Calculus and mathematical analysis Books

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 SynopsisThe unique feature of this compact student''s introduction to Mathematica and the Wolfram Language is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.Trade Review'This book is an easy-to-read introduction to Mathematica. It is interspersed with helpful hints that make interacting with Mathematica more efficient and examples to test the reader's comprehension. This book is good for learning how to use Mathematica to graph functions, perform algebraic manipulation, and approach topics from calculus and linear algebra. This new version shines some light on entity objects and accessing Wolfram's curated data which is needed because their structure is unintuitive and because of their growing prominence in the Wolfram ecosystem. The new final chapter on 3D printing gives readers the tools to quickly design and 3D print physical objects that embody mathematical surfaces. These two additions showcase recent advances in the Wolfram Language and ensure that the whole book remains relevant and up to date.' Christopher Hanusa, Queens College, City University of New York'Mathematica has the power to unravel some of the current mysteries of mathematics – but only if you know how to ask it the right questions. The 3rd edition of The Student's Introduction to Mathematica and the Wolfram Language can be your well-used guide for such exploration. Beginning and experienced Mathematica users will easily learn from the pages of this book especially given the recent changes to Mathematica. Even more, the 3rd edition moves into a new dimension, giving details on 3D printing! Grab one for yourself and another for a student you know.' Tim Chartier, Davidson College, North Carolina'This text, including the exercises and solutions, is written in a student-friendly style … Unlike most tutorial introductions to Mathematica, the authors go to significant lengths to provide explanations and rationales underlying what a newcomer would likely find confusing … I believe that this book would be a useful addition to any student's library in a college or university that uses Mathematica.' Marvin Schaefer, MAA ReviewsTable of ContentsPreface; 1. Getting started; 2. Working with Mathematica®; 3. Functions and their graphs; 4. Algebra; 5. Calculus; 6. Multivariable calculus; 7. Linear algebra; 8. Programming; 9. 3D printing; Index.

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Book SynopsisThe language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications. Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon. This book is the first systematic treatment of the theory of (co)ends. Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science. It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.Table of ContentsPreface; 1. Dinaturality and (co)ends; 2. Yoneda and Kan; 3. Nerves and realisations; 4. Weighted (co)limits; 5. Profunctors; 6. Operads; 7. Higher dimensional (co)ends; Appendix A. Review of category theory; Appendix B; References; Index.

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Book SynopsisDespite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful arTrade Review'an excellent resource for someone trying to enter the field of probabilistic number theory' Bookshelf by Notices of the American Mathematical Society'The book contains many exercises and three appendices presenting the material from analysis, probability and number theory that is used. Certainly the book is a good read for a mathematicians interested in the interaction between probability theory and number theory. The techniques used in the book appear quite advanced to us, so we would recommend the book for students at a graduate but not at an undergraduate level.' Jörg Neunhäuserer, Mathematical ReviewsTable of Contents1. Introduction; 2. Classical probabilistic number theory; 3. The distribution of values of the Riemann zeta function, I; 4. The distribution of values of the Riemann zeta function, II; 5. The Chebychev bias; 6. The shape of exponential sums; 7. Further topics; Appendix A. Analysis; Appendix B. Probability; Appendix C. Number theory; References; Index.

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Book SynopsisMultivariate Analysis Comprehensive Reference Work on Multivariate Analysis and its Applications The first edition of this book, by Mardia, Kent and Bibby, has been used globally for over 40 years. This second edition brings many topics up to date, with a special emphasis on recent developments. A wide range of material in multivariate analysis is covered, including the classical themes of multivariate normal theory, multivariate regression, inference, multidimensional scaling, factor analysis, cluster analysis and principal component analysis. The book also now covers modern developments such as graphical models, robust estimation, statistical learning, and high-dimensional methods. The book expertly blends theory and application, providing numerous worked examples and exercises at the end of each chapter. The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are appendices which provide a background in matrix algebra, a summary of univariate statistics, a collection of statistical tables and a discussion of computational aspects. The work includes coverage of: Basic properties of random vectors, copulas, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Discriminant analysis, cluster analysis, and multidimensional scaling New advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data Although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, the book will also be of interest to research workers and applied scientists.

