Calculus and mathematical analysis Books

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisOriginating from the authors' own graduate course at the University of North Carolina, this material has been thoroughly tried and tested over many years, making the book perfect for a two-term course or for self-study. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'take-off point' for them as they specialize in areas that exploit mathematical machinery.Table of ContentsPreface; Acknowledgements; 1. Point sets and certain classes of sets; 2. Measures: general properties and extension; 3. Measurable functions and transformations; 4. The integral; 5. Absolute continuity and related topics; 6. Convergence of measurable functions, Lp-spaces; 7. Product spaces; 8. Integrating complex functions, Fourier theory and related topics; 9. Foundations of probability; 10. Independence; 11. Convergence and related topics; 12. Characteristic functions and central limit theorems; 13. Conditioning; 14. Martingales; 15. Basic structure of stochastic processes; References; Index.

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Book SynopsisThe three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.Table of ContentsIntroduction; Part I. Metric and Topological Spaces: 1. Metric spaces and normed spaces; 2. Convergence, continuity and topology; 3. Topological spaces; 4. Completeness; 5. Compactness; 6. Connectedness; Part II. Functions of a Vector Variable: 7. Differentiating functions of a vector variable; 8. Integrating functions of several variables; 9. Differential manifolds in Euclidean space; Appendix A. Linear algebra; Appendix B. Quaternions; Appendix C. Tychonoff's theorem; Index.

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Book SynopsisProbability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.Trade Review'… packs a great deal of material into a moderate-sized book, starting with a synopsis of measure theory and ending with a taste of current research into random matrices and number theory. The book ranges more widely than the title might suggest … There are numerous exercises sprinkled throughout the book. Most of these are exhortations to fill in details left out of the main discussion or illustrative examples. The exercises are a natural part of the book, unlike the exercises in so many books that were apparently grafted on after-the-fact at a publisher's insistence. McKean has worked in probability and related areas since obtaining his PhD under William Feller in 1955. His book contains invaluable insights from a long career.' John D. Cook, MAA Reviews'The scope is wide, not restricted to 'elementary facts' only. There is an abundance of pretty details … This book is highly recommendable …' Jorma K. Merikoski, International Statistical ReviewTable of ContentsPreface; 1. Preliminaries; 2. Bernoulli trials; 3. The standard random walk; 4. The standard random walk in higher dimensions; 5. LLN, CLT, iterated log, and arcsine in general; 6. Brownian motion; 7. Markov chains; 8. The ergodic theorem; 9. Communication over a noisy channel; 10. Equilibrium statistical mechanics; 11. Statistical mechanics out of equilibrium; 12. Random matrices; Bibliography; Index.

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Book SynopsisThis short introduction is perfect for any 16- to 18-year-old, about to begin studies in mathematics, or anyone who would like to see a different account of the calculus from that given in the standard texts. Easy to read, this book will enthuse a new generation of mathematicians.Table of ContentsIntroduction; 1. Preliminary ideas; 2. The integral; 3. Functions, old and new; 4. Falling bodies; 5. Compound interest and horse kicks; 6. Taylor's theorem; 7. Approximations, good and bad; 8. Hills and dales; 9. Differential equations via computers; 10. Paradise lost; 11. Paradise regained; Bibliography; Index.

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Book SynopsisThe theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.Table of ContentsPreface; 1. Introduction; 2. Linear cocycles; 3. Extremal Lyapunov exponents; 4. Multiplicative ergodic theorem; 5. Stationary measures; 6. Exponents and invariant measures; 7. Invariance principle; 8. Simplicity; 9. Generic cocycles; 10. Continuity; References; Index.

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Book SynopsisLinear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.Trade Review'This is a book for anyone who wants to really understand linear algebra. Instead of mere cookbook recipes or dry proofs, it provides explanations, examples, pictures - and, yes, algorithms and proofs too, but only after the reader is able to understand them. And while it is aimed at beginners, even experts will have something to learn from this book.' John Baez, University of California, Riverside'This is an exciting and entertaining book. It keeps an informal tone, but without sacrificing accuracy or clarity. It takes care to address common difficulties (and the classroom testing shows), but without talking down to the reader. It uses the modern understanding of how to do linear algebra right, but remains accessible to first-time readers.' Tom Leinster, University of Edinburgh'Linear algebra is one of the most important topics in mathematics, as linearity is exploited throughout applied mathematics and engineering. Therefore, the tools from linear algebra are used in many fields. However, they are often not presented that way, which is a missed opportunity. The authors have written a linear algebra book that is useful for students from many fields (including mathematics). A great feature of this book is that it presents a formal linear algebra course that clearly makes (coordinate) matrices and vectors the fundamental tools for problem solving and computations.' Eric de Sturler, Virginia Polytechnic Institute and State University'It is a book well worth considering both for learning and teaching this important area of mathematics.' John Baylis, The Mathematical GazetteTable of Contents1. Linear systems and vector spaces; 2. Linear maps and matrices; 3. Linear independence, bases, and coordinates; 4. Inner products; 5. Singular value decomposition and the spectral theorem; 6. Determinants.

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Book SynopsisAt the heart of this monograph is the BrunnâMinkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp BrunnâMinkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.Trade ReviewReview of the first edition: 'Neither one of [the old classics] may be considered a substitute for the excellent detailed monograph written by Rolf Schneider. I recommend this book to everyone who appreciates the beauty of convexity theory or who uses the strength of geometric inequalities, and to any expert who needs a reliable reference book for his/her research.' V. Milman, Bulletin of the American Mathematical SocietyReview of the first edition: 'Professor Schneider's book is the first comprehensive account of the Brunn-Minkowski theory and will immediately become the standard reference for the Aleksandrov-Fenchel inequalities and the current knowledge concerning the cases of equality and estimates of their stability. The book is aimed at a broad audience from graduate students to working professionals. The presentation is very clear and I enjoyed reading it.' Bulletin of the London Mathematical SocietyTable of ContentsPreface to the second edition; Preface to the first edition; General hints to the literature; Conventions and notation; 1. Basic convexity; 2. Boundary structure; 3. Minkowski addition; 4. Support measures and intrinsic volumes; 5. Mixed volumes and related concepts; 6. Valuations on convex bodies; 7. Inequalities for mixed volumes; 8. Determination by area measures and curvatures; 9. Extensions and analogues of the Brunn–Minkowski theory; 10. Affine constructions and inequalities; Appendix. Spherical harmonics; References; Notation index; Author index; Subject index.

