Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.
The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important-a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions.
* Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing.
* Covers both non-mathematical and mathematical approaches to quaternions.
* Companion website with an assortment of quaternion utilities and sample code, data sets for the book's illustrations, and Mathematica notebooks with essential algebraic utilities.

As one of the most massive and successful business sectors, the pharmaceutical industry is a potent force for good in the community, yet its behaviour is frequently questioned: could it serve society at large better than it has done in the recent past? Its own internal ethics, both in business and science, may need a careful reappraisal, as may the extent to which the law - administrative, civil and criminal - succeeds in guiding (and where neccessary contraining) it.
The rules of behavior that may be considered to apply to today's pharmaceutical industry have emerged over a very long period and the process goes on. Even the immensely detailed standards for quality, safety and efficacy laid down in drug law and regulation during the second half of the twentieth century have their limitations as tools for ensuring that the public interest is well served. In particular, national and regional regulatory agencies are heavily dependent on industrial data for their decision-making, their standards and competence vary, and even the existing network of agencies does not cover the entire world. What is more there are many areas of law and regulation affecting the industry, concerning for example the pricing of medicines, the conduct of clinical studies, the health protection of workers and concern for the environment. In some fields it is indeed hardly possible to maintain standards through regulation.
Professor N.M. Graham Dukes, a physician and lawyer with long term experience in industrial research management, academic study and international drug policy, provides here a powerfully documented analysis into the way this industry thinks, acts, and is viewed, and examines the current trends pointing to change.
*Provides a balanced picture of the current role of the pharmaceutical industry in society
*Includes indices of conventions, laws, and regulations; as well as judicial and disciplinary cases
*This is the only book addressing the legal implications of big pharma activities and ethical standards

This volume illustrates the extent to which the traditional distinction between biochemical and physiological processes is being obliterated by molecular biology. It can hardly be doubted that the revolution in cell and molecular biology is leading to core knowledge that provides an outline of the integrative and reductionist approach. We view this as the beginning of a new era, that of the integration of learning.
As in the preceding volumes, the choice of topics has been deliberate not only because of the need to keep the volume within reasonable bounds but also because of the need to avoid information over-load. Several relevant topics are dealt with in other modules; for example, the role of G proteins in transmembrane signalling is covered in the Membranes and Cell Signalling module (i.e., Volume 7). Omissions are of course inevitable but they are minor. A case in point is the subject of phosphatases, the treatment of which does not take into account calcineurin. One of the key functions of this Ca2+ -activated protein phosphatase that is also regulated by calmodulin is to desphosphorylate voltage-dependent Ca2+ channels. The mere recognition of such omissions before or after consulting textbooks and journals should be a spur to a more complete discussion by the student of the subject in a small group teaching setting.

" Genetic Aberrancies and Neurodegenerative Disorders" presents critical reviews and emerging findings concerning the roles of genetic mutations and polymorphisms in the pathogenesis of a range of neurological disorders including Alzheimer's and Parkinson's diseases, trinucleotide repeat disorders, stroke, epilepsy and others. This volume, written by leading experts, brings together fundamental information concerning the roles of inherited traits in the pathogenesis of different neurodegenerative disorders. In addition to providing a catalogue of the known genetic alterations that are linked to specific neurodegenerative disorders, the chapters detail the current state of understanding of the cellular and biochemical mechanisms whereby the genetic aberrancies lead to neuronal dysfunction and degeneration. The emerging picture of each disorder, painted by pathological, biochemical and molecular brushes, suggests that they share key mechanisms including increased levels of oxidative stress, perturbed ion homeostasis, mitochondrial dysfunction and apoptotic proteolytic cascades. The existence of specific molecular defects provides the opportunity to design experiments that can establish the precise pathogenic mechanism of a specific mutation or genetic risk factor. The value of this approach is exemplified by recent studies of how mutations in Cu/Zn-superoxide dismutase cause amyotrophic lateral sclerosis and how presenilin mutations result in early-onset Alzheimer's disease. A theme developed among the different chapters is that events that occur during aging predispose neurons to genetic aberrancies that promote degenerative cascades, and that specific genetic defects exert their influence on particular populations of neurons in a disorder-specific manner. The chapters in this volume will stimulate readers to generate new hypotheses concerning the pathogenic mechanisms of genetic aberrancies that can be experimentally tested.