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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 easy way to conquer calculus Calculus is hardno doubt about itand students often need help understanding or retaining the key concepts covered in class. Calculus Workbook For Dummies serves up the concept review and practice problems with an easy-to-follow, practical approach. Plus, you'll get free access to a quiz for every chapter online. With a wide variety of problems on everything covered in calculus class, you'll find multiple examples of limits, vectors, continuity, differentiation, integration, curve-sketching, conic sections, natural logarithms, and infinite series.Plus, you'll get hundreds of practice opportunities with detailed solutions that will help you master the math that is critical for scoring your highest in calculus. Review key conceptsTake hundreds of practice problemsGet access to free chapter quizzes onlineUse as a classroom supplement or with a tutor Get ready to quickly and easily increase your confidence and improve your skills in calculus.Table of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Part 1: Pre-Calculus Review 5 Chapter 1: Getting Down to Basics: Algebra and Geometry 7 Fraction Frustration 7 Misc. Algebra: You Know, Like Miss South Carolina 9 Geometry: When Am I Ever Going to Need It? 11 Solutions for This Easy, Elementary Stuff 16 Chapter 2: Funky Functions and Tricky Trig 25 Figuring Out Your Functions 25 Trigonometric Calisthenics 29 Solutions to Functions and Trigonometry 33 Part 2: Limits and Continuity 41 Chapter 3: A Graph Is Worth a Thousand Words: Limits and Continuity 43 Digesting the Definitions: Limit and Continuity 44 Taking a Closer Look: Limit and Continuity Graphs 46 Solutions for Limits and Continuity 50 Chapter 4: Nitty-Gritty Limit Problems 53 Solving Limits with Algebra 54 Pulling Out Your Calculator: Useful “Cheating” 59 Making Yourself a Limit Sandwich 61 Into the Great Beyond: Limits at Infinity 63 Solutions for Problems with Limits 67 Part 3: Differentiation 77 Chapter 5: Getting the Big Picture: Differentiation Basics 79 The Derivative: A Fancy Calculus Word for Slope and Rate 79 The Handy-Dandy Difference Quotient 81 Solutions for Differentiation Basics 84 Chapter 6: Rules, Rules, Rules: The Differentiation Handbook 89 Rules for Beginners 89 Giving It Up for the Product and Quotient Rules 92 Linking Up with the Chain Rule 94 What to Do with Y’s: Implicit Differentiation 98 Getting High on Calculus: Higher Order Derivatives 101 Solutions for Differentiation Problems 103 Chapter 7: Analyzing Those Shapely Curves with the Derivative 117 The First Derivative Test and Local Extrema 117 The Second Derivative Test and Local Extrema 120 Finding Mount Everest: Absolute Extrema 122 Smiles and Frowns: Concavity and Inflection Points 126 The Mean Value Theorem: Go Ahead, Make My Day 129 Solutions for Derivatives and Shapes of Curves 131 Chapter 8: Using Differentiation to Solve Practical Problems 147 Optimization Problems: From Soup to Nuts 147 Problematic Relationships: Related Rates 150 A Day at the Races: Position, Velocity, and Acceleration 153 Solutions to Differentiation Problem Solving 157 Chapter 9: Even More Practical Applications of Differentiation 173 Make Sure You Know Your Lines: Tangents and Normals 173 Looking Smart with Linear Approximation 177 Calculus in the Real World: Business and Economics 179 Solutions to Differentiation Problem Solving 183 Part 4: Integration and Infinite Series 191 Chapter 10: Getting into Integration 193 Adding Up