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Book SynopsisThis textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.Trade Review'This book is a delightful and self-contained introduction to stochastic and Malliavin calculus that will guide the graduate students in probability theory from the basics of the theory to the borders of contemporary research. It is a must read written by two globally recognized experts!' Fabrice Baudoin, University of Connecticut'Malliavin calculus has seen a great revival of interest in recent years, after the discovery about ten years ago that Stein's method for probabilistic approximation and Malliavin calculus fit together admirably well. Such an interaction has led to some remarkable limit theorems for Gaussian, Poisson and Rademacher functionals. This monograph, written by two internationally renowned specialists of the field, provides a concise, self-contained and very pleasant exposition of different aspects of this rich and recent line of research. For sure, it is destined to quickly become a must-have reference book!' Ivan Nourdin, University of Luxembourg'The book provides a concise and self-contained exposition of the subject including recent developments.' Maria Gordina, MathSciNet'The book is written very clearly and precisely, and will be useful to anyone who wants to study the Malliavin calculus and its applications at the introductory level and then more deeply, as well as those who are ready to apply these results in their research. The book can be used to give lectures for graduate students.' Yuliya S. Mishura, zbMathTable of ContentsPreface; 1. Brownian motion; 2. Stochastic calculus; 3. Derivative and divergence operators; 4. Wiener chaos; 5. Ornstein-Uhlenbeck semigroup; 6. Stochastic integral representations; 7. Study of densities; 8. Normal approximations; 9. Jump processes; 10. Malliavin calculus for jump processes I; 11. Malliavin calculus for jump processes II; Appendix A. Basics of stochastic processes; References; Index.

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Book SynopsisProbability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.Trade Review'… packs a great deal of material into a moderate-sized book, starting with a synopsis of measure theory and ending with a taste of current research into random matrices and number theory. The book ranges more widely than the title might suggest … There are numerous exercises sprinkled throughout the book. Most of these are exhortations to fill in details left out of the main discussion or illustrative examples. The exercises are a natural part of the book, unlike the exercises in so many books that were apparently grafted on after-the-fact at a publisher's insistence. McKean has worked in probability and related areas since obtaining his PhD under William Feller in 1955. His book contains invaluable insights from a long career.' John D. Cook, MAA Reviews'The scope is wide, not restricted to 'elementary facts' only. There is an abundance of pretty details … This book is highly recommendable …' Jorma K. Merikoski, International Statistical ReviewTable of ContentsPreface; 1. Preliminaries; 2. Bernoulli trials; 3. The standard random walk; 4. The standard random walk in higher dimensions; 5. LLN, CLT, iterated log, and arcsine in general; 6. Brownian motion; 7. Markov chains; 8. The ergodic theorem; 9. Communication over a noisy channel; 10. Equilibrium statistical mechanics; 11. Statistical mechanics out of equilibrium; 12. Random matrices; Bibliography; Index.

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Book SynopsisThis is a perfect companion to any course on measure theory, integration, real and functional analysis, providing more than 300 examples and counterexamples to the otherwise often rather theoretical courses. By knowing 'what may go wrong' students will gain a better understanding of the standard course material.Trade Review'This book is an admirable counterpart, both to the first author's well-known text Measures, Integrals and Martingales (Cambridge, 2005/2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase the authors' preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.' N. H. Bingham, Imperial College'… an excellent reference text and companion reader for anyone interested in deepening their understanding of measure theory.' John Ross, MAA Reviews'… the unique nature of the book makes it an essential acquisition for any university with a doctoral program in pure mathematics … Essential.' M. Bona, Choice Connect'The book is well written, the demonstrations are clear and the bibliographic references are competent. We appreciate this work as extremely useful for those interested in measure theory and integration, starting with beginners and extending even to advanced researchers in the field.' Liviu Constantin Florescu, Mathematical Reviews/MathSciNet'Counterexamples in Measure and Integration is an ideal companion to help better understand canonically problematic examples in analysis … This collection of counterexamples is an excellent resource to researchers who rely on measure and integration theory. It would be helpful for students studying for their analysis qualifying exam as it draws on common misconceptions and enables readers to build intuition about why a given counterexample works and how conditions can be changed to make a particular statement hold.' Katelynn Kochalski, Notices of the AMSTable of ContentsPreface; User's guide; List of topics and phenomena; 1. A panorama of Lebesgue integration; 2. A refresher of topology and ordinal numbers; 3. Riemann is not enough; 4. Families of sets; 5. Set functions and measures; 6. Range and support of a measure; 7. Measurable and non-measurable sets; 8. Measurable maps and functions; 9. Inner and outer measure; 10. Integrable functions; 11. Modes of convergence; 12. Convergence theorems; 13. Continuity and a.e. continuity; 14. Integration and differentiation; 15. Measurability on product spaces; 16. Product measures; 17. Radon–Nikodým and related results; 18. Function spaces; 19. Convergence of measures; References; Index.

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Originally published in 1938, this book focuses on the area of elliptic and hyperelliptic integrals and allied theory. The text was a posthumous publication by William Westropp Roberts (18501935), who held the position of Vice-Provost at Trinity College, Dublin from 1927 until shortly before his death.

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Book SynopsisA careful and accessible exposition of a functional analytic approach to initial boundary value problems for semilinear parabolic differential equations, with a focus on the relationship between analytic semigroups and initial boundary value problems. This semigroup approach is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of pseudo-differential operators, one of the most influential works in the modern history of analysis. Complete with ample illustrations and additional references, this new edition offers both streamlined analysis and better coverage of important examples and applications. A powerful method for the study of elliptic boundary value problems, capable of further extensive development, is provided for advanced undergraduates or beginning graduate students, as well as mathematicians with an interest in functional analysis and partial differential equations.Table of Contents1. Introduction and main results; 2. Preliminaries from functional analysis; 3. Theory of analytic semigroups; 4. Sobolev imbedding theorems; 5. Lp theory of pseudo-differential operators; 6. Lp approach to elliptic boundary value problems; 7. Proof of theorem 1.1; 8. Proof of theorem 1.2; 9. Proof of theorems 1.3 and 1.4; Appendix A. The Laplace Transform; Appendix B. The Maximum Principle; Appendix C. Vector bundles; References; Index.

