Design Structure Matrix Methods and Applications

The subject of mineralogy is moving away from the traditional systematic treatment of mineral groups toward the study of the behaviour of minerals in relation to geological processes. A knowledge of how minerals respond to a changing geological environment is fundamental to our understanding of many dynamic earth processes. By adopting a materials science approach, An Introduction to Mineral Sciences explains the principles underlying the modern study of minerals, discussing the behaviour of crystalline materials with changes in temperature, pressure and chemical environment. The concepts required to understand mineral behaviour are often complex, but are presented here in simple, non-mathematical terms for undergraduate mineralogy students. After introductory chapters describing the principles of diffraction, imaging and the spectroscopic methods used to study minerals, the structure and behaviour of the main groups of rock-forming minerals are covered, and the role of defects in the

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

The second edition of Julien's textbook presents an analysis of rivers from mountain streams to river estuaries. The book is rooted in fundamental principles to promote sound engineering practice. State-of-the-art methods are presented to underline theory and engineering applications. River mechanics blends the dual concepts of water conveyance and sediment transport. Like the first edition, this textbook contains ample details on river equilibrium, river dynamics, bank stabilization, and river engineering. Complementary chapters also cover the physical and mathematical modeling of rivers. As well as being completely updated throughout, three new chapters have been added on watershed dynamics, hillslope stability, and stream restoration. Throughout the text, hundreds of examples, exercises, problems, and case studies assist the reader in learning the essential concepts of river engineering. The textbook is very well illustrated to enhance advanced student learning, while researchers an

Engage with the visual world of disease with this accessible introduction to molecular imaging. This book provides users of all levels with the characterization and measurement of biological processes on a cellular level, functioning within humans, and other living systems. This important new introduction to the field will enable the reader to recognize the major methods, modalities and varied applications of molecular imaging in an efficient and effective way. Featuring techniques from areas such as nuclear medicine, magnetic resonance spectroscopy, optical imaging, and nanotechnology, the book also covers the current movement towards precision medicine thereby driving exceptional hospital care, worldwide. Molecular Imaging provides valuable insight into the properties that improve patient diagnosis. Serving to inform experienced physicians, students, and beginners alike, this convenient introduction is tailored to an individual with the desire to effectively grasp the basic concepts

This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate stud

This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate stud

This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

In the new edition of this widely praised textbook, all the chapters have been revised and the authors have brought the work completely up to date by the addition of new material on numerous topics. In recent years, solid state chemistry has emerged as a very important element of mainstream chemistry and materials science. Students, teachers and researchers need to understand the chemistry of solids because of the crucial role this plays in determining the properties of materials. An understanding of solid state chemistry is also essential in materials design, and many fascinating relationships between the structure and properties of solids have been discovered by chemists. This text requires only an understanding of basic physics, chemistry and crystallography, and is enhanced with the most recent examples, case studies and references. It will be of value to advanced students and researchers studying solid state chemistry and materials science as a text and reference work.

The first introductory book on the subject, this book will provide a complete grounding to this pioneering field for students and professionals across biomedical engineering, biology and medicine. It features a comprehensive overview of original work in this revolutionary field. Topics discussed include drug delivery, cell-material interaction and gene therapy, accompanied by real-world examples and over 100 illustrations. The book teaches readers how to design and test their own nanomedical systems for real-world applications in biomedical engineering, medicine and pharmacy. Presenting a thorough discussion of the science and engineering of nanomedicine, it discusses vital environmental, social and ethical impacts of this revolutionary technology. Including over 200 thought-provoking study questions, allowing the reader to self-assess their understanding, this book is a rich source of information that will be of interest and importance in nanomedicine.

This beloved and market-leading Operations Management book has been completely updated in the 14th edition and provides a clear presentation of the field of Operations Management with current real-world examples and thoughtful student pedagogy. The comprehensive breadth of content is presented in more modular flexible chapters, so it may be used for different course levels ranging from undergrad to executive education. That flexibility allows for the choice of more or less quantitative material and flexibility in order of presentation since chapters do not depend on sequence.The topics covered include both strategic issues and practical applications. Among the topics are forecasting, product and service design, capacity planning, management of quality and quality control, inventory management, scheduling, supply chain management, and project management. The use of an adaptive online learning enhances the student experience and success.

