The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    The author has sought to utlilize the technology now available for the teaching and learning of calculus. The hand-held graphics calculator is one such form of technology that has been integrated into the book. Topics in algebra, trigonometry, and analytical geometry appear in the Appendix.

    Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include:Stronger focus on MCMC Revision of the computational advice in Part III New chapters on nonlinear models and decision analysis Several additional applied examples from the authors' recent research Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more Reorganization of chapters 6 and 7 on model checking and data collectionBayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.

    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

    The text is written for the one-term analytic geometry course, often taught in sequence with college algebra, and is designed for students with a reasonably sound background in algebra, geometry, and trigonometry.

    Also useful to professionals who use math on the job. Approximately 700 math terms are defined. Includes illustrative diagrams.

    Among its special features, the book: 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, discrete-time optimal control, and large-scale optimization 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet Much supplementary/support material can be found at the book's web page

    Now this version will quickly establish itself as the "user-friendly" edition. With a detailed table of contents and an extensive index listing over 6,000 entries, the 31st edition of this hugely successful handbook makes information even easier to locate.New in the 31st edition:Game theory and voting powerHeuristic search techniquesQuadratic fieldsReliabilityRisk analysis and decision rulesA table of solutions to Pell's equationA table of irreducible polynomials in Z2[x]An interpretation of powers of 10A collection of "proofs without words"Representations of groups of small orderCounting principlesTesselations and tilings...and much more!An indispensable, up-to-date resource, CRC Standard Mathematical Tables and Formulae, 31st Edition makes it effortless to find the equations, tables, and formulae you need most often.

    Abelson delves into the too-often dismissed problems of interpreting quantitative data and then presenting them in the context of a coherent story about one's research. Unlike too many books on statistics, this is a remarkably engaging read, filled with fascinating real-life (and real-research) examples rather than with recipes for analysis. It will be of true interest and lasting value to beginning graduate students and seasoned researchers alike.The focus of the book is that the purpose of statistics is to organize a useful argument from quantitative evidence, using a form of principled rhetoric. Five criteria, described by the acronym MAGIC (magnitude, articulation, generality, interestingness, and credibility) are proposed as crucial features of a persuasive, principled argument.Particular statistical methods are discussed, with minimum use of formulas and heavy data sets. The ideas throughout the book revolve around elementary probability theory, t tests, and simple issues of research design. It is therefore assumed that the reader has already had some access to elementary statistics. Many examples are included to explain the connection of statistics to substantive claims about real phenomena.

    Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The diagrams and pictures, many of which are in color, make this book particularly appealing and fun. A few of the discussions may be confusing to those who are not adept mathematicians; those who are may be irked that certain facts are mentioned without an accompanying proof. Nonetheless, The Book of Numbers will succeed in infecting any reader with an enthusiasm for numbers.

    An alternative text to Louis Leithold's The Calculus 7 (ISBN-0-673-46913-1) concentrating on single variables within the field of calculus.

    That text has been redesigned as two volumes: this one, which introduces all the important concepts in modern stellar astrophysics, a

    Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breathtaking economy of Newton's methods. This book will stimulate great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the steady gaze of Chandrasekhar's rare perception.

    Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is a graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

    Spivak then takes up non-linear functions and trigonometric functions. He places the magnifying glass on curves in the next chapter and effortlessly leads the reader to the idea of derivative. In the next chapterhe tackles speed and velocity, followed by the derivative of sine. Maxima and minima are next. Rolle's theorem and the MVT form the core of Chapter 11, "Watching Experts at Play." The Hitchhiker's Guide to Calculus closes with a chapter on the integral, the fundamental theorem, and applications of the integral.

    The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at the back of the book, full solutions. This book is a marvelous example of how to teach and learn mathematics by 'doing' mathematics. It will work well for classes taught in small groups and can also be used for self-study. After working their way through the book, students will understand not only the theorems of linear algebra, but also some of the questions which were asked which enabled the theorems to be discovered in the first place. They will gain confidence in their problem solving abilities and be better prepared to understand more advanced courses. As the author explains, 'I don't think I understand a subject until I know the questions I wrote this book to organize those questions, problems, in my own mind.' Try this book with your students and they too will be able to organize and understand the questions of linear algebra."