The book on Heavy-Fermion Systems is a part of the Book series "Handbook of Metal Physics," each volume of which is written to facilitate the research of Ph.D. students, faculty and other researchers in a specific area. The Heavy-Fermions (sometimes known as Heavy-Electrons) is a loosely defined collection of intermetallic compounds containing rare-earth (mostly Ce) or actinide (mostly U) elements. These unusual names were given due to the large effective mass (100-1,000 times greater than the mass of a free electron) below a critical temperature. They have a variety of ground states including superconducting, antiferromagnetic, paramagnetic or semiconducting. Some display unusual magnetic properties such as magnetic quantum critical point and metamagnetism. This book is essentially a summary as well as a critical review of the theoretical and experimental work done on Heavy Fermions.
- Extensive research references.
- Comprehensive review of a very rapidly growing number of theories.
- Summary of all important experiments.
- Comparison with other highly correlated systems such as High-Tc Superconductors.
- Possible Technological applications.

Lipobiology is a rapidly evolving interdisciplinary field which incorporates critical aspects of lipid and lipoprotein chemistry into the disciplines of cell biology and physiology. This series focuses on salient aspects of the role of lipids in metabolic regulation and cellular activation.

The air distribution in occupied spaces is a major issue of public concern. It is widely recognized that the quality of air and the nature of airflow can affect the health of occupants and the energy consumed in buildings and transport vehicles. ROOMVENT is the principal international conference in the field of air distribution. It was first initiated in 1987 by SCANVAC, the Scandinavian Federation of Heating, Ventilating and Sanitary Engineering Associations in Denmark, Finland, Iceland, Norway and Sweden.
The aim of the Conference is to bring together researchers from universities and research institutes, engineers from industry and government officials and policy makers, with the goal of experiencing the latest techniques for measuring and analyzing indoor air flow, the visualization of indoor air flow patterns, the evaluation of ventilation parameters and the most recent developments in computer simulation techniques of room airflow. It is hoped that the theme of ROOMVENT 2000 ""Ventilation for Health and Sustainable Environment"" will set the scene for room air distribution research and development for the new millennium.

This is the first of a 4-volume module that is an introduction to the study of cell chemistry and physiology. It is not intended to be encyclopedic in nature but rather a general survey of the subject with an emphasis on those topics that are central to an understanding of cell biology and those that are certain to become of increasing importance in the teaching of modern medicine.
We have followed what appeared to as to be the logical divisions of the subject beginning with proteins. Allewell and her colleagues stress the point that proteins fold spontaneously to form complex three-dimensional structures and that some of them unfold with the help of proteins called chaperones. Michaelis-Menten kinetics are shown by Nelsestuen to describe the behaviour of enzymes in the test tube. The formalism is particularly useful in the search for agents of therapeutic value, as exemplified by methotrexate. Uptake by mammalian cells of substrates and their metabolic conversions are discussed by van der Vusse and Reneman. However, both Welch and Savageau expound the view that the cell is not simply a bagful of enzymes. The biologist is urged by Savageau to abandon Michaelis-Menten formalism and apply the Power Law. The biologist is also told that the approach to arriving at a theory of metabolic control would have to be one of successive approximations requiring the use of the computer. Information gained from comparative biochemistry is shown by Storey and Brooks to have shed new light on mechanisms of metabolic rate depression and freeze tolerance, and to be applicable to organ transplantation technology. We are reminded that enzyme adaptation is partly the result of the presence of a hydrating shell of vicinal water that stabilises conformation of the enzyme. Vicinal water, according to Drost-Hausen and Singleton, lies adjacent to most solids and protein interfaces. The kinks or breaks observed in the slope of the Arrhenius plot are attributed to structural changes in vicinal water. Regulation of cell volume is shown by Hempling to involve regulation of cell water. It could be that the osmo-receptor or volume detection system is a protein that links the cytoskeleton to specific K and C1 channels. Additionally, it is interesting that aquaporins, which are water channel-forming membrane proteins, are now known to exist in both renal and extra-renal tissues. One of the renal porins is affected by vasopressin.
We then pass on to protein synthesis (Rattan) and other important topics including protein glycosylation (Hounsell), methylation (Clarke), ADP-ribosylation (Pearson) and prenylation (Gelb). Among the four types of lipids attached to membrane proteins are the prenyl groups. Ford and Gross in their chapter on lipobiology drive home the point that there is an accumulation of acyl carnitine and lysophospholipids during myocardial infarction.

