MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 25 per cent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox. Key features are:* A tutorial in Chapter 1 that gives a hands-on overview of MATLAB.* A thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers.* A web page provides example program files, updates, and links to MATLAB resources. The new edition:* Contains colour figures throughout. * Includes pithy discussions of related topics in new "Asides" boxes that augment the text. * Has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets.* Covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables.* Contains more on MATLAB workflow, including the Live Editor and unit tests.* Fully reflects major updates to the MATLAB graphics system. Features a tutorial in Chapter 1 that gives a hands-on overview of MATLAB, a thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers, and a web page that provides example program files, updates, and links to MATLAB resources. The new edition contains color figures throughout, includes pithy discussions of related topics in new "Asides" boxes that augment the text, has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets, covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables, contains more on MATLAB workflow, including the Live Editor and unit tests, and fully reflects major updates to the MATLAB graphics system.

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. * Features nearly 200 entries organized thematically and written by an international team of distinguished contributors* Presents the major ideas and branches of applied mathematics in a clear and accessible way* Explains important mathematical concepts, methods, equations, and applications* Introduces the language of applied mathematics and the goals of applied mathematical research* Gives a wide range of examples of mathematical modeling* Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more* Explores the connections between applied mathematics and other disciplines* Includes suggestions for further reading, cross-references, and a comprehensive index

The Anglo-Saxon period was crucial to the development of the English landscape, but is rarely studied. The essays here provide radical new interpretations of its development. Traditional opinion has perceived the Anglo-Saxons as creating an entirely new landscape from scratch in the fifth and sixth centuries AD, cutting down woodland, and bringing with them the practice of open field agriculture, and establishing villages. Whilst recent scholarship has proved this simplistic picture wanting, it has also raised many questions about the nature of landscape development at the time, the changing nature of systems of land management, and strategies for settlement. The papers here seek to shed new light on these complex issues. Taking a variety of different approaches, and with topics ranging from the impact of coppicing to medieval field systems, from the representation of the landscape in manuscripts to cereal production and the type of bread the population preferred, they offer striking new approaches to the central issues of landscape change across the seven centuries of Anglo-Saxon England, a period surely foundational to the rural landscape of today. NICHOLAS J. HIGHAM is Professor of Early Medieval and Landscape History at the University of Manchester; MARTIN J. RYAN lectures in Medieval History at the University of Manchester. Contributors: Nicholas J. Higham, Christopher Grocock, Stephen Rippon, Stuart Brookes, Carenza Lewis, Susan Oosthuizen, Tom Williamson, Catherine Karkov, David Hill, Debby Banham, Richard Hoggett, Peter Murphy.

A prominent scholar explores King Arthur's historical development, proposing that he began as a fictional character developed in the ninth century According to legend, King Arthur saved Britain from the Saxons and reigned over it gloriously sometime around A.D. 500. Whether or not there was a "real" King Arthur has all too often been neglected by scholars; most period specialists today declare themselves agnostic on this important matter. In this erudite volume, Nick Higham sets out to solve the puzzle, drawing on his original research and expertise to determine precisely when, and why, the legend began. Higham surveys all the major attempts to prove the origins of Arthur, weighing up and debunking hitherto claimed connections with classical Greece, Roman Dalmatia, Sarmatia, and the Caucasus. He then explores Arthur's emergence in Wales-up to his rise to fame at the hands of Geoffrey of Monmouth. Certain to arouse heated debate among those committed to defending any particular Arthur, Higham's book is an essential study for anyone seeking to understand how Arthur's story began.

Network Science is the emerging field concerned with the study of large, realistic networks. This interdisciplinary endeavor, focusing on the patterns of interactions that arise between individual components of natural and engineered systems, has been applied to data sets from activities as diverse as high-throughput biological experiments, online trading information, smart-meter utility supplies, and pervasive telecommunications and surveillance technologies. This unique text/reference provides a fascinating insight into the state of the art in network science, highlighting the commonality across very different areas of application and the ways in which each area can be advanced by injecting ideas and techniques from another. The book includes contributions from an international selection of experts, providing viewpoints from a broad range of disciplines. It emphasizes networks that arise in nature-such as food webs, protein interactions, gene expression, and neural connections-and in technology-such as finance, airline transport, urban development and global trade. Topics and Features: begins with a clear overview chapter to introduce this interdisciplinary field; discusses the classic network science of fixed connectivity structures, including empirical studies, mathematical models and computational algorithms; examines time-dependent processes that take place over networks, covering topics such as synchronisation, and message passing algorithms; investigates time-evolving networks, such as the World Wide Web and shifts in topological properties (connectivity, spectrum, percolation); explores applications of complex networks in the physical and engineering sciences, looking ahead to new developments in the field. Researchers and professionals from disciplines as varied as computer science, mathematics, engineering, physics, chemistry, biology, ecology, neuroscience, epidemiology, and the social sciences will all benefit from this topical and broad overview of current activities and grand challenges in the unfolding field of network science.