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Book Synopsis

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Book Synopsis

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Book Synopsis

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Book SynopsisAbout our authors Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago's South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening. Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school and colTable of ContentsTable of Contents Foundations: A Prelude to Functions F.1 The Distance and Midpoint Formulas F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry F.3 Lines F.4 Circles Chapter Project Functions and Their Graphs 1.1 Functions 1.2 The Graph of a Function 1.3 Properties of Functions 1.4 Library of Functions; Piecewise-defined Functions 1.5 Graphing Techniques: Transformations 1.6 Mathematical Models: Building Functions 1.7 Building Mathematical Models Using Variation Chapter Review Chapter Test Chapter Projects Linear and Quadratic Functions 2.1 Properties of Linear Functions and Linear Models 2.2 Building Linear Models from Data 2.3 Quadratic Functions and Their Zeros 2.4 Properties of Quadratic Functions 2.5 Inequalities Involving Quadratic Functions 2.6 Building Quadratic Models from Verbal Descriptions and from Data 2.7 Complex Zeros of a Quadratic Function 2.8 Equations and Inequalities Involving the Absolute Value Function Chapter Review Chapter Test Cumulative Review Chapter Projects Polynomial and Rational Functions 3.1 Polynomial Functions and Models 3.2 The Real Zeros of a Polynomial Function 3.3 Complex Zeros; Fundamental Theorem of Algebra 3.4 Properties of Rational Functions 3.5 The Graph of a Rational Function 3.6 Polynomial and Rational Inequalities Chapter Review Chapter Test Cumulative Review Chapter Projects Exponential and Logarithmic Functions 4.1 Composite Functions 4.2 One-to-One Functions; Inverse Functions 4.3 Exponential Functions 4.4 Logarithmic Functions 4.5 Properties of Logarithms 4.6 Logarithmic and Exponential Equations 4.7 Financial Models 4.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 4.9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter Review Chapter Test Cumulative Review Chapter Projects Trigonometric Functions 5.1 Angles and Their Measure 5.2 Trigonometric Functions: Unit Circle Approach 5.3 Properties of the Trigonometric Functions 5.4 Graphs of the Sine and Cosine Functions 5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 5.6 Phase Shift; Sinusoidal Curve Fitting Chapter Review Chapter Test Cumulative Review Chapter Projects Analytic Trigonometry 6.1 The Inverse Sine, Cosine, and Tangent Functions 6.2 The Inverse Trigonometric Functions (Continued) 6.3 Trigonometric Equations 6.4 Trigonometric Identities 6.5 Sum and Difference Formulas 6.6 Double-angle and Half-angle Formulas 6.7 Product-to-Sum and Sum-to-Product Formulas Chapter Review Chapter Test Cumulative Review Chapter Projects Applications of Trigonometric Functions 7.1 Right Triangle Trigonometry; Applications 7.2 The Law of Sines 7.3 The Law of Cosines 7.4 Area of a Triangle 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter Review Chapter Test Cumulative Review Chapter Projects Polar Coordinates; Vectors 8.1 Polar Coordinates 8.2 Polar Equations and Graphs 8.3 The Complex Plane; De Moivre’s Theorem 8.4 Vectors 8.5 The Dot Product 8.6 Vectors in Space 8.7 The Cross Product Chapter Review Chapter Test Cumulative Review Chapter Projects Analytic Geometry 9.1 Conics 9.2 The Parabola 9.3 The Ellipse 9.4 The Hyperbola 9.5 Rotation of Axes; General Form of a Conic 9.6 Polar Equations of Conics 9.7 Plane Curves and Parametric Equations Chapter Review Chapter Test Cumulative Review Chapter Projects Systems of Equations and Inequalities 10.1 Systems of Linear Equations: Substitution and Elimination 10.2 Systems of Linear Equations: Matrices 10.3 Systems of Linear Equations: Determinants 10.4 Matrix Algebra 10.5 Partial Fraction Decomposition 10.6 Systems of Nonlinear Equations 10.7 Systems of Inequalities 10.8 Linear Programming Chapter Review Chapter Test Cumulative Review Chapter Projects Sequences; Induction; the Binomial Theorem 11.1 Sequences 11.2 Arithmetic Sequences 11.3 Geometric Sequences; Geometric Series 11.4 Mathematical Induction 11.5 The Binomial Theorem Chapter Review Chapter Test Cumulative Review Chapter Projects Counting and Probability 12.1 Counting 12.2 Permutations and Combinations 12.3 Probability Chapter Review Chapter Test Cumulative Review Chapter Projects A Preview of Calculus: The Limit, Derivative, and Integral of a Function 13.1 Finding Limits Using Tables and Graphs 13.2 Algebra Techniques for Finding Limits 13.3 One-sided Limits; Continuous Functions 13.4 The Tangent Problem; The Derivative 13.5 The Area Problem; The Integral Chapter Review Chapter Test Chapter Projects Appendix A: Review A.1 Algebra Essentials A.2 Geometry Essentials A.3 Polynomials A.4 Factoring Polynomials A.5 Synthetic Division A.6 Rational Expressions A.7 nth Roots; Rational Exponents A.8 Solving Equations A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications A.10 Interval Notation; Solving Inequalities A.11 Complex Numbers Appendix B: Graphing Utilities B.1 The Viewing Rectangle B.2 Using a Graphing Utility to Graph Equations B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry B.4 Using a Graphing Utility to Solve Equations B.5 Square Screens B.6 Using a Graphing Utility to Graph Inequalities B.7 Using a Graphing Utility to Solve Systems of Linear Equations B.8 Using a Graphing Utility to Graph a Polar Equation B.9 Using a Graphing Utility to Graph Parametric Equations Answers Photo Credits Index

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Book SynopsisFactor analysis, a mathematical technique for studying matrices of data, has long been used in the behavioural sciences. This new edition of a work on its application to chemical problems has been thoroughly revised and includes an added chapter on special methods of factor analysis.Table of ContentsMain Steps; Mathematical Formulation of Target Factor Analysis; Effects of Experimental Error on Target Factor Analysis; Numerical Examples of Target Factor Analysis; Special Methods of Factor Analysis; Component Analysis; Nuclear Magnetic Resonance; Chromatography; Additional Applications; Appendices; Bibliography; Author Index; Subject Index.

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Book SynopsisGet a good grade in your precalculus course with PRECALCULUS, Seventh Edition. Written in a clear, student-friendly style, the book also provides a graphical perspective so you can develop a visual understanding of college algebra and trigonometry. With great examples, exercises, applications, and real-life data--and a range of online study resources--this book provides you with the tools you need to be successful in your course.Table of Contents1. FUNDAMENTALS. Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles. 2. EQUATIONS AND INEQUALITIES. Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS. The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Functions. Iteration. Inverse Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS: APPLICATIONS TO OPTIMIZATION. Linear Functions. Quadratic Functions. Using Iteration to Model Populations Growth (Optional Section). Setting Up Equations That Devine Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay. 6. AN INTRODUCTION TO TRIGONOMETRY VIA RIGHT TRIANGLES. Trigonometric Functions of Acute Angles. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities. 7. THE TRIGONOMETRIC FUNCTIONS. Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry. 8. GRAPHS OF TRIGONOMETRIC FUNCTIONS. Trigonometric Functions of Real Numbers. Graphs of the Sine and Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx-C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions. 9. ANALYTICAL TRIGONOMETRY. The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions. 10. ADDITIONAL TOPICS IN TRIGONOMETRY. Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane: A Geometric Approach. Vectors in the Plane: An Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates. DeMoivre's Theorem. 11. SYSTEMS OF EQUATIONS. Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities. 12. THE CONIC SECTIONS. The Basic Equations. The Parabola. Tangents to Parabolas (Optional Section). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes. 13. ROOTS OF POLYNOMIAL EQUATIONS. Division of Polynomials. The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes's Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions. 14. ADDITIONAL TOPICS IN ALGEBRA. Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. Introduction to Limits. Appendix A.1: Significant Digits. Appendix A.2: ���2 is Irrational. Appendix A.3: The Complex Number System. Answers. Index.