Turmeric has been used as a medicine, a condiment, and a dye since at least 600 B.C., while ginger has been used extensively throughout history for its medicinal purposes. "The Agronomy and Economy of Turmeric and Ginger" brings these two important plants together in one reference book, explaining their history, production techniques, and nutritional and medicinal properties in detail.

This book is intuitively organized by plant and use, allowing quick access to information. It puts the uniquely Indian use and history of turmeric and ginger plants into a global context of production and economic aspects. It explores the plants from a botanical perspective, and goes into details of their chemical composition as well. Rounding out the book are chapters on disease and pest control issues.

The book is a valuable resource for those involved in the production and marketing of these plants, as well as those looking for more information on the medicinal and nutritional properties of turmeric and ginger.
The first book to bring together extensive information about turmeric and gingerIncorporates medicinal, nutritional and agricultural aspects of the two plantsOffers a global perspective

The new edition of "Mathematical Modeling," the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries.

From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor. With mathematical modeling growing rapidly in so many scientific and technical disciplines, "Mathematical Modeling, Fourth Edition" provides a rigorous treatment of the subject. The book explores a range of approaches including optimization models, dynamic models and probability models.
Offers increased support for instructors, including MATLAB material as well as other on-line resourcesFeatures new sections on time series analysis and diffusion modelsProvides additional problems with international focus such as whale and dolphin populations, plus updated optimization problems

This monograph is practically oriented, presenting a survey and explanation of credit insurance services for protection of short-term trade receivables primarily against commercial risk of insolvency and protracted default. The subject matter (i.e., main functions, features and principles of credit insurance with detailed description of credit insurance coverage, insurance conditions, and credit insurance policy management) follows procedural stages and presents commercial, financial, legal, and practical points of view which emphasize the needs of both the providers of these services andtheir clients - existing and potential credit insured companies - as well asother practitioners.
Explains how credit insurance has changed from an esoteric type of property insurance into a flexible and frequently used credit risk mitigation tool used on a global basisCompares credit insurance with self-insurance and equivalent substitutesDescribes the types of insurance available and how to obtain and manage credit insurance policies"

Acronycine, a potent antitumor agent, was discovered in the bark of the small Australian Rutaceous tree, Acronychia baueri Schott. This new work presents a comprehensive survey of the isolation, structure determination, methods of synthesis, and the biological properties of acronycine, as well as an account of natural and synthetic analogues of acronycine, and their biological properties.
Solanum alkaloids were reviewed in 1990 and this book surveys the new developments (isolation procedures, structural elucidation methods) and critically updates earlier reviews.
In addition it presents the interesting chemistry and synthesis of cyclopeptide alkaloids. These cyclopeptide alkaloids have been isolated from ascidians, sea hares, and cyanobacteria.
Also included are reviews of the use of the functionalized lactam, pyroglutamic acid, as a chiral template for the synthesis of alkaloids.
The second review examines the on-line coupling of capillary electrophoresis (CE) and mass spectrometry (MS) for the analysis of alkaloid mixtures.
Finally a review of oxygenated analogs of the alkaloid Marcfortine for their potent antiparasitic activity is included at the end of this work.
Each chapter in this volume has been reviewed by at least one expert in the field. Indexes for both subjects and organisms are provided.