Network Science is the emerging field concerned with the study of large, realistic networks. This interdisciplinary endeavor, focusing on the patterns of interactions that arise between individual components of natural and engineered systems, has been applied to data sets from activities as diverse as high-throughput biological experiments, online trading information, smart-meter utility supplies, and pervasive telecommunications and surveillance technologies. This unique text/reference provides a fascinating insight into the state of the art in network science, highlighting the commonality across very different areas of application and the ways in which each area can be advanced by injecting ideas and techniques from another. The book includes contributions from an international selection of experts, providing viewpoints from a broad range of disciplines. It emphasizes networks that arise in nature-such as food webs, protein interactions, gene expression, and neural connections-and in technology-such as finance, airline transport, urban development and global trade. Topics and Features: begins with a clear overview chapter to introduce this interdisciplinary field; discusses the classic network science of fixed connectivity structures, including empirical studies, mathematical models and computational algorithms; examines time-dependent processes that take place over networks, covering topics such as synchronisation, and message passing algorithms; investigates time-evolving networks, such as the World Wide Web and shifts in topological properties (connectivity, spectrum, percolation); explores applications of complex networks in the physical and engineering sciences, looking ahead to new developments in the field. Researchers and professionals from disciplines as varied as computer science, mathematics, engineering, physics, chemistry, biology, ecology, neuroscience, epidemiology, and the social sciences will all benefit from this topical and broad overview of current activities and grand challenges in the unfolding field of network science.

Written in a clear, informal style for graduate students and practicing teachers embarking on their first qualitative research study in applied linguistics, leading authors introduce the principal research approaches and data creation methods to offer novice researchers an easy-to-follow and straightforward guide to qualitative inquiry.

Using a reader-friendly, structured approach, "Qualitative Research in Applied Linguistics: A Practical Introduction" presents an easy-to-follow and straightforward guide to qualitative inquiry. Written by leading authors in a clear, informal style, it is an essential companion for graduate students and practicing teachers embarking on their first qualitative research study in applied linguistics.
The ten central chapters introduce core qualitative research approaches and commonly used data collection methods. Each of these chapters offers:
- A comprehensive guide to help you understand and use each approach or method
- An illustrative example from applied linguistics research to help you see the approach or method 'in action'
- A succinct outline of how you can avoid common mistakes and improve the quality of your research
- Discussion questions and tasks to give you hands-on experience working with each research approach or data collection method
Additional chapters offer engaging introductions to the qualitative research cycle, ethics, and writing up your research. There is also a glossary of important key words.
This book has been carefully written to provide you with the essential research knowledge, skills - and confidence - you need to begin your qualitative research project.

The Anglo-Saxon period, stretching from the fifth to the late eleventh century, begins with the Roman retreat from the Western world and ends with the Norman takeover of England. Between these epochal events, many of the contours and patterns of English life that would endure for the next millennium were shaped. In this authoritative work, N. J. Higham and M. J. Ryan reexamine Anglo-Saxon England in the light of new research in disciplines as wide ranging as historical genetics, paleobotany, archaeology, literary studies, art history, and numismatics. The result is the definitive introduction to the Anglo-Saxon world, enhanced with a rich array of photographs, maps, genealogies, and other illustrations. The Anglo-Saxon period witnessed the birth of the English people, the establishment of Christianity, and the development of the English language. With an extraordinary cast of characters (Alfred the Great, the Venerable Bede, King Cnut), a long list of artistic and cultural achievements (Beowulf, the Sutton Hoo ship-burial finds, the Bayeux Tapestry), and multiple dramatic events (the Viking invasions, the Battle of Hastings), the Anglo-Saxon era lays legitimate claim to having been one of the most important in Western history.