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Book SynopsisIntroducing a revolutionary new model for the statistical analysis of experimental data In this important book, internationally acclaimed statistician, Chihiro Hirotsu, goes beyond classical analysis of variance (ANOVA) model to offer a unified theory and advanced techniques for the statistical analysis of experimental data. Dr. Hirotsu introduces the groundbreaking concept of advanced analysis of variance (AANOVA) and explains how the AANOVA approach exceeds the limitations of ANOVA methods to allow for global reasoning utilizing special methods of simultaneous inference leading to individual conclusions. Focusing on normal, binomial, and categorical data, Dr. Hirotsu explores ANOVA theory and practice and reviews current developments in the field. He then introduces three new advanced approaches, namely: testing for equivalence and non-inferiority; simultaneous testing for directional (monotonic or restricted) alternatives and change-point hypotheses; and analyses emerging from caTable of ContentsPreface xi Notation and Abbreviations xvii 1 Introduction to Design and Analysis of Experiments 1 1.1 Why Simultaneous Experiments? 1 1.2 Interaction Effects 2 1.3 Choice of Factors and Their Levels 4 1.4 Classification of Factors 5 1.5 Fixed or Random Effects Model? 5 1.6 Fisher’s Three Principles of Experiments vs. Noise Factor 6 1.7 Generalized Interaction 7 1.8 Immanent Problems in the Analysis of Interaction Effects 7 1.9 Classification of Factors in the Analysis of Interaction Effects 8 1.10 Pseudo Interaction Effects (Simpson’s Paradox) in Categorical Data 8 1.11 Upper Bias by Statistical Optimization 9 1.12 Stage of Experiments: Exploratory, Explanatory or Confirmatory? 10 2 Basic Estimation Theory 11 2.1 Best Linear Unbiased Estimator 11 2.2 General Minimum Variance Unbiased Estimator 12 2.3 Efficiency of Unbiased Estimator 14 2.4 Linear Model 18 2.5 Least Squares Method 19 2.6 Maximum Likelihood Estimator 31 2.7 Sufficient Statistics 34 3 Basic Test Theory 41 3.1 Normal Mean 41 3.2 Normal Variance 53 3.3 Confidence Interval 56 3.4 Test Theory in the Linear Model 58 3.5 Likelihood Ratio Test and Efficient Score Test 62 4 Multiple Decision Processes and an Accompanying Confidence Region 71 4.1 Introduction 71 4.2 Determining the Sign of a Normal Mean – Unification of One- and Two-Sided Tests 71 4.3 An Improved Confidence Region 73 5 Two-Sample Problem 75 5.1 Normal Theory 75 5.2 Non-parametric Tests 84 5.3 Unifying Approach to Non-inferiority, Equivalence and Superiority Tests 92 6 One-Way Layout, Normal Model 113 6.1 Analysis of Variance (Overall F-Test) 113 6.2 Testing the Equality of Variances 115 6.3 Linear Score Test (Non-parametric Test) 118 6.4 Multiple Comparisons 121 6.5 Directional Tests 128 7 One-Way Layout, Binomial Populations 165 7.1 Introduction 165 7.2 Multiple Comparisons 166 7.3 Directional Tests 167 8 Poisson Process 193 8.1 Max acc. t1 for the Monotone and Step Change-Point Hypotheses 193 8.2 Max acc. t2 for the Convex and Slope Change-Point Hypotheses 197 9 Block Experiments 201 9.1 Complete Randomized Blocks 201 9.2 Balanced Incomplete Blocks 205 9.3 Non-parametric Method in Block Experiments 211 10 Two-Way Layout, Normal Model 237 10.1 Introduction 237 10.2 Overall ANOVA of Two-Way Data 238 10.3 Row-wise Multiple Comparisons 244 10.4 Directional Inference 256 10.5 Easy Method for Unbalanced Data 260 11 Analysis of Two-Way Categorical Data 273 11.1 Introduction 273 11.2 Overall Goodness-of-Fit Chi-Square 275 11.3 Row-wise Multiple Comparisons 276 11.4 Directional Inference in the Case of Natural Ordering Only in Columns 281 11.5 Analysis of Ordered Rows and Columns 291 12 Mixed and Random Effects Model 299 12.1 One-Way Random Effects Model 299 12.2 Two-Way Random Effects Model 306 12.3 Two-Way Mixed Effects Model 314 12.4 General Linear Mixed Effects Model 322 13 Profile Analysis of Repeated Measurements 329 13.1 Comparing Treatments Based on Upward or Downward Profiles 329 13.2 Profile Analysis of 24-Hour Measurements of Blood Pressure 338 14 Analysis of Three-Way Categorical Data 347 14.1 Analysis of Three-Way Response Data 348 14.2 One-Way Experiment with Two-Way Categorical Responses 361 14.3 Two-Way Experiment with One-Way Categorical Responses 375 15 Design and Analysis of Experiments by Orthogonal Arrays 383 15.1 Experiments by Orthogonal Array 383 15.2 Ordered Categorical Responses in a Highly Fractional Experiment 393 15.3 Optimality of an Orthogonal Array 397 References 399 Appendix 401 Index 407