the Area of Rectangles: Kid Stuff 193 Sigma Notation and Riemann Sums: Geek Stuff 196 Close Isn’t Good Enough: The Definite Integral and Exact Area 200 Finding Area with the Trapezoid Rule and Simpson’s Rule 202 Solutions to Getting into Integration 205 Chapter 11: Integration: Reverse Differentiation 213 The Absolutely Atrocious and Annoying Area Function 213 Sound the Trumpets: The Fundamental Theorem of Calculus 216 Finding Antiderivatives: The Guess-and-Check Method 219 The Substitution Method: Pulling the Switcheroo 221 Solutions to Reverse Differentiation Problems 225 Chapter 12: Integration Rules for Calculus Connoisseurs 229 Integration by Parts: Here’s How u du It 229 Transfiguring Trigonometric Integrals 233 Trigonometric Substitution: It’s Your Lucky Day! 235 Partaking of Partial Fractions 237 Solutions for Integration Rules 241 Chapter 13: Who Needs Freud? Using the Integral to Solve Your Problems 255 Finding a Function’s Average Value 255 Finding the Area between Curves 256 Volumes of Weird Solids: No, You’re Never Going to Need This 258 Arc Length and Surfaces of Revolution 265 Solutions to Integration Application Problems 268 Chapter 14: Infinite (Sort of) Integrals 277 Getting Your Hopes Up with L’Hôpital’s Rule 278 Disciplining Those Improper Integrals 280 Solutions to Infinite (Sort of) Integrals 283 Chapter 15: Infinite Series: Welcome to the Outer Limits 287 The Nifty nth Term Test 287 Testing Three Basic Series 289 Apples and Oranges . . . and Guavas: Three Comparison Tests 291 Ratiocinating the Two “R” Tests 295 He Loves Me, He Loves Me Not: Alternating Series 297 Solutions to Infinite Series 299 Part 5: The Part of Tens 309 Chapter 16: Ten Things about Limits, Continuity, and Infinite Series 311 The 33333 Mnemonic 311 First 3 over the “l”: 3 parts to the definition of a limit 312 Fifth 3 over the “l”: 3 cases where a limit fails to exist 312 Second 3 over the “i”: 3 parts to the definition of continuity 312 Fourth 3 over the “i”: 3 cases where continuity fails to exist 312 Third 3 over the “m”: 3 cases where a derivative fails to exist 313 The 13231 Mnemonic 313 First 1: The nth term test of divergence 313 Second 1: The nth term test of convergence for alternating series 313 First 3: The three tests with names 313 Second 3: The three comparison tests 314 The 2 in the middle: The two R tests 314 Chapter 17: Ten Things You Better Remember about Differentiation 315 The Difference Quotient 315 The First Derivative Is a Rate 315 The First Derivative Is a Slope 316 Extrema, Sign Changes, and the First Derivative 316 The Second Derivative and Concavity 316 Inflection Points and Sign Changes in the Second Derivative 316 The Product Rule 317 The Quotient Rule 317 Linear Approximation 317 “PSST,” Here’s a Good Way to Remember the Derivatives of Trig Functions 317 Index 319

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Book SynopsisA valuable new edition of a standard reference The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data. Adding to the value in the new edition is: Illustrations of the use of R software to perform all the analyses in the book A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis New sections in many chapters introducing the Bayesian approach for the methodTable of ContentsPreface ix About the Companion Website xiii 1 Introduction 1 1.1 Categorical Response Data 1 1.2 Probability Distributions for Categorical Data 3 1.3 Statistical Inference for a Proportion 5 1.4 Statistical Inference for Discrete Data 10 1.5 Bayesian Inference for Proportions * 13 1.6 Using R Software