Method

Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. While mastery of these equations is essential, adhering to any one method of solving them is not: this book stresses alternative examples and analyses by means of which the student can build an understanding of a number of approaches to finding solutions and understanding their behaviour. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application. An important resource for the advanced undergradute, this book would be equally useful for the beginning graduate student investigating further approaches to these essential equations.

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading.

This 1997 volume provides an overview of statistical energy analysis and its applications in structural vibration. Statistical energy analysis is a powerful method for predicting and analysing the vibrational behaviour of structures. Its main use is for structures that can be considered as assemblies of interconnected subsystems which are subject to medium to high frequency vibration sources. This volume brings together nine articles by experts from around the world. The opening chapter gives an introduction and overview of the technique describing its key successes, potential and limitations. Following chapters look in more detail at a selection of cases and examples which together illustrate the scope and power of the technique. This book is based on a Royal Society Philosophical Transactions issue under the title 'Statistical Energy Analysis', but an extra chapter, by Chohan, Price, Keane and Beshara, discussing nonconservatively coupled systems is included in this edition.

本書主要以讓讀者學會表現空間設計所需的素描，也就是所謂的透視素描為目標。空間的表達常常採用較具說服力的透視圖法（perspective drawing method），但是空間的意境則並非僅靠透視就可以完整地表達出來。真正的透視素描應將其中生命感的意境予以活生生傳達出來。因此透視素描不單是僅將所設計的空間予以畫出，更重要的是將生活與感情、故事中空間感的意境細膩的表達出來。

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints.

This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints.

This book is about the conceptual foundations of an intermediate way between liberalism and socialism: a synthesis of classical (Ricardian) and Keynesian political economy. Classical theory deals with proportions between individuals or collectives and society in tackling problems of distribution and value. Keynesian theory is concerned with the scale of economic activity as explained by effective demand. The economy considered is primarily a monetary production economy, not a market or a planned economy. The author sets up a system linking political economy with other social sciences, i.e. sociology, law and politics in the traditional sense, thus establishing the unity of the social sciences. To complete the picture, issues of method associated with the theory of knowledge in the social sciences and the problem of linking theory with historical reality are also covered.

This book presents fifteen essays, written over the past dozen years, on egalitarianism. The essays explore contemporary philosophical debates on this subject, using the tools of modern economic theory, general equilibrium theory, game theory, and the theory of mechanism design. Egalitarian Perspectives is divided into four parts: the theory of exploitation; equality of resources; bargaining theory and distributive justice; and market socialism and public ownership. The first part presents Roemer's influential reconceptualisation of the Marxian theory of exploitation as a theory of distributive justice. The second part offers a critique of Ronald Dworkin's equality-of-resources theory, and puts forward a new egalitarian proposal based upon a specific method of measuring individual responsibility. The third part introduces a novel application of the theory of mechanism design to the study of political philosophy, and raises new concerns about the limitations of that application. The fou

Over the past thirty years family history has been one of the most important and controversial growth areas in the development of social history. In this guide to the burgeoning literature on the Western family Professor Anderson reviews the main findings of historians and considers them in the light of the problems inherent in the interpretation of family history. He focuses particularly on the strengths and limitations of the different approaches that have been adopted, showing that although this variety of method has complicated matters, it has also produced a more rounded understanding of the history of the family. Updated to include work published between 1980 and 1994, this book will be invaluable to students of family history, and to scholars who are non-specialist in the field.

Robotic manipulators are becoming increasingly important in research and industry, and an understanding of statics and kinematics is essential to solving problems of robotics. This book, written by an eminent researcher and practitioner, provides a thorough introduction to statics and first-order instantaneous kinematics with applications to robotics. The emphasis is on serial and parallel planar manipulators and mechanisms. The text differs from others in that it is based solely upon the concepts of classical geometry. It describes how to introduce linear springs into the connectors of parallel manipulators and to provide a proper geometric method for controlling the force and motion of a rigid lamina. Both students and practising engineers will find this book easy to follow, with a clearly written text and abundant illustrations, as well as exercises and real-world projects to work on.