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Book SynopsisThe relative motion between the transmitter and the receiver modifies the nonstationarity properties of the transmitted signal. In particular, the almost-cyclostationarity property exhibited by almost all modulated signals adopted in communications, radar, sonar, and telemetry can be transformed into more general kinds of nonstationarity. A proper statistical characterization of the received signal allows for the design of signal processing algorithms for detection, estimation, and classification that significantly outperform algorithms based on classical descriptions of signals.Generalizations of Cyclostationary Signal Processingaddresses these issues and includes the following key features: Presents the underlying theoretical framework, accompanied by details of their practical application, for the mathematical models of generalized almost-cyclostationary processes and spectrally correlated processes; two classes of signals finding growing importance in areas sTrade Review“This book is written both for advanced readers with the background of graduate students in engineering and for specialists (e.g., mathematicians).” (Zentralblatt MATH, 1 May 2013) Table of ContentsDedication iii Acknowledgements xiii Introduction xv 1 Background 1 1.1 Second-Order Characterization of Stochastic Processes 1 1.1.1 Time-Domain Characterization 1 1.1.2 Spectral-Domain Characterization 2 1.1.3 Time-Frequency Characterization 4 1.1.4 Wide-Sense Stationary Processes 5 1.1.5 Evolutionary Spectral Analysis 5 1.1.6 Discrete-Time Processes 7 1.1.7 Linear Time-Variant Transformations 8 1.2 Almost-Periodic Functions 10 1.2.1 Uniformly Almost-Periodic Functions 11 1.2.2 AP Functions in the Sense of Stepanov,Weyl, and Besicovitch 12 1.2.3 Weakly AP Functions in the Sense of Eberlein 13 1.2.4 Pseudo AP Functions 14 1.2.5 AP Functions in the Sense of Hartman and Ryll-Nardzewski 15 1.2.6 AP Functions Defined on Groups and with Values in Banach and Hilbert Spaces 16 1.2.7 AP Functions in Probability 16 1.2.8 AP Sequences 17 1.2.9 AP Sequences in Probability 18 1.3 Almost-Cyclostationary Processes 18 1.3.1 Second-OrderWide-Sense Statistical Characterization 18 1.3.2 Jointly ACS Signals 20 1.3.3 LAPTV Systems 24 1.3.4 Products of ACS Signals 27 1.3.5 Cyclic Statistics of Communications Signals 29 1.3.6 Higher-Order Statistics 30 1.3.7 Cyclic Statistic Estimators 32 1.3.8 Discrete-Time ACS Signals 32 1.3.9 Sampling of ACS Signals 33 1.3.10 Multirate Processing of Discrete-Time ACS Signals 37 1.3.11 Applications 37 1.4 Some Properties of Cumulants 38 1.4.1 Cumulants and Statistical Independence 38 1.4.2 Cumulants of Complex Random Variables and Joint Complex Normality 392 Generalized Almost-Cyclostationary Processes 43 2.1 Introduction 43 2.2 Characterization of GACS Stochastic Processes 47 2.2.1 Strict-Sense Statistical Characterization 48 2.2.2 Second-OrderWide-Sense Statistical Characterization 49 2.2.3 Second-Order Spectral Characterization 59 2.2.4 Higher-Order Statistics 61 2.2.5 Processes with Almost-Periodic Covariance 65 2.2.6 Motivations and Examples 66 2.3 Linear Time-Variant Filtering of GACS Processes 70 2.4 Estimation of the Cyclic Cross-Correlation Function 72 2.4.1 The Cyclic Cross-Correlogram 72 2.4.2 Mean-Square Consistency of the Cyclic Cross-Correlogram 76 2.4.3 Asymptotic Normality of the Cyclic Cross-Correlogram 80 2.5 Sampling of GACS Processes 84 2.6 Discrete-Time Estimator of the Cyclic Cross-Correlation Function 87 2.6.1 Discrete-Time Cyclic Cross-Correlogram 87 2.6.2 Asymptotic Results 91 2.6.3 Asymptotic Results 95 2.6.4 Concluding Remarks 102 2.7 Numerical Results 104 2.7.1 Aliasing in Cycle-Frequency Domain 105 2.7.2 Simulation Setup 105 2.7.3 Cyclic Correlogram Analysis with Varying N 105 2.7.4 Cyclic Correlogram Analysis with Varying N and T 106 2.7.5 Discussion 111 2.7.6 Conjecturing the Nonstationarity Type of the Continuous-Time Signal 114 2.7.7 LTI Filtering of GACS Signals 116 2.8 Summary 116 3 Complements and Proofs on Generalized Almost-Cyclostationary Processes 123 3.1 Proofs for Section 2.2.2 “Second-OrderWide-Sense Statistical Characterization” 123 3.2 Proofs for Section 2.2.3 “Second-Order Spectral Characterization” 125 3.3 Proofs for Section 2.3 “Linear Time-Variant Filtering of GACS Processes” 129 3.4 Proofs for Section 2.4.1 “The Cyclic Cross-Correlogram” 131 3.5 Proofs for Section 2.4.2 “Mean-Square Consistency of the Cyclic Cross-Correlogram” 136 3.6 Proofs for Section 2.4.3 “Asymptotic Normality of the Cyclic Cross-Correlogram” 147 3.7 Conjugate Covariance 150 3.8 Proofs for Section 2.5 “Sampling of GACS Processes” 151 3.9 Proofs for Section 2.6.1 “Discrete-Time Cyclic Cross-Correlogram” 152 3.10 Proofs for Section 2.6.2 “Asymptotic Results as 158 3.11 Proofs for Section 2.6.3 “Asymptotic Results as 168 3.12 Proofs for Section 2.6.4 “Concluding Remarks” 176 3.13 Discrete-Time and Hybrid Conjugate Covariance 177 4 Spectrally Correlated Processes 181 4.1 Introduction 182 4.2 Characterization of SC Stochastic Processes 186 4.2.1 Second-Order Characterization 186 4.2.2 Relationship among ACS, GACS, and SC Processes 194 4.2.3 Higher-Order Statistics 195 4.2.4 Motivating Examples 200 4.3 Linear Time-Variant Filtering of SC Processes 205 4.3.1 FOT-Deterministic Linear Systems 205 4.3.2 SC Signals and FOT-Deterministic Systems 207 4.4 The Bifrequency Cross-Periodogram 208 4.5 Measurement of Spectral Correlation – Unknown Support Curves 215 4.6 The Frequency-Smoothed Cross-Periodogram 222 4.7 Measurement of Spectral Correlation – Known Support Curves 225 4.7.1 Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram 225 4.7.2 Asymptotic Normality of the Frequency-Smoothed Cross-Periodogram 229 4.7.3 Final Remarks 231 4.8 Discrete-Time SC Processes 233 4.9 Sampling of SC Processes 236 4.9.1 Band-Limitedness Property 237 4.9.2 Sampling Theorems 239 4.9.3 Illustrative Examples 243 4.10 Multirate Processing of Discrete-Time Jointly SC Processes 256 4.10.1 Expansion 257 4.10.2 Sampling 260 4.10.3 Decimation 262 4.10.4 Expansion and Decimation 265 4.10.5 Strictly Band-Limited SC Processes 267 4.10.6 Interpolation Filters 268 4.10.7 Decimation Filters 270 4.10.8 Fractional Sampling Rate Converters 271 4.11 Discrete-Time Estimators of the Spectral Cross-Correlation Density 272 4.12 Numerical Results 273 4.12.1 Simulation Setup 273 4.12.2 Unknown Support Curves 273 4.12.3 Known Support Curves 274 4.13 Spectral Analysis with Nonuniform Frequency Resolution 281 4.14 Summary 2865 Complements and Proofs on Spectrally Correlated Processes 291 5.1 Proofs for Section 4.2 “Spectrally Correlated Stochastic Processes” 291 5.2 Proofs for Section 4.4 “The Bifrequency Cross-Periodogram” 292 5.3 Proofs for Section 4.5 “Measurement of Spectral Correlation – Unknown Support Curves” 298 5.4 Proofs for Section 4.6 “The Frequency-Smoothed Cross-Periodogram” 306 5.5 Proofs for Section 4.7.1 “Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram” 309 5.6 Proofs for Section 4.7.2 “Asymptotic Normality of the Frequency-Smoothed Cross-Periodogram” 325 5.7 Alternative Bounds 333 5.8 Conjugate Covariance 334 5.9 Proofs for Section 4.8 “Discrete-Time SC Processes” 337 5.10 Proofs for Section 4.9 “Sampling of SC Processes” 339 5.11 Proofs for Section 4.10 “Multirate Processing of Discrete-Time Jointly SC Processes” 3426 Functional Approach for Signal Analysis 355 6.1 Introduction 355 6.2 Relative Measurability 356 6.2.1 Relative Measure of Sets 356 6.2.2 Relatively Measurable Functions 357 6.2.3 Jointly Relatively Measurable Functions 358 6.2.4 Conditional Relative Measurability and Independence 360 6.2.5 Examples 361 6.3 Almost-Periodically Time-Variant Model 361 6.3.1 Almost-Periodic Component Extraction Operator 361 6.3.2 Second-Order Statistical Characterization 363 6.3.3 Spectral Line Regeneration 365 6.3.4 Spectral Correlation 366 6.3.5 Statistical Function Estimators 367 6.3.6 Sampling, Aliasing, and Cyclic Leakage 369 6.3.7 FOT-Deterministic Systems 371 6.3.8 FOT-Deterministic Linear Systems 372 6.4 Nonstationarity Classification in the Functional Approach 374 6.5 Proofs of FOT Counterparts of Some Results on ACS and GACS Signals 3757 Applications to Mobile Communications and Radar/Sonar 381 7.1 Physical Model for the Wireless Channel 381 7.1.1 Assumptions on the Propagation Channel 381 7.1.2 Stationary TX, Stationary RX 382 7.1.3 Moving TX, Moving RX 383 7.1.4 Stationary TX, Moving RX 387 7.1.5 Moving TX, Stationary RX 388 7.1.6 Reflection on Point Scatterer 388 7.1.7 Stationary TX, Reflection on Point Moving Scatterer, Stationary RX (Stationary Bistatic Radar) 390 7.1.8 (Stationary)Monostatic Radar 391 7.1.9 Moving TX, Reflection on a Stationary Scatterer, Moving RX 392 7.2 Constant Velocity Vector 393 7.2.1 Stationary TX, Moving RX 393 7.2.2 Moving TX, Stationary RX 394 7.3 Constant Relative Radial Speed 395 7.3.1 Moving TX, Moving RX 395 7.3.2 Stationary TX, Moving RX 398 7.3.3 Moving TX, Stationary RX 401 7.3.4 Stationary TX, Reflection on a Moving Scatterer, Stationary RX (Stationary Bistatic Radar) 404 7.3.5 (Stationary)Monostatic Radar 406 7.3.6 Moving TX, Reflection on a Stationary Scatterer, Moving RX 406 7.3.7 Non synchronized TX and RX oscillators 407 7.4 Constant Relative Radial Acceleration 407 7.4.1 Stationary TX, Moving RX 408 7.4.2 Moving TX, Stationary RX 408 7.5 Transmitted Signal: Narrow-Band Condition 409 7.5.1 Constant Relative Radial Speed 411 7.5.2 Constant Relative Radial Acceleration 414 7.6 Multipath Doppler Channel 416 7.6.1 Constant Relative Radial Speeds – Discrete Scatterers 416 7.6.2 Continuous Scatterer 416 7.7 Spectral Analysis of Doppler-Stretched Signals – Constant Radial Speed 417 7.7.1 Second-Order Statistics (Continuous-Time) 417 7.7.2 Multipath Doppler Channel 422 7.7.3 Doppler-Stretched Signal (Discrete-Time) 427 7.7.4 Simulation of Discrete-Time Doppler-Stretched Signals 430 7.7.5 Second-Order Statistics (Discrete-Time) 432 7.7.6 Illustrative Examples 437 7.7.7 Concluding Remarks 443 7.8 Spectral Analysis of Doppler-Stretched Signals – Constant Relative Radial Acceleration 448 7.8.1 Second-Order Statistics (Continuous-Time) 449 7.9 Other Models of Time-Varying Delays 452 7.9.1 Taylor Series Expansion of Range and Delay 452 7.9.2 Periodically Time-Variant Delay 454 7.9.3 Periodically Time-Variant Carrier Frequency 454 7.10 Proofs 4558 Bibliographic Notes 463 8.1 Almost-Periodic Functions 463 8.2 Cyclostationary Signals 463 8.3 Generalizations of Cyclostationarity 464 8.4 Other Nonstationary Signals 464 8.5 Functional Approach and Generalized Harmonic Analysis 464 8.6 Linear Time-Variant Processing 465 8.7 Sampling 465 8.8 Complex Random Variables, Signals, and Systems 465 8.9 Stochastic Processes 465 8.10 Mathematics 466 8.11 Signal Processing and Communications 466 References 467 List of Abbreviations 475

