are fully covered, including the synchrotron as a source of X-rays, methods of solving structures from power data and the full range of techniques for solving structures from single-crystal data. A suite of computer programs is provided for carrying out many operations of data-processing and solving crystal structures - including by direct methods. While these are limited to two dimensions they ful