This unique and comprehensive introduction offers an unrivalled and in-depth understanding of the computational-based thermodynamic approach and how it can be used to guide the design of materials for robust performances, integrating basic fundamental concepts with experimental techniques and practical industrial applications, to provide readers with a thorough grounding in the subject. Topics covered range from the underlying thermodynamic principles, to the theory and methodology of thermodynamic data collecting, analysis, modeling, and verification, with details on free energy, phase equilibrium, phase diagrams, chemical reactions, and electrochemistry. In thermodynamic modelling, the authors focus on the CALPHAD method and first-principles calculations. They also provide guidance for use of YPHON, a mixed-space phonon code developed by the authors for polar materials based on the supercell approach. Including worked examples, case studies, and end-of-chapter problems, this is an es

This book is concerned with the underlying science and design of laser materials. It emphasizes the principles of crystal–field engineering and discusses the basic physical concepts that determine laser gain and nonlinear frequency conversion in optical crystals. A concise review of the essential underlying science is presented, and the predictive capabilities of crystal-field engineering are developed to show how modification of the symmetry and composition of optical centres can improve laser performance. Applications of the principles of crystal-field engineering to a variety of optical crystals are also discussed in relation to the performances of laser devices. This book will be of considerable interest to physical, chemical and material scientists and to engineers involved in the science and technology of solid state lasers. It will be used by senior undergraduate and postgraduate students as well as by established scientists.

This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, a package for computation of these maps.

This book is concerned with the underlying science and design of laser materials. It emphasizes the principles of crystal–field engineering and discusses the basic physical concepts that determine laser gain and nonlinear frequency conversion in optical crystals. A concise review of the essential underlying science is presented, and the predictive capabilities of crystal-field engineering are developed to show how modification of the symmetry and composition of optical centres can improve laser performance. Applications of the principles of crystal-field engineering to a variety of optical crystals are also discussed in relation to the performances of laser devices. This book will be of considerable interest to physical, chemical and material scientists and to engineers involved in the science and technology of solid state lasers. It will be used by senior undergraduate and postgraduate students as well as by established scientists.

The atomic structures of macromolecules provide the key to understanding how life works. Aaron Klug led the way in the development of methods for solving such structures and is one of the pioneers of structural molecular biology. He was awarded a Nobel Prize in 1982 for his work. Illuminating both his personal life and scientific achievements, this unique biography begins with Klug's youth in Durban and his studies at Johannesburg, Cape Town and then Trinity College, Cambridge. Holmes proceeds to explore Klug's career from his work on the structure of viruses with Rosalind Franklin at Birkbeck College, London to his time as Director of the MRC Laboratory of Molecular Biology (LMB) in Cambridge and as President of the Royal Society. Drawing on their long-term collaboration, interviews and unique access to Klug's archives, Holmes provides a fascinating account of an innovative man and his place in the history of structural molecular biology.

International human rights law has expanded remarkably since the 1990s. It is therefore more important than ever to identify, beyond specific controversies, its deeper structure and the general pattern of evolution. Moreover, it has a logic of its own: though part of international law, it borrows many of its principles from domestic constitutional law. This leading textbook meets both challenges. It has been significantly updated for the new third edition, introducing sections on subjects including business and human rights, amongst other key areas. Features include forty new cases from various jurisdictions or expert bodies, and figures offering visual descriptions of the procedures discussed in the text. The 'questions for discussion' have also been systematically updated. The text retains its student-friendly design, and the features which made the previous editions so engaging and accessible remain. This popular textbook continues to be an essential tool for all students of human r

Because of their widespread use in mainframes, PCs, and mobile audio and video devices, DRAMs are being manufactured in ever increasing volume, both in stand-alone and in embedded form as part of a system on chip. Due to the optimum design of their components-access transistor, storage capacitor, and peripherals-DRAMs are the cheapest and densest semiconductor memory currently available. As a result, most of DRAM structure research and development focuses on the technology used for its constituent components and their interconnections.However, only a few books are available on semiconductor memories in general and fewer on DRAMs. Dynamic RAM: Technology Advancements provides a holistic view of the DRAM technology with a systematic description of the advancements in the field since the 1970s, and an analysis of future challenges. Topics Include:DRAM cells of all types, including planar, three-dimensional (3-D) trench or stacked, COB or CUB, vertical, and mechanically robust cells using

String matching is one of the oldest algorithmic techniques, yet still one of the most pervasive in computer science. The past 20 years have seen technological leaps in applications as diverse as information retrieval and compression. This copiously illustrated collection of puzzles and exercises in key areas of text algorithms and combinatorics on words offers graduate students and researchers a pleasant and direct way to learn and practice with advanced concepts. The problems are drawn from a large range of scientific publications, both classic and new. Building up from the basics, the book goes on to showcase problems in combinatorics on words (including Fibonacci or Thue-Morse words), pattern matching (including Knuth-Morris-Pratt and Boyer-Moore like algorithms), efficient text data structures (including suffix trees and suffix arrays), regularities in words (including periods and runs) and text compression (including Huffman, Lempel-Ziv and Burrows-Wheeler based methods).