    The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an introduction to the far-reaching methodology of Neuro-Dynamic Programming. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use. The second volume is oriented towards mathematical analysis and computation, and treats infinite horizon problems extensively. The text contains many illustrations, worked-out examples, and exercises.

    It introduces them to the important math principles through problems designed for the electrical profession and offers them an excellent opportunity to develop and practice problem-solving skills while at the same time providing a valuable review of electrical terminology. This new edition uses the same straightforward writing style and simple, step-by-step explanations that made previous editions so reader-friendly. It minimizes theory and emphasizes problem solving techniques and practice problems. This new edition also includes updated illustrations and information for a better learning experience than ever before! The book begins with basic arithmetic and then, once these basic topics have been mastered, progresses to algebra and concludes with trigonometry. Practical problems with real-world scenarios from the electrical field are used throughout, allowing readers to apply key mathematical concepts while developing an awareness of basic electrical terms and practices. This is the perfect resource for anyone entering the electrical industry or simply looking to brush up on the necessary math.

    

    It will improve your ability to solve all kinds of mathematical problems whether in mathematics, science, engineering, business, or purely recreational mathematical problems (puzzles, games, etc.).In the pages of this book you'll discover seven indispensable problem-solving techniques: inference, classification of action sequences, state evaluation and hill climbing, subgoals, contradiction, working backward and relations between problems. Based on modern advances in the fields of artificial intelligence and computer simulation of thought, the techniques are taught here by an effective problem-solving methodology. Dr. Wickelgren, formerly a Professor of Psychology at MIT and the University of Oregon, first defines a problem-solving method, then illustrates its application to simple recreational mathematics problems that require no more background than a year of high school algebra and a year of plane geometry. By devoting the majority of the book to such "puzzle" problems, which require less background and information than more advanced mathematics and science problems, the author reaches the widest possible audience. In the final chapter, however, Dr. Wickelgren deals with specific problems from mathematics, science, and engineering. Throughout the book, sample problems illustrate each method and the author has supplied hints and complete solutions.Carefully and clearly written, this indispensable guide will help students in every discipline avoid countless hours of frustration and wasted effort. It is an ideal book for early undergraduate courses in mathematics, physical science, engineering, computer science, economics and other fields that require problem solving. Preface. Introduction. References.Index. 73 line illustrations.

    Also included is a theory of abstract complex manifolds of one complex dimension; holomorphic functions; Cauchy's integral, more. Exercises. 1973 edition.

    Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory.For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter.New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical financeIntroduction of Girsanov transformation and the Feynman-Kac formulaExpanded discussion of It�'s formula and the Black-Scholes formula for pricing optionsNew topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motionApplicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.

    This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant real-world mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but provide clear explanations for material beyond elementary calculus, probability, and algebra. This volume will become the standard introduction for advanced undergraduate students to this exciting new field.

    Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results--the convergence theorems.

    Introductory chapters discuss potential theory with emphasis on those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, conduction of heat, and spherical harmonic analysis. Later chapters apply these theoretical concepts specifically to the interpretation of gravity and magnetic anomalies, with emphasis on anomalies caused by crustal and lithospheric sources. The book is ideal for graduate students and researchers in applied geophysics.

    This book introduces the basic concepts in the design and analysis of randomized algorithms. The first part of the text presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. Although written primarily as a text for advanced undergraduates and graduate students, this book should also prove invaluable as a reference for professionals and researchers.

    This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences.

    Because the sequences are presented in the most natural form, and arranged for easy reference, this book is easier to use than the authors earlier classic A Handbook of Integer Sequences. The Encyclopedia gives the name, mathematical description, and citations to literature for each sequence. Following sequences of particular interest, thereare essays on their origins, uses, and connections to related sequences (all cross-referenced). A valuable new feature to this text is the inclusion of a number of interesting diagrams and illustrations related to selected sequences. The initial chapters are both amusing and enlightening. They serve as a delightful introduction to the subject and a short course on how to identify and work with integer sequences. This encyclopedia brings Sloanes ground-breaking Handbook up to date, more than doubling its size, and linking both the old and the new material to an extensive bibliography (over 25 pages long), of current and classic references. An index to all the sequences in the book is also available separately on disk in Macintosh and IBM formats.