Handbook of Writing for the Mathematical Sciences provides advice on all aspects of scientific writing, with a particular focus on writing mathematics. Its readable style and handy format, coupled with an extensive bibliography and comprehensive index, make it useful for everyone from undergraduates to seasoned professionals. This third edition revises, updates, and expands the best-selling second edition to reflect modern writing and publishing practices and builds on the author’s extensive experience in writing and speaking about mathematics. Key features: coverage of fundamentals of writing, including English usage, revising a draft, and writing when your first language is not English; thorough treatment of mathematical writing, including how to choose notation, how to choose between words and symbols, and how to format equations; many tips for exploiting LATEX and BibTEX; advice on how to write and publish a paper, covering the entire publication process; and anecdotes, quotes, and unusual facts that enliven the presentation. The new edition: has been reorganized to make the book easier to use for reference; treats modern developments in publishing such as open access, DOIs, and ORCID; has a new chapter on workflow covering text editors, markup languages, version control, and much more; has a new chapter that discusses the principles of indexing and how to prepare an index in LATEX; has a new chapter on reviewing a paper, book proposal, or book; has a new chapter “Writing a Book” that includes advice on choosing a publisher and LATEX tips particular to books; contains more on poster design, and discusses e-posters and the poster blitz; and has a new chapter giving advice on writing a blog post.

This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks. Although introductory, the book covers a range of modern research topics, including Ito versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlinear problems, multilevel Monte Carlo, approximation of double stochastic integrals, and tau leaping for chemical and biochemical reaction networks. An Introduction to the Numerical Simulation of Stochastic Differential Equations is appropriate for undergraduates and postgraduates in mathematics, engineering, physics, chemistry, finance, and related disciplines, as well as researchers in these areas. The material assumes only a competence in algebra and calculus at the level reached by a typical first-year undergraduate mathematics class, and prerequisites are kept to a minimum. Some familiarity with basic concepts from numerical analysis and probability is also desirable but not necessary.

An exploration of the landscape of Anglo-Saxon England, particularly through the prism of place-names and what they can reveal. The landscape of modern England still bears the imprint of its Anglo-Saxon past. Villages and towns, fields, woods and forests, parishes and shires, all shed light on the enduring impact of the Anglo-Saxons. The essays in this volume explore the richness of the interactions between the Anglo-Saxons and their landscape: how they understood, described, and exploited the environments of which they were a part. Ranging from the earliest settlement period through to the urban expansion of late Anglo-Saxon England, this book draws on evidence from place-names, written sources, and the landscape itself to provide fresh insights into the topic. Subjects explored include the history of thestudy of place-names and the Anglo-Saxon landscape; landscapes of particular regions and the exploitation of particular landscape types; the mechanisms of the transmission and survival of written sources; and the problems and potentials of interdisciplinary research into the Anglo-Saxon landscape. Nicholas J. Higham is Professor of Early Medieval and Landscape History at the University of Manchester; Martin Ryan lectures in Medieval History at the University of Manchester. Contributors: Ann Cole, Linda M. Corrigan, Dorn Van Dommelen, Simon Draper, Gillian Fellows-Jensen, Della Hooke, Duncan Probert, Alexander R. Rumble, Martin J. Ryan, Peter A. Stokes, Richard Watson.

Essays on the brief but tumultuous reign of Harold II, and one of our most important sources of knowledge of the time - the Bayeux Tapestry. Harold II is chiefly remembered today, perhaps unfairly, for the brevity of his reign and his death at the Battle of Hastings. The papers collected here seek to shed new light on the man and his milieu before and after that climax. They explore the long career and the dynastic network behind Harold Godwinesson's accession on the death of King Edward the Confessor in January 1066, looking in particular at the important questions as to whether Harold's kingship was opportunist or long-planned; a usurpation or a legitimate succession in terms of his Anglo-Scandinavian kinships? They also examine the posthumous legends that Harold survived Hastings and lived on as a religious recluse.The essays in the second part of the volume focus on the Bayeux Tapestry, bringing out the small details which would have resonated significantly for contemporary audiences, both Norman and English, to suggest how they judged Harold and the other players in the succession drama of 1066. Other aspects of the Tapestry are also covered: the possible patron and locations the Tapestry was produced for; where and how it was designed; and the various sources - artistic and real - employed by the artist. Contributors: H.E.J. Cowdrey, Nicholas J. Higham, Ian Howard, Gillian Fellows-Jensen, Stephen Matthews, S.L. Keefer, Gale R. Owen-Crocker, Chris Henige, Catherine Karkov, Shirley Ann Brown, C.R. Hart, Michael Lewis. GALE OWEN-CROCKER is Professor of Anglo-Saxon Culture at the University of Manchester.

