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The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature.The following topics are particularly emphasised:• existence, uniqueness and continuation of solutions,• continuous dependence on initial data,• flows,• qualitative behaviour of solutions,• limit sets,• stability theory,• invariance principles,• introductory control theory,• feedback and stabilization.The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability.Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

Mathematics for Finance: An Introduction to Financial Engineering combines financial motivation with mathematical style. Assuming only basic knowledge of probability and calculus, it presents three major areas of mathematical finance, namely Option pricing based on the no-arbitrage principle in discrete and continuous time setting, Markowitz portfolio optimisation and Capital Asset Pricing Model, and basic stochastic interest rate models in discrete setting.

An Introduction to Computer Graphics for Artists is an application-independent, reader-friendly primer for anyone with a serious desire to understand 3D Computer Graphics. Written by a veteran of the computer graphics industry whose previous career included film animation and various spells as Art Director for video games, Andrew Paquette draws on his experiences both as an artist and a manager. Far too often artists, even professionals, lack a basic understanding of the principles of computer graphics. The result is inefficiency and lower quality of work. This book addresses these issues by providing fundamental information in a university course format, with theoretical material, detailed illustrations, and projects to test the reader’s understanding of the concepts covered.Opening with the first and most basic elements of computer graphics, the book rapidly advances into progressively more complex concepts. Each of the elements, however simple, are important to understand because each is an essential link in a chain that allows an artist to master any computer graphics application. With this accomplished, the artist can use technology to satisfy his goals, instead of the technology being master of the artist.All students wanting to learn more about computer graphics from an artistic viewpoint, particularly those intending to pursue a career in computer game design or film animation, will find this book invaluable.

Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real life and using real data, the authors show how the fundamentals of probabilistic and statistical theories arise intuitively. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to students. In addition there are over 350 exercises, half of which have answers, of which half have full solutions. A website gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to modern methods such as the bootstrap.

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

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 methodso Runge--Kutta methodso Linear multistep methodso Convergenceo Stabilityand a range of modern themes:o Adaptive stepsize selectiono Long term dynamicso Modified equationso Geometric integrationo Stochastic differential equationsThe 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

In Europe's Space Programme - to Ariane and Beyond, author Brian Harvey begins with the fledgling European rocket effort of the 1930s and the key pioneers of the period, examining the significance of the V-2 and the technological advances represented by its development. He shows how the Russians and Americans put their captured V-2s to work, but the European countries were slower to respond. Both Britain and France developed national space programmes in the 1950s and 1960s and the early attempts at European co-operation for launcher development - ELDO and ESRO - are described. The formation of the European Space Agency and the origins of the successful Ariane launcher programme are discussed and Europe's subsequent success in the world launcher market, its cutting-edge role in space applications and European manned spaceflight, are all described in detail.

"Risks in Technological Systems" is an interdisciplinary university textbook and a book for the educated reader on the risks of today’s society. In order to understand and analyze risks associated with the engineering systems on which modern society relies, other concerns have to be addressed, besides technical aspects. In contrast to many academic textbooks dealing with technological risks, this book has a unique interdisciplinary character that presents technological risks in their own context.Twenty-four scientists have come together to present their views on risks in technological systems. Their scientific disciplines cover not only engineering, economics and medicine, but also history, psychology, literature and philosophy. Taken together these contributions provide a broad, but accurate, interdisciplinary introduction to a field of increasing global interest, as well as rich opportunities to achieve in-depth knowledge of the subject.

"Risks in Technological Systems" is an interdisciplinary university textbook and a book for the educated reader on the risks of today’s society. In order to understand and analyze risks associated with the engineering systems on which modern society relies, other concerns have to be addressed, besides technical aspects. In contrast to many academic textbooks dealing with technological risks, this book has a unique interdisciplinary character that presents technological risks in their own context.Twenty-four scientists have come together to present their views on risks in technological systems. Their scientific disciplines cover not only engineering, economics and medicine, but also history, psychology, literature and philosophy. Taken together these contributions provide a broad, but accurate, interdisciplinary introduction to a field of increasing global interest, as well as rich opportunities to achieve in-depth knowledge of the subject.