When is it correct to say that a person's freedom is restricted? Can poverty constrain freedom? Can you constrain your own freedom, for instance through weakness of the will or self-deception, and are you not truly free unless you act on a rational choice? Kristján Kristjánsson offers a critical analysis of the main components of a theory of negative liberty: the nature of obstacles and constraints, the weight of obstacles and the relation of freedom to power and autonomy. Through this discussion, which examines much of the contemporary work on political freedom, he develops his own theory of negative liberty, the so-called 'responsibility view', which meets many of the goals of advocates of positive liberty while retaining its distinctive 'negative' nature. He also argues for, and implements, a method of naturalistic revision as a way of solving conceptual disputes in social philosophy.

These seminal essays introduce the reader to the interdisciplinary approach of New Testament scholarship which is affecting the way the Book of Acts is studied and interpreted. Insights from the social sciences, narratological studies, Greek and Roman rhetoric and history, and classics, set the Acts of the Apostles in its original historical, literary and social context; these methods of interpretation have not always been applied to biblical study in a systematic way. The discussions from a shared general perspective range over genre and method, historical and theological problems, and issues of literary criticism. History, Literature and Society in the Book of Acts is an interesting and valuable overview of some of the chief preoccupations of biblical studies with contributions from leading scholars in the Old and New Testaments and the history of antiquity.

Physical Metallurgy elucidates the microstructure, transformation and properties of metallic materials by means of solid state physics and chemical thermodynamics. Experimental methods of physical metallurgy are also treated. This third edition includes new sections on the permeation of hydrogen in metals, the Landau theory of martensitic transformation, and order hardening and plasticity of intermetallics. Numerous other sections have been brought up to date in the light of new developments (e.g. scanning tunnelling microscopy, CALPHAD-method, diffusion in glasses, DIGM, recrystallisation). New artwork and references have also been added. Professor Haasen's clear and concise coverage of a remarkably wide range of topics will appeal both to physics students at the threshold of their metallurgical careers, and to metallurgists who are interested in the physical foundation of their field.

Physical Metallurgy elucidates the microstructure, transformation and properties of metallic materials by means of solid state physics and chemical thermodynamics. Experimental methods of physical metallurgy are also treated. This third edition includes new sections on the permeation of hydrogen in metals, the Landau theory of martensitic transformation, and order hardening and plasticity of intermetallics. Numerous other sections have been brought up to date in the light of new developments (e.g. scanning tunnelling microscopy, CALPHAD-method, diffusion in glasses, DIGM, recrystallisation). New artwork and references have also been added. Professor Haasen's clear and concise coverage of a remarkably wide range of topics will appeal both to physics students at the threshold of their metallurgical careers, and to metallurgists who are interested in the physical foundation of their field.

Modern technology depends on materials with precisely controlled properties. Ion beams are a favoured method to achieve controlled modification of surface and near-surface regions. In every integrated circuit production line, for example, there are ion implantation systems. In addition to integrated circuit technology, ion beams are used to modify the mechanical, tribological and chemical properties of metal, intermetallic and ceramic materials without altering their bulk properties. Ion–solid interactions are the foundation that underlies the broad application of ion beams to the modification of materials. This text is designed to cover the fundamentals and applications of ion–solid interactions and is aimed at graduate students and researchers interested in electronic devices, surface engineering, reactor and nuclear engineering and material science issues associated with metastable phase synthesis.

With the international consensus towards community care of the mentally ill, there came a growing need for meaningful evaluation of services. Redressing the lack of guidance this book describes how to do mental health service research. It comprehensively reviews developments in research design, method and measurement at the level of both whole service systems and individual programmes within mental health services. Each of the issues is adeptly illustrated with practical descriptions of comprehensive evaluation projects. The important advances already achieved in knowledge about effective services are highlighted along with descriptions of future work that will further develop our understanding of meeting patient requirements. This volume will appeal to all who are involved in mental health service research as well as those who make use of their results.