    The book is intended as a graduate text as weil as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teach ing at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl-Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985."

    This lively and accessible exploration of the nature of mathematics examines the role of the mathematician as well as the four major branches: number theory, algebra, geometry, and analysis.

    Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment--such as visualization, explanation, and understanding--can nonetheless be subjected to philosophical analysis.The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of a short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representational systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.

    KEY TOPICS: Theoretical aspects of fuzzy set theory and fuzzy logic are covered in Part I of the text, including: basic types of fuzzy sets; connections between fuzzy sets and crisp sets; the various aggregation operations of fuzzy sets; fuzzy numbers and arithmetic operations on fuzzy numbers; fuzzy relations and the study of fuzzy relation equations. Part II is devoted to applications of fuzzy set theory and fuzzy logic, including: various methods for constructing membership functions of fuzzy sets; the use of fuzzy logic for approximate reasoning in expert systems; fuzzy systems and controllers; fuzzy databases; fuzzy decision making; and engineering applications. MARKET: For everyone interested in an introduction to fuzzy set theory and fuzzy logic.

    The brainy and infuriatingly fun-to-solve problems that have kept the best Russian math and physics students biting their pencils as far back as the time of the czars.

    Unfortunately, in many textbooks, mathematical proofs and techniques obscure a fundamental understanding of the physical principles. In a clear and didactic manner, this book explains to the student why particular advanced mathematical techniques are useful for solving certain problems. The aim is to convey a deeper appreciation of mathematical methods that are applicable to physics and engineering through a discussion of a wide range of real physical problems. The topics covered include simultaneous equations, three-dimensional geometry and vectors, complex numbers, differential equations, partial derivatives, Taylor series, and Lagrange multipliers.

    Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

    A number of special, user-friendly features make it possible for readers to develop a firm grasp of the concepts of roundoff errors, stability, condition, and accuracy, as well as to develop an appreciation for the core algorithms, their usefulness, and implementations.

    This book presents empirical methods for studying complex computer programs: exploratory tools to help find patterns in data, experiment designs and hypothesis-testing tools to help data speak convincingly, and modeling tools to help explain data. Although many of these techniques are statistical, the book discusses statistics in the context of the broader empirical enterprise. The first three chapters introduce empirical questions, exploratory data analysis, and experiment design. The blunt interrogation of statistical hypothesis testing is postponed until chapters 4 and 5, which present classical parametric methods and computer-intensive (Monte Carlo) resampling methods, respectively. This is one of few books to present these new, flexible resampling techniques in an accurate, accessible manner.Much of the book is devoted to research strategies and tactics, introducing new methods in the context of case studies. Chapter 6 covers performance assessment, chapter 7 shows how to identify interactions and dependencies among several factors that explain performance, and chapter 8 discusses predictive models of programs, including causal models. The final chapter asks what counts as a theory in AI, and how empirical methods--which deal with specific systems--can foster general theories. Mathematical details are confined to appendixes and no prior knowledge of statistics or probability theory is assumed. All of the examples can be analyzed by hand or with commercially available statistics packages.The Common Lisp Analytical Statistics Package (CLASP), developed in the author's laboratory for Unix and Macintosh computers, is available from The MIT Press.A Bradford Book

    Lotteries, casino gambling, the al- most non-stop polling which seems to mold public policy more and more- these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re- moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac- ing quantum mechanics, has a world view that is at its core probabilistic in nature, contrary to the deterministic one of classical physics. In addition to all this muscular evidence of the importance of probability ideas it should also be said that probability can be lots of fun. It is a subject where you can start thinking about amusing, interesting, and often difficult problems with very little mathematical background. In this book, I wanted to introduce a reader with at least a fairly decent mathematical background in elementary algebra to this world of probabil- ity, to the way of thinking typical of probability, and the kinds of problems to which probability can be applied. I have used examples from a wide variety of fields to motivate the discussion of concepts.