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150 of them have complete solutions, to facilitate self-study.Mathematical Writing will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations.

Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances.In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors.

This book nds its origin in the WIDE PhD School on Networked Control Systems, which we organized in July 2009 in Siena, Italy. Having gathered experts on all the aspects of networked control systems, it was a small step to go from the summer school to the book, certainly given the enthusiasm of the lecturers at the school. We felt that a book collecting overviewson the important developmentsand open pr- lems in the eld of networked control systems could stimulate and support future research in this appealing area. Given the tremendouscurrentinterests in distributed control exploiting wired and wireless communication networks, the time seemed to be right for the book that lies now in front of you. The goal of the book is to set out the core techniques and tools that are ava- able for the modeling, analysis and design of networked control systems. Roughly speaking, the book consists of three parts. The rst part presents architectures for distributed control systems and models of wired and wireless communication n- works. In particular, in the rst chapter important technological and architectural aspects on distributed control systems are discussed. The second chapter provides insight in the behavior of communication channels in terms of delays, packet loss and information constraints leading to suitable modeling paradigms for commu- cation networks.

Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology. A background in calculus and differential equations is assumed, although the main results required are collected in the appendices. A dedicated website at www.springer.co.uk/britton/ accompanies the book and provides furtherexercises, more detailed solutions to exercises in the book, and links to other useful sites.

A close analysis of the framework of existing governance and the existing jurisdictional arrangements for shipping and ports reveals that while policy-making is characterized by national considerations through flags, institutional representation at all jurisdictions and the inviolability of the state, the commercial, financial, legal and operational environment of the sector is almost wholly global. This governance mismatch means that in practice the maritime industry can avoid policies which it dislikes by trading nations off against one another, while enjoying the freedoms and benefits of a globalized economy. A Post-modern interpretation of this globalized society prompts suggestions for change in maritime policy-making so that the governance of the sector better matches more closely the environment in which shipping and ports operate. Maritime Governance and Policy-Making is a controversial commentary on the record of policy-making in the maritime sector and assesses whether the reason for continued policy failure rests with the inadequate governance of the sector. Maritime Governance and Policy-Making  addresses fundamental questions of governance, jurisdiction and policy and applies them to the maritime sector. This makes it of much more interest to a much wider audience – including students, researchers, government officials, and those with industrial and commercial interests in the shipping and ports areas - and also of more value as it places the specific maritime issues into their wider context.Maritime Governance and Policy-Making  addresses fundamental questions of governance, jurisdiction and policy and applies them to the maritime sector. This makes it of much more interest to a much wider audience – including students, researchers, government officials, and those with industrialand commercial interests in the shipping and ports areas - and also of more value as it places the specific maritime issues into their wider context.

“Designing Inclusive Futures” reflects the need to explore, in a coherent way, the issues and practicalities that lie behind design that is intended to extend our active future lives. This encompasses design for inclusion in daily life at home but also extends to the workplace and for products within these contexts. For example, given trends in employment sector growth, skills requirements, labour supply and demographic change, there is a need to predict the critical areas where individual capabilities are mismatched with the physical, social and organisational demands of work. This mismatch, which can be addressed within the domain of inclusive design, is pervasively linked to real artefacts in workspaces and their intersection with the health factors that relate to ageing. This book is the result of the fourth CWUAAT workshop held in Cambridge, England in April 2008.

Models of dynamical systems are of great importance in almost all fields of science and engineering and specifically in control, signal processing and information science. A model is always only an approximation of a real phenomenon so that having an approximation theory which allows for the analysis of model quality is a substantial concern. The use of rational orthogonal basis functions to represent dynamical systems and stochastic signals can provide such a theory and underpin advanced analysis and efficient modelling. It also has the potential to extend beyond these areas to deal with many problems in circuit theory, telecommunications, systems, control theory and signal processing.Modelling and Identification with Rational Orthogonal Basis Functions affords a self-contained description of the development of the field over the last 15 years, furnishing researchers and practising engineers working with dynamical systems and stochastic processes with a standard reference work.