This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behaviour, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behaviour, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among other applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding

The Shaping of Art History examines art history's formation in the German academy in the late nineteenth century. Focusing on the work of Wilhelm Vöge and Adolph Goldschmidt, two influential scholars of medieval art, Kathryn Brush analyses their methods and particularly those scholarly projects that were critical to the development of their approaches. Her work combines intellectual and institutional history with the study of artistic monuments and biography. It considers how the study of the pioneering scholarship in the field of medieval art is critical to an understanding of the formulation of art historical method as a whole.

This book deals with the effect of crystal symmetry in determining the tensor properties of crystals. Although this is a well-established subject, the author provides a new approach using group theory and, in particular, the method of symmetry coordinates, which has not been used in any previous book. Using this approach, all tensors of a given rank and type can be handled together, even when they involve very different physical phenomena. Applications to technologically important phenomena as diverse as the electro-optic, piezoelectric, photoelastic, piezomagnetic, and piezoresistance effects, as well as magnetothermoelectric power and third-order elastic constants, are presented. Attention is also given to 'special magnetic properties', that is those that require the concepts of time reversal and magnetic symmetry, an important subject not always covered in other books in this area. This book will be of interest to researchers in solid-state physics and materials science, and will al

This book develops a statistical mechanical analysis of the stability of biological macromolecules. The author's approach is valid both for the long time-scale needed for DNA bond disruption, and also for highly co-operative transitions needed to explain helix melting. A new theoretical approach for executing macromolecule calculations is developed. In particular, the author devises a method for describing chemical bond disruption in these large systems, which are then used to determine when the helix melts and how drugs can dissociate from the helix. Melting temperatures are found to be in excellent agreement with experimental observations. The book will be of interest to biomolecular dynamics researchers, especially to graduate students in biological physics, theoretical chemistry and molecular biology.

The eighteenth and nineteenth centuries witnessed a change in the perception of the arts and of philosophy. In the arts this transition occurred around 1800, with, for instance, the breakdown of Vitruvianism in architecture, while in philosophy the foundationalism of which Descartes and Spinoza were paradigmatic representatives, which presumed that philosophy and the sciences possessed a method of ensuring the demonstration of truths, was undermined by the idea, asserted by Nietzsche and Wittgenstein, that there exist alternative styles of enquiry among which a choice is open. The essays in this book examine the circumstances, features, and consequences of this historical transition, exploring in particular new aspects and instances of the inter-relatedness of content and its formal representation in both the arts and philosophy.

Many students find quantum mechanics conceptually difficult when they first encounter the subject. In this book, the postulates and key applications of quantum mechanics are well illustrated by means of a carefully chosen set of problems, complete with detailed, step-by-step solutions. Beginning with a chapter on orders of magnitude, a variety of topics are then covered, including the mathematical foundations of quantum mechanics, Schrödinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, multielectron atoms, transitions and scattering. Throughout, the physical interpretation or application of certain results is highlighted, thereby providing useful insights into a wide range of systems and phenomena. This approach will make the book invaluable to anyone taking an undergraduate course in quantum mechanics.

Many students find quantum mechanics conceptually difficult when they first encounter the subject. In this book, the postulates and key applications of quantum mechanics are well illustrated by means of a carefully chosen set of problems, complete with detailed, step-by-step solutions. Beginning with a chapter on orders of magnitude, a variety of topics are then covered, including the mathematical foundations of quantum mechanics, Schrödinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, multielectron atoms, transitions and scattering. Throughout, the physical interpretation or application of certain results is highlighted, thereby providing useful insights into a wide range of systems and phenomena. This approach will make the book invaluable to anyone taking an undergraduate course in quantum mechanics.