Collaboratively written by top international experts and established scientists in various fields of agricultural research, this book focuses on the state of food production and sustainability; the problems with degradation of valuable sources of land, water, and air and their effects on food crops;the increasing demand of food resources; and the challenges of food security worldwide. The book provides cutting edge scientific tools and methods of research as well as solid background information that is accessible for those who have a strong interest in agricultural research and development and want to learn more on the challenges facing the global agricultural production systems.
Provides cutting edge scientific tools and available technologies for researchAddresses the effects of climate change and the population explosion on food supply and offers solutions to combat themWritten by a range of experts covering a broad range of agriculture-related disciplines"

In the 11 articles in this first of two parts, top scholars summarize and analyze recent scholarship incorporate finance. Covering subjects from corporate taxes to behavioral corporate finance and econometric issues, their articlesreveal how specializations resonate with each other and indicate likely directions for future research. By includingboth established and emerging topics, Volume 2 will have the same long shelf life and high citations that characterize Volume 1 (2003).
Presents coherent summaries of major finance fields, marking important advances and revisionsDescribes the best corporate finance research created about the 2008 financial crisesExposes readers to a wide range of subjects described and analyzed by the best scholars"

"Heterogeneous Computing with OpenCL "teaches OpenCL and parallel programming for complex systems that may include a variety of device architectures: multi-core CPUs, GPUs, and fully-integrated Accelerated Processing Units (APUs) such as AMD Fusion technology. Designed to work on multiple platforms and with wide industry support, OpenCL will help you more effectively program for a heterogeneous future.

Written by leaders in the parallel computing and OpenCL communities, this book will give you hands-on OpenCL experience to address a range of fundamental parallel algorithms. The authors explore memory spaces, optimization techniques, graphics interoperability, extensions, and debugging and profiling. Intended to support a parallel programming course, "Heterogeneous Computing with OpenCL" includes detailed examples throughout, plus additional online exercises and other supporting materials.
Explains principles and strategies to learn parallel programming with OpenCL, from understanding the four abstraction models to thoroughly testing and debugging complete applications.Covers image processing, web plugins, particle simulations, video editing, performance optimization, and more.Shows how OpenCL maps to an example target architecture and explains some of the tradeoffs associated with mapping to various architecturesAddresses a range of fundamental programming techniques, with multiple examples and case studies that demonstrate OpenCL extensions for a variety of hardware platforms

Quartz, zeolites, gemstones, perovskite type oxides, ferrite, carbon allotropes, complex coordinated compounds and many more -- all products now being produced using hydrothermal technology. Handbook of Hydrothermal Technology brings together the latest techniques in this rapidly advancing field in one exceptionally useful, long-needed volume. The handbook provides a single source for understanding how aqueous solvents or mineralizers work under temperature and pressure to dissolve and recrystallize normally insoluble materials, and decompose or recycle any waste material. The result, as the authors show in the book, is technologically the most efficient method in crystal growth, materials processing, and waste treatment. The book gives scientists and technologists an overview of the entire subject including: A Evolution of the technology from geology to widespread industrial use. A Descriptions of equipment used in the process and how it works. A Problems involved with the growth of crystals, processing of technological materials, environmental and safety issues. A Analysis of the direction of today's technology.