This book presents the human hand from an overall perspective – from the first appearance of hand-like structures in the fins of big fishes living millions of years ago to today´s and the future’s mind-controlled artificial hands. Much focus is given to the extremely well-developed sensation of the hand, its importance and its linkage to brain plasticity mechanisms. How can active hands rapidly expand their representational area in the brain? How can the sense of touch substitute for other deficient senses, such as in Braille reading where hand sensation substitutes for missing vision? How can the mere observation of active hands, belonging to others, activate the hand area in the observer’s own brain and what is the importance of this phenomenon for learning by imitation and the understanding of other peoples’ actions, gestures and body language? Why are some of us left-handed and what are the consequences from cultural and physiological viewpoints? Why does phantom sensation and phantom pain occur after hand amputation, and what can we do about it? Why can salamanders regenerate new extremities while humans can not? Is it possible to transplant a hand from a diseased individual to an amputee? Can artificial robotic hands be controlled by our mind, and can they ever gain the role of a normal hand? What role did the hand and the brain play during evolution in tool construction and development of language and cognitive functions? The hand has a high symbolic value in religion, literature and art and our hands have a key role in gestures and body language.   The Hand and the Brain is aimed at anybody with interest in life sciences, in the medical field especially hand surgeons, orthopaedic specialists, neurologists and general practitioners, and those working in rehabilitation medicine and pain treatment. The original Swedish version of The Hand and the Brain has also become very popular among physiotherapists, occupational therapists, psychologists, and among a general population with an interest in science.

This book brings together current knowledge concerning all aspects of the treatment of osteoporosis and osteoporotic fractures in one volume.It covers both surgical and pharmacological treatment options: General Aspects on Osteoporosis and Fracture, Fracture Healing, Orthopedic Management Options, Non-Pharmacological Prevention of Osteoporotic Fractures, and Identification and Management of Secondary or Localized Bone Loss. Individual chapters cover diagnosis and prevention, as well as discussing the treatment of individuals who have already sustained various osteoporotic fractures.The book will be of great interest to all individuals involved with osteoporosis prevention and management programs, including orthopedic and trauma surgeons, rehabilitation professionals, physio- and occupational therapists, and trainees within these fields.

Computer science abounds with applications of discrete mathematics, yet s- dents of computer science often study discrete mathematics in the context of purely mathematical applications. They have to ?gure out for themselves how to apply the ideas of discrete mathematics to computing problems. It is not easy. Most students fail to experience broad success in this enterprise, which is not surprising, since many of the most important advances in science and engineeringhavebeen, precisely, applicationsofmathematicstospeci?cscience and engineering problems. Tobesure,mostdiscretemathtextbooksincorporatesomeaspectsapplying discrete math to computing, but it usually takes the form of asking students to write programs to compute the number of three-ball combinations there are in a set of ten balls or, at best, to implement a graph algorithm. Few texts ask students to use mathematical logic to analyze properties of digital circuits or computer programs or to apply the set theoretic model of functions to understand higher-order operations. A major aim of this text is to integrate, tightly, the study of discrete mathematics with the study of central problems of computer science.

Models of dynamical systems are of great importance in almost all fields of science and engineering and specifically in control, signal processing and information science. A model is always only an approximation of a real phenomenon so that having an approximation theory which allows for the analysis of model quality is a substantial concern. The use of rational orthogonal basis functions to represent dynamical systems and stochastic signals can provide such a theory and underpin advanced analysis and efficient modelling. It also has the potential to extend beyond these areas to deal with many problems in circuit theory, telecommunications, systems, control theory and signal processing.Modelling and Identification with Rational Orthogonal Basis Functions affords a self-contained description of the development of the field over the last 15 years, furnishing researchers and practising engineers working with dynamical systems and stochastic processes with a standard reference work.