    The second volume is oriented towards mathematical analysis and computation, and treats infinite horizon problems extensively. New features of the 3rd edition are: 1) A major enlargement in size and scope: the length has increased by more than 50%, and most of the old material has been restructured and/or revised. 2) Extensive coverage (more than 100 pages) of recent research on simulation-based approximate dynamic programming (neuro-dynamic programming), which allow the practical application of dynamic programming to large and complex problems. 3) An in-depth development of the average cost problem (more than 100 pages), including a full analysis of multichain problems, and an extensive analysis of infinite-spaces problems. 4) An introduction to infinite state space stochastic shortest path problems. 5) Expansion of the theory and use of contraction mappings in infinite state space problems and in neuro-dynamic programming. 6) A substantive appendix on the mathematical measure-theoretic issues that must be addressed for a rigorous theory of stochastic dynamic programming. Much supplementary material can be found in the book's web page

    The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.

    Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more up-to-date and significant.This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zero-knowledge proofs and RSA encryption. The topology chapter builds on the existing real analysis material. The computer science chapters connect basic set theory and logic with current hot topics in the technology sector. Presenting ideas at the cutting edge of modern cryptography and security analysis, the cryptography chapter shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques.Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. It gives them the background, tools, and skills needed in more advanced courses.

    Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

    Students soon discover that they can assess the likelihood of an event actually occurring.

    This book presents a unified view of wavelets and subband coding with a signal processing perspective. Covers the discrete-time case, or filter banks; development of wavelets; continuous wavelet and local Fourier transforms; efficient algorithms for filter banks and wavelet computations; and signal compression. *provides broad coverage of theory and applications and a different perspective based on signal processing. *gives framework for applications in speech, audio, image and video compression as used in multimedia. *includes sufficient background material so that people without signal processing knowledge will find it useful.

    . . "Truly a book that can be read by practitioners...Anyone who deals with designing experiments, the statistical analysis and modeling of data, and especially product or process improvement, including optimization, should have this book as a reference." -Technometrics "An excellent book for practitioners. Ownership...is a professional necessity." -Journal of the American Statistical Association Identifying and fitting an appropriate response surface model from experimental data requires knowledge of statistical experimental design fundamentals, regression modeling techniques, and elementary optimization methods. This book integrates these three topics into a comprehensive, state-of-the-art presentation of response surface methodology (RSM). This new second edition has been substantially rewritten and updated to include new topics and material, new examples, and to more fully illustrate modern applications of RSM. The authors have made the computer a more integral part of their presentation, employing the most common and useful software packages. They bring an applied focus to the subject of RSM, emphasizing methods that are useful in industry for product and process design and development. Features include: * Coverage of two-level factorial and fractional factorial design, and empirical modeling of RSM * Optimization techniques useful in RSM, including multiple responses * Classical and modern response surface designs, including computer-generated designs * The RSM approach to robust parameter design and process robustness studies * Comprehensive treatment of mixture experiments * Revised and expanded end-of-chapter problems, an extensive reference section, and valuable technical appendices on RSM * Supported by Design-Expert software Response Surface Methodology develops the underlying theory of RSM, describes the assumptions and conditions necessary to successfully apply it, and provides comprehensive and authoritative discussion of current topics for statisticians, engineers, and students.

    It covers important formulas, relations, and methods from algebra, triginometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated fifth edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, though results are also taken from various other reference works.

    Kolmogorov's first attempt to predict the properties of flow, this textbook presents a modern account of turbulence, one of the greatest challenges in physics. "Fully developed turbulence" is ubiquitous in both cosmic and natural environments, in engineering applications and in everyday life. Elementary presentations of dynamical systems ideas, probabilistic methods (including the theory of large deviations) and fractal geometry make this a self-contained textbook. This is the first book on turbulence to use modern ideas from chaos and symmetry breaking. The book will appeal to first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, as well as professional scientists and engineers.

    It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.