for Statistical Inference about Proportions * 17 Exercises 21 2 Analyzing Contingency Tables 25 2.1 Probability Structure for Contingency Tables 26 2.2 Comparing Proportions in 2 × 2 Contingency Tables 29 2.3 The Odds Ratio 31 2.4 Chi-Squared Tests of Independence 36 2.5 Testing Independence for Ordinal Variables 42 2.6 Exact Frequentist and Bayesian Inference * 46 2.7 Association in Three-Way Tables 52 Exercises 56 3 Generalized Linear Models 65 3.1 Components of a Generalized Linear Model 66 3.2 Generalized Linear Models for Binary Data 68 3.3 Generalized Linear Models for Counts and Rates 72 3.4 Statistical Inference and Model Checking 76 3.5 Fitting Generalized Linear Models 82 Exercises 84 4 Logistic Regression 89 4.1 The Logistic Regression Model 89 4.2 Statistical Inference for Logistic Regression 94 4.3 Logistic Regression with Categorical Predictors 98 4.4 Multiple Logistic Regression 102 4.5 Summarizing Effects in Logistic Regression 107 4.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation 110 Exercises 113 5 Building and Applying Logistic Regression Models 123 5.1 Strategies in Model Selection 123 5.2 Model Checking 130 5.3 Infinite Estimates in Logistic Regression 136 5.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression * 140 5.5 Alternative Link Functions: Linear Probability and Probit Models * 145 5.6 Sample Size and Power for Logistic Regression * 150 Exercises 151 6 Multicategory Logit Models 159 6.1 Baseline-Category Logit Models for Nominal Responses 159 6.2 Cumulative Logit Models for Ordinal Responses 167 6.3 Cumulative Link Models: Model Checking and Extensions * 176 6.4 Paired-Category Logit Modeling of Ordinal Responses * 184 Exercises 187 7 Loglinear Models for Contingency Tables and Counts 193 7.1 Loglinear Models for Counts in Contingency Tables 194 7.2 Statistical Inference for Loglinear Models 200 7.3 The Loglinear – Logistic Model Connection 207 7.4 Independence Graphs and Collapsibility 210 7.5 Modeling Ordinal Associations in Contingency Tables 214 7.6 Loglinear Modeling of Count Response Variables * 217 Exercises 221 8 Models for Matched Pairs 227 8.1 Comparing Dependent Proportions for Binary Matched Pairs 228 8.2 Marginal Models and Subject-Specific Models for Matched Pairs 230 8.3 Comparing Proportions for Nominal Matched-Pairs Responses 235 8.4 Comparing Proportions for Ordinal Matched-Pairs Responses 239 8.5 Analyzing Rater Agreement * 243 8.6 Bradley–Terry Model for Paired Preferences * 247 Exercises 249 9 Marginal Modeling of Correlated, Clustered Responses 253 9.1 Marginal Models Versus Subject-Specific Models 254 9.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach 255 9.3 Marginal Modeling for Clustered Multinomial Responses 260 9.4 Transitional Modeling, Given the Past 263 9.5 Dealing with Missing Data * 266 Exercises 268 10 Random Effects: Generalized Linear Mixed Models 273 10.1 Random Effects Modeling of Clustered Categorical Data 273 10.2 Examples: Random Effects Models for Binary Data 278 10.3 Extensions to Multinomial Responses and Multiple Random Effect Terms 284 10.4 Multilevel (Hierarchical) Models 288 10.5 Latent Class Models * 291 Exercises 295 11 Classification and Smoothing * 299 11.1 Classification: Linear Discriminant Analysis 300 11.2 Classification: Tree-Based Prediction 302 11.3 Cluster Analysis for Categorical Responses 306 11.4 Smoothing: Generalized Additive Models 310 11.5 Regularization for High-Dimensional Categorical Data (Large p) 313 Exercises 321 12 A Historical Tour of Categorical Data Analysis * 325 Appendix: Software for Categorical Data Analysis 331 A.1 R for Categorical Data Analysis 331 A.2 SAS for Categorical Data Analysis 332 A.3 Stata for Categorical Data Analysis 342 A.4 SPSS for Categorical Data Analysis 346 Brief Solutions to Odd-Numbered Exercises 349 Bibliography 363 Examples Index 365 Subject Index 369