Pseudodifferential operators arise naturally in the solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. A pseudodifferential operator may also be described by invariance under action of a Lie-group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution and the relation of the hyperbolic theory to the propagation of maximal ideals. This book will be of particular interest to researchers in partial differential equations and mathematical physics.

This book analyses the crucial features of unionised labour markets. The models in the book refer to labour contracts between unions and management, but the method of analysis is also applicable to non-union labour markets where workers have some market power. In this book, Alison Booth, a researcher in the field, emphasises the connection between theoretical and empirical approaches to studying unionised labour markets. She also highlights the importance of taking into account institutional differences between countries and sectors when constructing models of the unionised labour market. While the focus of the book is on the US and British unionised labour markets, the models and analytical methods are applicable to other industrialised countries with appropriate modifications.

This book analyses the crucial features of unionised labour markets. The models in the book refer to labour contracts between unions and management, but the method of analysis is also applicable to non-union labour markets where workers have some market power. In this book, Alison Booth, a researcher in the field, emphasises the connection between theoretical and empirical approaches to studying unionised labour markets. She also highlights the importance of taking into account institutional differences between countries and sectors when constructing models of the unionised labour market. While the focus of the book is on the US and British unionised labour markets, the models and analytical methods are applicable to other industrialised countries with appropriate modifications.

Social network analysis is used widely in the social and behavioral sciences, as well as in economics, marketing, and industrial engineering. The social network perspective focuses on relationships among social entities and is an important addition to standard social and behavioral research, which is primarily concerned with attributes of the social units. Social Network Analysis: Methods and Applications reviews and discusses methods for the analysis of social networks with a focus on applications of these methods to many substantive examples. It is a reference book that can be used by those who want a comprehensive review of network methods, or by researchers who have gathered network data and want to find the most appropriate method by which to analyze it. It is also intended for use as a textbook as it is the first book to provide comprehensive coverage of the methodology and applications of the field.

Explicit Brauer Induction is an important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this 1994 book it is derived algebraically, following a method of R. Boltje - thereby making the technique, previously topological, accessible to algebraists. Once developed, the technique is used, by way of illustration, to re-prove some important known results in new ways and to settle some outstanding problems. As with Brauer's original result, the canonical formula can be expected to have numerous applications and this book is designed to introduce research algebraists to its possibilities. For example, the technique gives an improved construction of the Oliver–Taylor group-ring logarithm, which enables the author to study more effectively algebraic and number-theoretic questions connected with class-groups of rings.

This textbook by Martin Hollis offers an exceptionally clear and concise introduction to the philosophy of social science. It examines questions which give rise to fundamental philosophical issues. Are social structures better conceived of as systems of laws and forces, or as webs of meanings and practices? Is social action better viewed as rational behaviour, or as self-expression? By exploring such questions, the reader is led to reflect upon the nature of scientific method in social science. Is the aim to explain the social world after a manner worked out for the natural world, or to understand the social world from within?

The origins of angiosperms are still debated, despite many years of work by scientists from differing disciplines. The progress made toward resolving the problem is reviewed in this book. The author suggests that the only fruitful method of study is the total integrated use of the fossil record, particularly dispersed palynomorphs. This includes the use of electron microscopy and refined data handling to record the occurrence of microscopic fossils, rather than the extensive use of morphology and cladistics. The methods advocated in this book could result in a rethink of the current classification of living plants. The ideas presented will initiate discussion between both professionals and students of palaeontology and plant science on the wider possibilities that may clarify the enigmatic origins of the dominant flowering plant groups.

This book develops quantum field theory starting from its foundation in quantum mechanics. Quantum field theory is the basic theory of elementary particle physics. In recent years, many techniques have been developed which extend and clarify this theory. This book incorporates these modern methods, giving a thoroughly modern pedagogic account which starts from first principles. The path integral formulation is introduced right at the beginning. The method of dimensional continuation is employed to regulate and renormalize the theory. This facilitates the introduction of the concepts of the renormalization group at an early stage. The notion of spontaneous symmetry breakdown is also introduced early on by the example of superfluid helium. Topics in quantum electrodynamics are described which have an analog in quantum chromodynamics. Some novel techniques are employed, such as the use of dimensional continuation to compute the Lamb shift. Many problems are included.