String matching is one of the oldest algorithmic techniques, yet still one of the most pervasive in computer science. The past 20 years have seen technological leaps in applications as diverse as information retrieval and compression. This copiously illustrated collection of puzzles and exercises in key areas of text algorithms and combinatorics on words offers graduate students and researchers a pleasant and direct way to learn and practice with advanced concepts. The problems are drawn from a large range of scientific publications, both classic and new. Building up from the basics, the book goes on to showcase problems in combinatorics on words (including Fibonacci or Thue-Morse words), pattern matching (including Knuth-Morris-Pratt and Boyer-Moore like algorithms), efficient text data structures (including suffix trees and suffix arrays), regularities in words (including periods and runs) and text compression (including Huffman, Lempel-Ziv and Burrows-Wheeler based methods).

This three-volume series presents the ideas, models and approaches essential to understanding plasma dynamics and self-organization for researchers and graduate students in plasma physics, controlled fusion and related fields such as plasma astrophysics. Volume I develops the physical kinetics of plasma turbulence through a focus on quasi-particle models and dynamics. It discusses the essential physics concepts and theoretical methods for describing weak and strong fluid and phase space turbulence in plasma systems far from equilibrium. The book connects the traditionally 'plasma' topic of weak or wave turbulence theory to more familiar fluid turbulence theory, and extends both to the realm of collisionless phase space turbulence. This gives readers a deeper understanding of these related fields, and builds a foundation for future applications to multi-scale processes of self-organization in tokamaks and other confined plasmas. This book emphasizes the conceptual foundations and physic

Nanooptics which describes the interaction of light with matter at the nanoscale, is a topic of great fundamental interest to physicists and engineers and allows the direct observation of quantum mechanical phenomena in action. This self-contained and extensively referenced text describes the underlying theory behind nanodevices operating in the quantum regime for use both in advanced courses and as a reference for researchers in physics, chemistry, electrical engineering, and materials science. Presenting an extensive theoretical toolset for design and analysis of nanodevices, the authors demonstrate the art of developing approximate quantum models of real nanodevices. The rudimentary mathematical knowledge required to master the material is carefully introduced, with detailed derivations and frequent worked examples allowing readers to gain a thorough understanding of the material. More advanced applications are gradually introduced alongside analytical approximations and simplifying

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

This book introduces a new, unique, and far-reaching industry technology, Business Service Orchestration (BSO). BSO encompasses the art of orchestrating the interactions between business services. These business services may represent internal business processes of organizations. Integration of many of these internal legacy, custom and COTS applications may, in turn, create these services. This book focuses on the importance of orchestration and how it enables IT professionals to develop and design highly effective and efficient business systems of the future. The book is divided into three major sections. Section I provides a detailed overview of business services and their orchestration and describes an in-depth architecture necessary to provide a web of business services, and orchestration of their interactions, including a methodology for modeling the BSO. Section II focuses on technologies necessary to orchestrate business services, ranging from component models to programming lan

Thermochemical Surface Engineering of Steels, Second Edition presents up to date information on a range of techniques and their applications. This edition expands upon the material presented in the first edition, now including a discussion of high temperature process for stainless steels as well as a new chapter on solution nitriding, as well as fully updating the current materials. The book is comprised of five parts, which take the reader from theory through to application. Part 1 presents foundational information regarding Thermodynamics; Part 2 discusses the requirements for improved fatigue resistance for materials exposed to thermochemical treatments. Parts 3 looks at nitriding, nitrocarburizing and carburizing, followed by a look at specific low temperature carburizing and nitriding; The book concludes with a discussion of various thermochemical surface engineering methods.

Photoelectrochemical Engineering for Solar Harvesting provides an up-to-date appraisal of the photon engineering of innovative catalysts for solar energy harvesting. Sunlight-driven fuel synthesis is the most sustainable and potentially economical option for producing energy vectors through water splitting. Thus this book focuses on the design of photocatalysts and water oxidation catalysts, as artificial photosynthesis and hydrogen fuel production via water oxidation (in place of fossil fuels) are two promising approaches towards renewable energy. The book critically analyzes the overall progress, potential challenges, and the possibility of industrialization of new catalysts in the near future. The primary emphasis of the discussion is on experimental approaches from materials synthesis to device applications, however, there will also be some introduction to relevant photochemistry concepts. Photoelectrochemical Engineering for Solar Harvesting is suitable for materials scientists an

Geographical Information Systems has moved from the domain of the computer specialist into the wider archaeological community, providing it with an exciting new research method. This clearly written but rigorous book provides a comprehensive guide to that use. Topics covered include: the theoretical context and the basics of GIS; data acquisition including database design; interpolation of elevation models; exploratory data analysis including spatial queries; statistical spatial analysis; map algebra; spatial operations including the calculation of slope and aspect, filtering and erosion modeling; methods for analysing regions; visibility analysis; network analysis including hydrological modeling; the production of high quality output for paper and electronic publication; and the use and production of metadata. Offering an extensive range of archaeological examples, it is an invaluable source of practical information for all archaeologists, whether engaged in cultural resource manageme