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Book SynopsisThis book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? SINGLE VARIABLE ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 550 pages--two-fifths the size of Stewart's other calculus texts (CALCULUS, Seventh Edition and CALCULUS: EARLY TRANSCENDENTALS, Seventh Edition) and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as promineTable of Contents1. FUNCTIONS AND LIMITS. Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. 2. DERIVATIVES. Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. 3. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives. 4. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. 5. INVERSE FUNCTIONS. Inverse Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. 6. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. 7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations. 8. SERIES. Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. 9. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. Appendix A: Trigonometry Appendix B: Proofs Appendix C: Sigma Notation

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Book SynopsisTable of Contents1. FUNCTIONS, GRAPHS, AND LIMITS. The Cartesian Plane and the Distance Formula. Graphs of Equations. Lines in the Plane and Slope. Functions. Limits. Continuity. 2. DIFFERENTIATION. The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change: Velocity and Marginals. The Product and Quotient Rules. The Chain Rule. Higher-Order Derivatives. Implicit Differentiation. Related Rates. 3. APPLICATIONS OF THE DERIVATIVE. Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative Test. Optimization Problems. Business and Economics Applications. Asymptotes. Curve Sketching: A Summary. Differentials and Marginal Analysis. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay. 5. INTEGRATION AND ITS APPLICATIONS. Antiderivatives and Indefinite Integrals. Integration by Substitution and the General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. The Definite Integral as the Limit of a Sum. 6. TECHNIQUES OF INTEGRATION. Integration by Parts and Present Value. Integration Tables. Numerical Integration. Improper Integrals. 7. FUNCTIONS OF SEVERAL VARIABLES. The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Least Squares Regression Analysis. Double Integrals and Area in the Plane. Applications of Double Integrals.