This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

This work provides a lucid and rigorous account of the foundations of algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Here in this volume, the authors have again confined their attention to varieties defined on a ground field without characteristic. In order to familiarize the reader with the different techniques available to algebraic geometers, they have not confined themselves to one method and on occasion have deliberately used more advanced methods where elementary ones would serve, when by so doing it has been possible to illustrate the power of the more advanced techniques, such as valuation theory. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.

This book presents fifteen essays, written over the past dozen years, on egalitarianism. The essays explore contemporary philosophical debates on this subject, using the tools of modern economic theory, general equilibrium theory, game theory, and the theory of mechanism design. Egalitarian Perspectives is divided into four parts: the theory of exploitation; equality of resources; bargaining theory and distributive justice; and market socialism and public ownership. The first part presents Roemer's influential reconceptualisation of the Marxian theory of exploitation as a theory of distributive justice. The second part offers a critique of Ronald Dworkin's equality-of-resources theory, and puts forward a new egalitarian proposal based upon a specific method of measuring individual responsibility. The third part introduces a novel application of the theory of mechanism design to the study of political philosophy, and raises new concerns about the limitations of that application. The fou

This is the companion volume to Gregory Vlastos' highly acclaimed work Socrates: Ironist and Moral Philosopher. Four ground-breaking papers which laid the basis for his understanding of Socrates are collected here, in revised form: they examine Socrates' elenctic method of investigative argument, his disavowal of knowledge, his concern for definition, and the complications of his relationship with the Athenian democracy. The fifth chapter is a new and provocative discussion of Socrates' arguments in the Protagoras and Laches. The epilogue 'Socrates and Vietnam' suggests that Socrates was not, as Plato claimed, the most just man of his time. The papers have been prepared for publication by Professor Myles Burnyeat with the minimum of editorial intervention.

Atmospheric analysis is the method of transforming the enormous and scattered database of atmospheric observations into the powerful mathematical and physical tools required to meet the growing demand for atmospheric data. Atmospheric Data Analysis is intended to fill a void in the atmospheric science literature and curricula. The book is self contained, and includes topics important in several other fields outside atmospheric observation, including atmospheric dynamics and statistics. It outlines the physical and mathematical basis of all aspects of atmospheric analysis. The emphasis is on the theoretical foundation of the subject and most of the development is analytic, but many practical considerations and examples are introduced. There are numerous exercises at the end of each chapter to aid the student in comprehending the material.

As the analysis of social networks, or networks of interpersonal and social relationships among social groups, has become an increasingly important method of research in several of the social and behavioural sciences, the gathering of network data has outpaced the development of new methods for its analysis. Addressing the need for analytical tools, Philippa Pattison presents a number of algebraic models for the analysis of network data, explaining in the process the rationale for an algebraic approach. Models are developed for both complete networks, meaning those representing the social ties between all pairs of members in a given group, and local networks, meaning those structured around the social ties of one particular group member. Many applications are presented and the ways that these methods can address a number of important issues confronting network analysis are explained.

This series of A-level social biology topic books responds to the changing demands of social biology syllabuses, with each text dealing with a particular area of interest. Although the series is primarily intended for students of A-level social biology, the books will appeal to students studying a wide range of biological subjects at A-level. Environmental Concerns covers topics common to several A-level human and social biology syllabuses. It is particularly relevant to the human ecology and conservation options. The text focuses on the social and economic implications of current ecological issues as well as the basic biological concepts involved. It deals with the causes, effects and prevention of atmospheric and water pollution as well as with the disruption of ecosystems by changes in land use. The conflict of interests between conservation and exploitation is discussed, along with management techniques including the controversial method of culling to maintain diversity. The moral