    This second edition of Thermodynamics continues to provide an accessible introduction to thermodynamics, which maintains an appropriate rigor to prepare newcomers for subsequent, more advanced topics.The book presents a logical methodology for solving problems in the context of conservation laws and property tables or equations. The authors elucidate the terms around which thermodynamics has historically developed, such as work, heat, temperature, energy, and entropy. Using a pedagogical approach that builds from basic principles to laws and eventually corollaries of the laws, the text enables students to think in clear and correct thermodynamic terms as well as solve real engineering problems.For those just beginning their studies in the field, Thermodynamics, Second Edition provides the core fundamentals in a rigorous, accurate, and accessible presentation.

    There are new sections in almost every chapter, and many new examples have been included throughout.

    A principal aim of this text is to highlight this connection. It provides an introduction to both fractals and chaos and proceeds to show how certain fractals (attractors of iterated function systems) spawn chaos.

    Undergraduate-level text emphasizes application of the theory of differential equations to problems in biology, economics, engineering, and physics.

    Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretical nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered con secutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

    With an early introduction to vectors and vector functions, the approach is ideal for engineering students who use vectors early in their curriculum. Stewart begins by introducing vectors in Chapter 1, along with their basic operations, such as addition, scalar multiplication, and dot product. The definition of vector functions and parametric curves is given at the end of Chapter 1 using a two-dimensional trajectory of a projectile as motivation. Limits, derivatives, and integrals of vector functions are interwoven throughout the subsequent chapters. As with the other texts in his Calculus series, in Early Vectors Stewart makes us of heuristic examples to reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject. This heuristic or discovery approach in the examples give students an intuitive feeling for analysis.

    Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions.Whether you need a course supplement, help preparing for an exam, or a concise reference for the subject, CliffsQuickReview Differential Equations can help. This guide covers first-order and second-order equations, power series, and more. In no time, you'll be tackling topics such as Linear and homogeneous equations Integrating factors The Laplace transform operator Simple harmonic motion Orthogonal trajectories CliffsQuickReview Differential Equations acts as a supplement to your other learning materials. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. You can flip through the book until you find what you're looking for — it's organized to gradually build on key concepts. You can also get a feel for the scope of the book by checking out the Contents pages that give you a chapter-by-chapter list of topics. Tabs at the top of each page that tell you what topic is being covered. Heading and subheading structure that breaks sections into clearly identifiable bites of information. Keywords in boldface type throughout the text. Wealth of formulas and figures designed to provide visual references. With titles available for all the most popular high school and college courses, CliffsQuickReview guides are comprehensive resources that can help you get the best possible grades.

    Real Computing Made Real offers practical advice on detecting and removing bugs. It also outlines techniques for preserving significant figures, avoiding extraneous solutions, and finding efficient iterative processes for solving nonlinear equations.Those who compute with real numbers (for example, floating-point numbers stored with limited precision) tend to develop techniques that increase the frequency of useful answers. But although there might be ample guidance for those addressing linear problems, little help awaits those negotiating the nonlinear world. This book, geared toward upper-level undergraduates and graduate students, helps rectify that imbalance. Its examples and exercises (with answers) help readers develop problem-formulating skills and assist them in avoiding the common pitfalls that software packages seldom detect. Some experience with standard numerical methods is assumed, but beginners will find this volume a highly practical introduction, particularly in its treatment of often-overlooked topics.

    Features include syllabus analysis, step-by-step coverage of topics, practice questions, and advice on study and coursework.

    The aim of Knots and Surfaces is to change all that. Knots and Surfaces guides the reader through Euler's formula, one and two-sided surfaces, and knot theory using games and examples. By means of a series of carefully selected tasks, this book leads the reader on to discover some real mathematics. There are no formulas to memorize; no procedures to follow. This book is a guide to the mathematics - it starts you in the right direction and brings you back if you stray too far. Discovery is left to you. This book is aimed at undergraduates and those with little background knowledge of mathematics.

    

    The argument rests on a close description of the practices of Greek mathematics, principally the use of lettered diagrams and the regulated, formulaic use of language.

    The field is covered broadly rather than in depth, and includes references to more extended works on various topics. This new edition is slightly expanded, and includes additional new material in the applications sections.

    These books help develop fluency, vocabulary and comprehension.