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Table of Contents1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Parent Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros of Polynomial Functions. Rational Functions. Nonlinear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 1-3. Proofs in Mathematics. P.S. Problem Solving. 4. TRIGONOMETRY. Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 5. ANALYTIC TRIGONOMETRY. Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 6. ADDITIONAL TOPICS IN TRIGONOMETRY. Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. The Complex Plane. Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 4-6. Proofs in Mathematics. P.S. Problem Solving. 7. SYSTEMS OF EQUATIONS AND INEQUALITIES. Linear and Nonlinear Systems of Equations. Two-Variable Linear Systems. Multivariable Linear Systems. Partial Fractions. Systems of Inequalities. Linear Programming. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 8. MATRICES AND DETERMINANTS. Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 9. SEQUENCES, SERIES, AND PROBABILITY. Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Mathematical Induction. The Binomial Theorem. Counting Principles. Probability. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 7-9. Proofs in Mathematics. P.S. Problem Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A. Review of Fundamental Concepts of Algebra. A.1 Real Numbers and Their Properties. A.2 Exponents and Radicals. A.3 Polynomials and Factoring. A.4 Rational Expressions. A.5 Solving Equations. A.6 Linear Inequalities in One Variable. A.7 Errors and the Algebra of Calculus. APPENDIX B. Concepts in Statistics (Web). B.1 Representing Data. B.2 Analyzing Data. B.3 Modeling Data.

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Book SynopsisSmartly conceived and fast paced, his book offers something for anyone curious about math and its impacts.Trade ReviewThe wide ranging essays touch on history, art, architecture, biology, astrophysics, geology, economics, engineering, and many aspects of everyday life. They are supplemented with helpful graphics and written in a lively and clear style appropriate for non-specialist readers, including high school students. Mathematical Reviews An intriguing, thought provoking and humorous book... Highly entertaining treatises for nature lovers as well as science, mathematics and art enthusiasts. London Mathematical Society Newsletter Henshaw's stories about each formula are interesting, humorous, and oftentimes surprising. The range of formulas in [ An Equation for Every Occasion] is appealing, no matter where one's interests lie... This book is a must for teachers who teach formulas. This book provides both interesting stories and historial context to pass on to students Mathematical Association of America From the links between music and math and the importance of the concept of friction to either the success or failure of athletes to estimating the size of a crowd by understanding principles of density, these applications are not only lively discussions of daily living, but require no prior math knowledge from their readers, making An Equation for Every Occasion a recommended pick for lay audiences interested in math's intersections with real-world concerns. Donovan's Literary Services Recommended. All readers. ChoiceTable of ContentsPreface1. As the Earth Draws the Apple2. And All the Children Are Above Average3. The Lady with the Mystic Smile4. The Heart Has Its Reasons5. AC/DC6. The Doppler Effect7. Do I Look Fat in These Jeans?8. Zeros and Ones9. Tsunami10. When the Chips Are Down11. A Stretch of the Imagination12. Woodstock Nation13. What Is (Pi)?14. No Sweat15. Road Range16. The Bends17. It's Not the Heat, It's the Humidity18. The World's Most Beautiful Equation19. Breaking the Law20. The Mars Curse21. Eureka!22. A Penny Saved . . .23. If I Only Had a Brain24. Because It Was There25. Four Eyes26. Bee Sting27. Here Comes the Sun28. A Leg to Stand On29. Love Is a Roller Coaster30. Loss Factor31. A Slippery Slope32. Transformers33. A House of Cards34. Let There Be Light35. Smarty Pants36. As Old as the Hills37. Can You Hear Me Now?38. Decay Heat39. Zero, One, Infinity40. Terminal Velocity41. Water, Water, Everywhere42. Dog Days43. Body Heat44. Red Hot45. A Bolt from the Blue46. Like Oil and Water47. Fish Story48. Making Waves49. A Drop in the Bucket50. Fracking Unbelievable51. Take Two Aspirins and Call Me in the Morning52. The World's Most Famous EquationBibliographyIndex

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Book SynopsisA fresh approach to topology makes this complex topic easier for students to master. Topologythe branch of mathematics that studies the properties of spaces that remain unaffected by stretching and other distortionscan present significant challenges for undergraduate students of mathematics and the sciences. Understanding Topology aims to change that. The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not. This groundbreaking new text: presents Euclidean, abstract, and basic algebraic topology explains metric topTrade ReviewA perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the textbook's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles, and might reasonably be expected to become a standard reference for teaching backgrounds of topology in the years to come.—Marek Golasinski (Olsztyn), Zentralblatt MathA useful book for undergraduates, with the initial introduction to concepts being at the level of intuition and analogy, followed by mathematical rigour.—John Bartlett CMath MIMA, Mathematics TodayTable of ContentsPrefaceI Euclidean Topology1. Introduction to Topology1.1 Deformations1.2 Topological Spaces2. Metric Topology in Euclidean Space2.1 Distance2.2 Continuity and Homeomorphism2.3 Compactness and Limits2.4 Connectedness2.5 Metric Spaces in General3. Vector Fields in the Plane3.1 Trajectories and Phase Portraits3.2 Index of a Critical Point3.3 *Nullclines and Trapping RegionsII Abstract Topology with Applications4. Abstract Point-Set Topology4.1 The Definition of a Topology4.2 Continuity and Limits4.3 Subspace Topology and Quotient Topology4.4 Compactness and Connectedness4.5 Product and Function Spaces4.6 *The Infinitude of the Primes5. Surfaces5.1 Surfaces and Surfaces-with-Boundary5.2 Plane Models and Words5.3 Orientability5.4 Euler Characteristic6. Applications in Graphs and Knots6.1 Graphs and Embeddings6.2 Graphs, Maps, and Coloring Problems6.3 Knots and Links6.4 Knot ClassificationIII Basic Algebraic Topology7. The Fundamental Group7.1 Algebra of Loops7.2 Fundamental Group as Topological Invariant7.3 Covering Spaces and the Circle7.4 Compact Surfaces and Knot Complements7.5 *Higher Homotopy Groups8. Introduction to Homology8.1 Rational Homology8.2 Integral HomologyAppendixesA. Review of Set Theory and FunctionsA.1 Sets and Operations on SetsA.2 Relations and FunctionsB. Group Theory and Linear AlgebraB.1 GroupsB.2 Linear AlgebraC. Selected SolutionsD. NotationsBibliographyIndex