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.

It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.

Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.

The book covers key foundation topics:

o Taylor series methods

o Runge--Kutta methods

o Linear multistep methods

o Convergence

o Stability

and a range of modern themes:

o Adaptive stepsize selection

o Long term dynamics

o Modified equations

o Geometric integration

o Stochastic differential equations

The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

A prominent scholar explores King Arthur's historical development, proposing that he began as a fictional character developed in the ninth century According to legend, King Arthur saved Britain from the Saxons and reigned over it gloriously sometime around A.D. 500. Whether or not there was a "real" King Arthur has all too often been neglected by scholars; most period specialists today declare themselves agnostic on this important matter. In this erudite volume, Nick Higham sets out to solve the puzzle, drawing on his original research and expertise to determine precisely when, and why, the legend began. Higham surveys all the major attempts to prove the origins of Arthur, weighing up and debunking hitherto claimed connections with classical Greece, Roman Dalmatia, Sarmatia, and the Caucasus. He then explores Arthur's emergence in Wales-up to his rise to fame at the hands of Geoffrey of Monmouth. Certain to arouse heated debate among those committed to defending any particular Arthur, Higham's book is an essential study for anyone seeking to understand how Arthur's story began.

This annual review of the literature provides a comprehensive and critical survey of a vast field of study involving organophosphorus compounds, ranging from phosphines, their chalcogenide derivatives and phosphonium salts, phosphorus (III) acid derivatives, phosphorus (V) acids, penta- and hexa-coordinated phosphorus compounds, phosphazenes and related phosphorus-nitrogen bonded compounds. Coverage in applications as reagents in green synthetic procedures is also given. With an emphasis on interdisciplinary content, this book will appeal to the worldwide organic chemistry and engineering research communities.

This annual review of the literature, the 50th volume in the present series, provides a comprehensive and critical survey of a vast field of study involving organophosphorus compounds, ranging from phosphines, their chalcogenide derivatives and phosphonium salts, phosphorus (III) acid derivatives, phosphorus (V) acids, penta- and hexa-coordinated phosphorus compounds, phosphazenes and related phosphorus-nitrogen bonded compounds. Coverage is also presented of applications of organophosphorus compounds in homogeneous catalysis for synthesis of bulk and fine chemicals and also in applications as reagents in green synthetic procedures.

Building on the authors' many years of experience running creativity workshops, How to Be Creative: A Practical Guide for the Mathematical Sciences: Gives a six-step process for generating great ideas that can be used by individuals or groups. Provides examples demonstrating how these concepts have been or might be used in practice in the mathematical sciences. Presents seven cases of tried and tested briefs that can be used at creativity workshops. With mathematically oriented models, this book is for anyone in the mathematical sciences who wants to be more creative or who wishes to train others in creativity.

This annual review of the literature presents a comprehensive and critical survey of the vast field of study involving organophosphorus compounds, from phosphines and related P-C bonded compounds to phosphorus acids, phosphine chalcogenides and nucleotides. The Editors have added to the content with a timely chapter on the recent developments in green synthetic approaches in organophosphorus chemistry to reflect current interests in the area. With an emphasis on interdisciplinary content, this book is aimed at the worldwide organic chemistry and engineering research communities.

The only book devoted exclusively to matrix functions, this research monograph gives a thorough treatment of the theory of matrix functions and numerical methods for computing them. The author's elegant presentation focuses on the equivalent definitions of f(A) via the Jordan canonical form, polynomial interpolation, and the Cauchy integral formula, and features an emphasis on results of practical interest and an extensive collection of problems and solutions. Functions of Matrices more than just a monograph on matrix functions; its wide-ranging content-including an overview of applications, historical references, and miscellaneous results, tricks, and techniques with an f(A) connection-makes it useful as a general reference in numerical linear algebra. Other key features of the book include development of the theory of conditioning and properties of the Frechet derivative; an emphasis on the Schur decomposition, the block Parlett recurrence, and judicious use of Pade approximants; the inclusion of new, unpublished research results and improved algorithms; a chapter devoted to the f(A)b problem; and a MATLAB(R) toolbox providing implementations of the key algorithms.

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-contained.