The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise.Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This textbook contains many worked examples and several chapters have been updated and expanded for the second edition. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Modelsis designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.

Networked and Distributed Predictive Control presents rigorous, yet practical, methods for the design of networked and distributed predictive control systems – the first book to do so. The design of model predictive control systems using Lyapunov-based techniques accounting for the influence of asynchronous and delayed measurements is followed by a treatment of networked control architecture development. This shows how networked control can augment dedicated control systems in a natural way and takes advantage of additional, potentially asynchronous and delayed measurements to maintain closed loop stability and significantly to improve closed-loop performance. The text then shifts focus to the design of distributed predictive control systems that cooperate efficiently in computing optimal manipulated input trajectories that achieve desired stability, performance and robustness specifications but spend a fraction of the time required by centralized control systems. Key features of this book include: • new techniques for networked and distributed control system design; • insight into issues associated with networked and distributed predictive control and their solution; • detailed appraisal of industrial relevance using computer simulation of nonlinear chemical process networks and wind- and solar-energy-generation systems; and • integrated exposition of novel research topics and rich resource of references to significant recent work. A full understanding of Networked and Distributed Predictive Control requires a basic knowledge of differential equations, linear and nonlinear control theory and optimization methods and the book is intended for academic researchers and graduate students studying control and for process control engineers. The constant attention to practical matters associated with implementation of the theory discussed will help each of these groups understand the application of the book’s methods in greater depth.

This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can  be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty.Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.

Production development is about improving existing production systems and developing new ones. The production system should be developed in integration with the product, as a part of the overall product realization process, and not in sequence after the product has already been designed. Production Development: Design and Operation of Production Systems takes a holistic viewpoint on the production system and its design process during the whole system life cycle. A working procedure demonstrating how to design and realize the production system is presented, together with a number of related production development aspects.Production Development: Design and Operation of Production Systems is illustrated with a large number of figures and industrial examples. The book can be used as a reference for teachers and students, or as a manual for professionals within the field of production.

Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential.Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions.The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments.Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh’s Probability Models, and T. S. Blyth & E.F. Robertsons’ Basic Linear Algebra and Further Linear Algebra.

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. The book provides a thorough exposition of all the standard necessary results of the theory and, in addition, includes selected topics not normally found in introductory books, such as: the Tietze Extension Theorem; the Hausdorff metric and its completeness; and the existence of curves of minimum length.With its many examples, careful illustrations, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications.

Laser technology is constantly evolving and progressing. The use of laser therapy is vastly expanding and for this reason a medical book of this magnitude is necessary. Lasers and Light Therapy includes an up-to-date comprehensive look at lasers and light therapy not only in the field of Cutaneous Laser Surgery, but in other medical specialties as well.

This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.

The development of the di?erential calculus was one of the major achievements of seventeenth century European mathematics, originating in the work of N- ton, Leibniz and others. Integral calculus can be traced back to the work of Archimedes in the third century B. C. Since its inception, calculus has dev- oped in two main directions. One is the growth of applications and associated techniques,indiverse?eldssuchasphysics,engineering,economics,probability and biology. The other direction is that of analytical foundations, where the intuitive and largely geometrical approach is replaced by an emphasis on logic and the development of an axiomatic basis for the real number system whose properties underpin many of the results of calculus. This approach occupied many mathematicians through the eighteenth and nineteenth centuries, c- minating in the work of Dedekind and Cantor, leading into twentieth century developments in Analysis and Topology. We can learn much about calculus by studying its history, and a good starting point is the St Andrews’ History of Mathematics website www-history. mcs. st-and. ac. uk/history/ Thisbookisdesignedforbeginninguniversitystudents,boththosestudying mathematics as a major subject, and those whose main specialism requires the use and understanding of calculus. In the latter case we would expect that lecturers would customise the treatment with applications from the relevant subject area. Thepre-universityschoolmathematicscurriculaofmostEuropeancountries all include some calculus, and this book is intended to provide, among other things, a transition between school and university calculus. In some countries suchastheU. K.