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Book Synopsis-Preface.-1. The How, When, and Why of Mathematics.- 2. Logically Speaking.- 3.Introducing the Contrapositive and Converse.- 4. Set Notation and Quantifiers.- 5. Proof Techniques.- 6. Sets.- 7. Operations on Sets.- 8. More on Operations on Sets.- 9. The Power Set and the Cartesian Product.- 10. Relations.- 11. Partitions.- 12. Order in the Reals.- 13. Consequences of the Completeness of (Bbb R).- 14. Functions, Domain, and Range.-15. Functions, One-to-One, and Onto.- 16. Inverses.- 17. Images and Inverse Images.- 18. Mathematical Induction.- 19. Sequences.- 20. Convergence of Sequences of Real Numbers.- 21. Equivalent Sets.- 22. Finite Sets and an Infinite Set.- 23. Countable and Uncountable Sets.- 24. The Cantor-Schröder-Bernstein Theorem.- 25. Metric Spaces.- 26. Getting to Know Open and Closed Sets.- 27. Modular Arithmetic.- 28. Fermat's Little Theorem.- 29. Projects.- Appendix.- References.- Index.Trade ReviewFrom the reviews of the second edition:“The book is written in an informal way, which could please the beginners and not offend the more experienced reader. A reader can find a lot of problems for independent study as well as a lot of illustrations encouraging him/her to draw pictures as an important part of the process of mathematical thinking.”—European Mathematical Society, September 2011"Several areas like sets, functions, sequences and convergence are dealt with and several exercises and projects are provided for deepening the understanding. …It is the impression of the author of this review that the book can be particularly strongly recommended for teacher students to enable them to catch and transfer the “essence” of mathematical thinking to their pupils. But also everybody else interested in mathematics will enjoy this very well written book.—Burkhard Alpers (Aalen), zbMATH“The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. … a mathematically-conventional but pedagogically-innovative take on transition courses.” —Allen Stenger, The Mathematical Association of America, September, 2011Table of Contents-Preface. -1. The How, When, and Why of Mathematics.- 2. Logically Speaking.- 3.Introducing the Contrapositive and Converse.- 4. Set Notation and Quantifiers.- 5. Proof Techniques.- 6. Sets.- 7. Operations on Sets.- 8. More on Operations on Sets.- 9. The Power Set and the Cartesian Product.- 10. Relations.- 11. Partitions.- 12. Order in the Reals.- 13. Consequences of the Completeness of (\Bbb R).- 14. Functions, Domain, and Range.- 15. Functions, One-to-One, and Onto.- 16. Inverses.- 17. Images and Inverse Images.- 18. Mathematical Induction.- 19. Sequences.- 20. Convergence of Sequences of Real Numbers.- 21. Equivalent Sets.- 22. Finite Sets and an Infinite Set.- 23. Countable and Uncountable Sets.- 24. The Cantor-Schröder-Bernstein Theorem.- 25. Metric Spaces.- 26. Getting to Know Open and Closed Sets.- 27. Modular Arithmetic.- 28. Fermat’s Little Theorem.- 29. Projects.- Appendix.- References.- Index.

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Book SynopsisThe first three editions of this popular textbook attracteda loyal readership and widespread use. Students find the book to be concise, accessible, andcomplete. Instructors find the book to be clear, authoritative, and dependable.The goal of this new edition is to make real analysis relevant and accessibleto a broad audience of students with diverse backgrounds. Real analysis is a basic tool for all mathematical scientists, ranging from mathematicians to physicists toengineers to researchers in the medical profession. This text aims to be thegenerational touchstone for the subject and the go-to text for developing youngscientists.In this new edition we endeavor to make the book accessible to a broaderaudience. This edition includes more explanation, more elementary examples, and the author stepladders the exercises. Figures are updated and clarified. We make the sections more concise, and omit overly

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Book SynopsisThis book concerns testing hypotheses in non-parametric models. Classical non-parametric tests (goodness-of-fit, homogeneity, randomness, independence) of complete data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed. Table of ContentsPreface xi Terms and Notation xv Chapter 1. Introduction 1 1.1. Statistical hypotheses 1 1.2. Examples of hypotheses in non-parametric models 2 1.3. Statistical tests 5 1.4. P-value 7 1.5. Continuity correction 10 1.6. Asymptotic relative efficiency 13 Chapter 2. Chi-squared Tests 17 2.1. Introduction 17 2.2. Pearson’s goodness-of-fit test: simple hypothesis 17 2.3. Pearson’s goodness-of-fit test: composite hypothesis 26 2.4. Modified chi-squared test for composite hypotheses 34 2.5. Chi-squared test for independence 52 2.6. Chi-squared test for homogeneity 57 2.7. Bibliographic notes 64 2.8. Exercises 64 2.9. Answers 72 Chapter 3. Goodness-of-fit Tests Based on Empirical Processes 77 3.1. Test statistics based on the empirical process 77 3.2. Kolmogorov–Smirnov test 82 3.3. ω2, Cramér–von-Mises and Andersen–Darling tests 86 3.4. Modifications of Kolmogorov–Smirnov, Cramér–von-Mises and Andersen–Darling tests: composite hypotheses 91 3.5. Two-sample tests 98 3.6. Bibliographic notes 104 3.7. Exercises106 3.8. Answers 109 Chapter 4. Rank Tests 111 4.1. Introduction 111 4.2. Ranks and their properties 112 4.3. Rank tests for independence 117 4.4. Randomness tests 139 4.5. Rank homogeneity tests for two independent samples 146 4.6. Hypothesis on median value: the Wilcoxon signed ranks test 168 4.7. Wilcoxon’s signed ranks test for homogeneity of two related samples 180 4.8. Test for homogeneity of several independent samples: Kruskal–Wallis test 181 4.9. Homogeneity hypotheses for k related samples: Friedman test 191 4.10. Independence test based on Kendall’s concordance coefficient 204 4.11. Bibliographic notes 208 4.12. Exercises 209 4.13. Answers 212 Chapter 5. Other Non-parametric Tests 215 5.1. Sign test 215 5.2. Runs test 221 5.3. McNemar’s test 231 5.4. Cochran test 238 5.5. Special goodness-of-fit tests 245 5.6. Bibliographic notes 268 5.7. Exercises 269 5.8. Answers 271 APPENDICES 275 Appendix A. Parametric Maximum Likelihood 277 Appendix B. Notions from the Theory of 281 BBibliography 293 Index 305

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Book SynopsisCuenta con un enfoque integrador, combina el contenido con el entorno de aprendizaje actual, desde la resoluci?n de problemas en clase hasta la tarea en l?nea, utiliza comentarios espec?ficos y tutoriales. M?s amigable para los estudiantes que nunca, el texto incluye nuevos ejercicios ricos en contexto, problemas conceptuales, y pedagog?a educativa s?lida. Las ilustraciones, tablas, cuadros, gr?ficas y los ejemplos detallados trabajados complementan el lenguaje conciso y las instrucciones meticulosas por las cuales Raymond A. Serway y John W. Jewett Jr. son conocidos. Adem?s, WebAssign, el sistema de tareas m?s f?cil de usar del mundo, le proporciona la soluci?n definitiva a sus deberes y necesidades de evaluaci?n para maximizar el ?xito de su curso.

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