In addition, readers get a close look at the hydrothermal synthesis of zeolites, fluorides, sulfides, tungstates, and molybdates, as well as native elements and simple oxides. Delving into the commercial production of various types, the authors clarify the effects of temperature, pressure, solvents, and various other chemical components on the hydrothermal processes.
Gives an overview of the evolution of HydrothermalTechnology from geology to widespread industrial useDescribes the equipment used in the process and how it worksDiscusses problems involved with the growth of crystals, processing of technological materials, and environmental and safety issues "

This book explains how UHF tags and readers communicate wirelessly. It gives an understanding of what limits the read range of a tag, how to increase it (and why that might result in breaking the law), and the practical things that need to be addressed when designing and implementing RFID technology. Avoiding heavy math but giving breadth of coverage with the right amount of detail, it is an ideal introduction to radio communications for engineers who need insight into how tags and readers work.

New to this edition:

Examples of near-metal antenna techniques

Discussion of the wakeup challenge for battery-assisted tags, with a BAT architecture example

Latest development of protocols: EPC Gen 1.2.0

Update 18000-6 discussion with battery-assisted tags, sensor tags, Manchester tags and wakeup provisions
Named a 2012 Notable Computer Book for Computer Systems Organization by Computing ReviewsThe only book to give an understanding of radio communications, the underlying technology for radio frequency identification (RFID)Praised for its readability and clarity, it balances breadth and depth of coverage New edition includes latest developments in chip technology, antennas and protocols"

Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology.

Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

While most books on dentistry describe the clinical and medical procedures involved, this book expands the field to examine the role of dentistry and teeth in everything from biology to biography. This book offers facts and figures regarding famous historical figures, such as John Hunter, Dr Crippen, Doc Holliday, and Paul Revere, exploring how their connections to dentistry shaped them, as well as the story of the two young dentists who discovered the principles of general anaesthesia. Other chapters focus on the amazing ranges of teeth in animals, from the teeth in piranhas to the tusks and ivory of elephants and narwhals, looking at their biological and cultural significance. The importance of teeth in understanding the evolution of humans and in revolutionizing the study of archaeology is also evaluated. This book is appropriate for dentists, medical and dentistry students, and non-specialists to introduce the myriad interesting aspects relating to teeth.

Please note that print volumes do not include full colour.
Includes well-illustrated and thoroughly explained examples and anecdotesPresents both popular and little-known instances of teeth s importance in historyWritten in an engaging tone appropriate for academics and the wider public"

A former member of the American Stock Exchange introduces trading and financial markets to upper-division undergraduates and graduate students who are planning to work in the finance industry. Unlike standard investment texts that cover trading as one of many subjects, "Financial Trading and Investing"gives primary attention to trading, trading institutions, markets, and the institutions that facilitate and regulate trading activities what economists call "market microstructure." Thetext will be accompanied by a website that can be used in conjunction with "TraderEx," "Markit," "StocklinkU," "Virtual Trade," "Vecon Lab Experiment," "Tradingsim," "IB Student Trading Lab," "Brenexa," "Stock Trak "and "How the Market Works."
Introduces the financial markets and the quantitative tools used in them so students learn how the markets operate and gain experience with their principal toolsHelps students develop their skills with the most popular trading simulation programs so they can reuse the book to solve day-to-day problems Stretches from investor behavior to hedging strategies and noise trading, capturing recent advances in an up-to-date reference source"

Learning about Learning Disabilities, 4e continues to provide equal attention to the intellectual, conceptual, and practical aspects of learning disabilities. The Fourth Edition of this popular title presents 80% new material, keeping the chapters up to date in this fast-moving field. With new contributors, and 11 new chapters, coverage is both comprehensive and thorough, encompassing the classification and identification of learning disabilities, learning disabilities in reading, writing, math, and social studies, interventions, and the issues germane to different age ranges of the learning disabled: children, adolescents, and adults. Readers will find Learning About Learning Disabilities, Fourth Edition suitable for use as a reference source for researchers or as a graduate level text.