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Book SynopsisTimely update of a popular edition on permutation testing with numerous case studies included throughout The newly revised and updated Second Edition of Permutation Tests for Complex Data describes permutation tests from the point of view of experimental design, with methodological details and illustrating the process of devising an appropriate permutation test through case studies. In addition to the text, this book includes two open source packages for permutation tests in Python and R which include a comprehensive code base to implement common permutation tests as well as code to implement each of the book's case studies. The focus of this book is the permutation approach to a variety of univariate and multivariate problems of hypothesis testing in a typical nonparametric framework. The book examines the most up-to-date methodologies of univariate and multivariate permutation testing, includes real case studies from both experimental and observational studies, and presents and discu

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Book SynopsisA concise, straightforward overview of research design and analysis, helping readers form a general basis for designing and conducting research The practice of designing and analyzing research continues to evolve with advances in technology that enable greater technical analysis of datastrengthening the ability of researchers to study the interventions and relationships of factors and assisting consumers of research to understand and evaluate research reports. Research Design and Analysis is an accessible, wide-ranging overview of how to design, conduct, analyze, interpret, and present research. This book helps those in the sciences conduct their own research without requiring expertise in statistics and related fields and enables informed reading of published research. Requiring no background in statistics, this book reviews the purpose, ethics, and rules of research, explains the fundamentals of research design and validity, and describes how to select Table of ContentsList of Figures xiii List of Tables xv Introduction xix Section 1 The Purpose, Ethics, and Rules of Research 1 1 The Purpose and Ethics of Research 3 1.1 The Purpose and Risks of Research 3 1.2 History of Harm to Humans 4 1.3 Ethical Issues in the Social Sciences 9 1.4 History of Harm to Animal Subjects in Research 10 1.4.1 Summary 12 1.5 Ethics, Principles, and Guidelines 12 1.6 Statutes and Regulations Protecting Humans and Animals in Research 16 1.7 More About Informed Consent 18 1.8 The Importance of Freedom to Withdraw 22 1.9 Separation of Provider–Researcher Role 22 1.10 Undue Influence 24 1.11 Anonymity 24 1.12 Summary 25 Section 2 Basic Research Designs and Validity 27 2 Research Validity 29 2.1 Internal Validity 30 2.1.1 History 30 2.1.2 Maturation 31 2.1.3 Measurement Error 32 2.1.4 Selection Bias and Random Assignment 33 2.1.5 Attrition 35 2.1.6 Experimenter Bias 35 2.1.7 Expectation 36 2.1.8 Sensitization and Practice Effects 36 2.1.9 Incorrect Conclusions of Causality 37 2.2 External Validity 37 2.3 Summary 45 3 Research Designs 47 3.1 The Lingo 47 3.2 Between‐Subjects Designs 49 3.2.1 More Examples of Between‐Subjects Designs 49 