A programming course should concentrate as much as possible on a program's logical structure and design rather than simply show how to write code. The Functional Approach to Programming achieves this aim because logical concepts are evident and programs are transparent so can be written quickly and cleanly. In this book the authors emphasise the notions of function and function application which relate programming to familiar concepts from mathematics and logic. They introduce functional programming via examples but also explain what programs compute and how to reason about them. They show how the ideas can be implemented in the Caml language, a dialect of the ML family, and give examples of how complex programs from a variety of areas (such as arithmetic, tree algorithms, graph algorithms, text parsing and geometry) can be developed in close agreement with their specifications. Many exercises and examples are included throughout the book; solutions are also available.

Transcranial stimulation encompasses noninvasive methods that transmit physical fields-such as magnetic, electric, ultrasound, and light-to the brain to modulate its function. The most widespread approach, transcranial magnetic stimulation (TMS), has emerged as an important tool in several areas of neuroscience as well as in clinical applications in psychiatry and neurology. Originally envisioned as a way to measure the responsiveness and conduction speed of neurons and synapses in the brain and spinal cord, TMS has also become an important tool for changing the activity of brain neurons and the functions they subserve as well as an causal adjunct to brain imaging and mapping techniques. Along with transcranial electrical stimulation techniques, TMS has diffused far beyond the borders of clinical neurophysiology and into cognitive, perceptual, behavioural, and therapeutic investigation and attracted a highly diverse group of users and would-be users. Another major success of TMS has be

Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.

The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.

This text provides deep and comprehensive coverage of the mathematical background for data science, including machine learning, optimal recovery, compressed sensing, optimization, and neural networks. In the past few decades, heuristic methods adopted by big tech companies have complemented existing scientific disciplines to form the new field of Data Science. This text embarks the readers on an engaging itinerary through the theory supporting the field. Altogether, twenty-seven lecture-length chapters with exercises provide all the details necessary for a solid understanding of key topics in data science. While the book covers standard material on machine learning and optimization, it also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces, spectral clustering, optimal recovery, compressed sensing, group testing, and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendice

This 1998 book, about the nature and techniques of mathematical modeling, is oriented towards simple efficient implementations on computers. The text is in three sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications. The text is complemented by extensive worked problems.

Solitons are waves with exceptional stability properties which appear in many areas of physics. The basic properties of solitons are introduced here using examples from macroscopic physics (e.g. blood pressure pulses and fibre optical communications). The book then presents the main theoretical methods before discussing applications from solid state or atomic physics such as dislocations, excitations in spin chains, conducting polymers, ferroelectrics and Bose–Einstein condensates. Examples are also taken from biological physics and include energy transfer in proteins and DNA fluctuations. Throughout the book the authors emphasise a fresh approach to modelling nonlinearities in physics. Instead of a perturbative approach, nonlinearities are treated intrinsically and the analysis based on the soliton equations introduced in this book. Based on the authors' graduate course, this textbook gives an instructive view of the physics of solitons for students with a basic knowledge of general p

Solitons are waves with exceptional stability properties which appear in many areas of physics. The basic properties of solitons are introduced here using examples from macroscopic physics (e.g. blood pressure pulses and fibre optical communications). The book then presents the main theoretical methods before discussing applications from solid state or atomic physics such as dislocations, excitations in spin chains, conducting polymers, ferroelectrics and Bose–Einstein condensates. Examples are also taken from biological physics and include energy transfer in proteins and DNA fluctuations. Throughout the book the authors emphasise a fresh approach to modelling nonlinearities in physics. Instead of a perturbative approach, nonlinearities are treated intrinsically and the analysis based on the soliton equations introduced in this book. Based on the authors' graduate course, this textbook gives an instructive view of the physics of solitons for students with a basic knowledge of general p

This book examines the development of calculus in Britain during the century following Newton. It is usually maintained that this was a period of decline in British mathematics. However, the author's research has shown that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus. Even when 'decline' was at its worst point, in mid-century, the foundations of the reform, which were to change the direction and nature of the mathematics community, were being laid. The book considers the importance of the work of mathematicians such as Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring. It will be useful to science historians and philosophers studying the period, and to students of British history studying the teaching of mathematics.

This book examines the development of calculus in Britain during the century following Newton. It is usually maintained that this was a period of decline in British mathematics. However, the author's research has shown that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus. Even when 'decline' was at its worst point, in mid-century, the foundations of the reform, which were to change the direction and nature of the mathematics community, were being laid. The book considers the importance of the work of mathematicians such as Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring. It will be useful to science historians and philosophers studying the period, and to students of British history studying the teaching of mathematics.

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of th