Reviews of previous editions:

"This text provides a balanced focus on both the conceptual and practical aspects of learning disabilities. Its research coverage is more comprehensive and of greater depth than any other LD textbook, and it is distinctive in its treatment of such important areas as consultation skills and service delivery." -CHILD ASSESSMENT NEWS .".. provides a broad overview of some important issues in relation to the education and development of pupils with learning disabilities... Wong has succeeded in providing detailed descriptions and comments within a book which covers a broad range of topics. Without exception the chapters are clearly written and accessible, and many provide the reader with challenging ideas and practical suggestions." -BRITISH JOURNAL OF SPECIAL EDUCATION
Learning Disabilities occur in 20% of the population. Three million children in the US have a learning disability and receive special education in school.

30% of children with learning disabilities drop out of high school, and 48% of those with learning disabilities are out of the workforce or unemployed.

Discusses different types of learning disabilities including problems with attention, memory, language, math, reading, and writing

Encompasses the impact of LD on learning as well as social competence and self-regulation

Provides research summaries on most effective ways to teach children with LD

Encompasses a lifespan perspective on LD, discussing the impact on children, adolescents, and adults

Obesity is a continuing issue around the world and in many contexts. The growing number of obese people is an increasing concern for those in the medical profession, and obesity can pose specific challenges in relation to fertility and pregnancy. Patients who are obese require specific considerations and knowledge. Bringing together experts from a variety of specialties to examine the issues and challenges of obesity, this book discusses how obesity affects fertility, reproduction, and pregnancy. Beginning with an exploration of the epidemiology of obesity, further chapters focus on specific issues related to obesity and both male and female reproduction, the complications of obesity during pregnancy and labour, and the long term effects of obesity. This is the most comprehensive resource to examine the topic of obesity and reproductive issues, making it invaluable for medical students, professionals, and researchers in public policy and medicine.
Comprehensive examination of fertility issues arising from male and female obesityClinical knowledge and expertise given to the subjectsIn-depth examination through 47 chapters of a growing, but often overlooked, issue in fertility and pregnancy

Health is maintained by the coordinated operation of all the biological systems that make up the individual. "The Introduction to Psychoneuroimmunology, 2e, "presents an overview of what has been discovered by scientists regarding how bodily systems respond to environmental challenges and intercommunicate to sustain health. The book touches on the main findings from the current literature without being overly technical and complex. The result is a comprehensive overview of psychoneuroimmunology, which avoids oversimplification, but does not overwhelm the reader.

Single authored for consistency of breadth and depth, with no redundancy of coverage between chapters

Covers endocrine-immune modulation, neuro-immune modulation, and the enhancing or inhibiting processes of one or more systems on the others

Expanded use of figures, tables, and text boxes

Online test bank for professors

Newly updated with over 150 pages of material on the latest Tcl extensions, "Tcl/Tk: A Developer s Gu"ide is a unique practical tutorial for professional programmers and beginners alike. Starting with a clear picture of the basics, Tcl/Tk covers the variety of tools in this "Swiss army knife" of programming languages, giving you the ability to enhance your programs, extend your application's capabilities, and become a more effective programmer.

This updated edition covers all of the new features of version 8.6, including object-oriented programming and the creation of megawidgets, existing data structure implementations, themed widgets and virtual events. Extensive code snippets and online tutorials in various languages will give you a firm grasp on how to use the Tcl/Tk libraries and interpreters and, most importantly, on what constitutes an effective strategy for using Tcl/Tk.
Includes the latest features of Tcl/Tk 8.6Covers Tcl development tools, popular extensions, and packages to allow developers to solve real-world problems with Tcl/Tk immediatelyProvides straightforward explanations for beginners and offers tips, style guidelines, and debugging techniques for advanced usersCompanion website includes Tcl/Tk tutorials, applications, distributions, and more tools"

Hirsch, Devaney, and Smale s classic "Differential Equations, Dynamical Systems, and an Introduction to Chaos" has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.
Classic text bythree of the world s most prominent mathematicians Continues the tradition of expository excellenceContains updated material and expanded applications for use in applied studies"