3.2.2 Statistical Analyses for Between‐Subjects Designs 50 3.3 Within‐Subjects Designs/Repeated Measures 52 3.3.1 Statistical Analyses for Within‐Subjects Designs 53 3.4 Between–Within Subjects Designs (Mixed Factorial/Split‐Plot Designs) 54 3.4.1 Statistical Analyses for Between–Within Subjects Designs 55 3.5 Latin Square Designs 57 3.5.1 Summary 59 3.5.2 Double Latin Square Designs 59 3.5.3 Graeco‐Latin and Hyper Graeco‐Latin Square Designs 59 3.6 Nesting 60 3.7 Matching 60 3.8 Blocking 61 3.9 Nonexperimental Research 62 3.10 Case Studies 62 3.11 Summary 64 Section 3 The Nuts and Bolts of Data Analysis 65 4 Interpretation 67 4.1 Probability and Significance 67 4.2 The Null Hypothesis, Type I (α), and Type II (β) Errors 68 4.3 Power 69 4.4 Managing Error Variance to Improve Power 71 4.5 Power Analyses 72 4.6 Effect Size 72 4.7 Confidence Intervals and Precision 74 4.8 Summary 76 5 Parametric Statistical Techniques 77 5.1 A Little More Lingo 77 5.1.1 Population Parameters Versus Sample Statistics 78 5.1.2 Data 78 5.1.2.1 Ratio and Interval Data 78 5.1.2.2 Ordinal Data 78 5.1.2.3 Nominal Data 79 5.1.3 Central Tendency 79 5.1.3.1 Mode 79 5.1.3.2 Median 79 5.1.3.3 Mean 86 5.1.4 Distributions 86 5.1.5 Dependent Variables 92 5.1.5.1 To Scale or Not to Scale 95 5.1.6 Summary 97 5.2 t Tests 97 5.2.1 Independent Samples t Tests 97 5.2.2 Matched Group Comparison 98 5.2.3 Assumptions of t Tests 99 5.2.4 More Examples of Studies Employing t Tests 100 5.2.5 Statistical Software Packages for Conducting t Tests 101 5.3 The NOVAs and Mixed Linear Model Analysis 101 5.3.1 ANOVA 102 5.3.1.1 ANOVA with a Multifactorial Design 104 5.3.1.2 Main Effects and Interactions 104 5.3.1.3 More Illustrations of Interactions and Main Effects 106 5.3.1.4 Assumptions of ANOVA 107 5.3.2 ANCOVA 109 5.3.3 MANOVA/MANCOVA 111 5.3.4 Statistical Software Packages for Conducting ANOVA/ANCOVA/MANOVA 114 5.3.5 Repeated Measures: ANOVA‐RM and Mixed Linear Model Analysis 114 5.3.5.1 ANOVA‐RM 114 5.3.5.2 Mixed Linear Model Analysis 116 5.3.5.3 ANCOVA 117 5.3.5.4 Statistical Software Packages for Conducting Repeated Measures Analyses 117 5.3.6 Summary 119 5.4 Correlation and Regression 120 5.4.1 Correlation and Multiple Correlation 120 5.4.2 Regression and Multiple Regression 121 5.4.3 Statistical Software Packages for Conducting Correlation and Regression 124 5.5 Logistic Regression 126 5.5.1 Statistical Software Packages for Conducting Logistic Regression 128 5.6 Discriminant Function Analysis 128 5.6.1 Statistical Software Packages for Conducting Discriminant Function Analysis 128 5.7 Multiple Comparisons 129 5.8 Summary 131 6 Nonparametric Statistical Techniques 133 6.1 Chi‐Square 134 6.1.1 Statistical Software Packages for Conducting Chi‐Square 136 6.2 Median Test 137 6.2.1 Statistical Software Packages for Conducting Median Tests 137 6.3 Phi Coefficient 137 6.3.1 Statistical Software Packages for Calculating the Phi Coefficient 139 6.4 Mann–Whitney U Test (Wilcoxon Rank Sum Test) 139 6.4.1 Statistical Software Packages for Conducting a Mann–Whitney U Test 141 6.5 Sign Test and Wilcoxon Signed‐rank Test 142 6.5.1 Statistical Software Packages for Conducting Sign Tests 143 6.6 Kruskal–Wallis Test 144 6.6.1 Statistical Software Packages for Conducting a Kruskal–Wallis Test 144 6.7 Rank‐Order Correlation 145 6.7.1 Statistical Software Packages for Conducting Rank‐order Correlations 146 6.8 Summary 147 7 Meta‐Analytic Studies 149 7.1 The File Drawer Effect 150 7.2 Analyzing the Meta‐Analytic Data 151 7.3 How to Read and Interpret a Paper Reporting a Meta‐Analysis 153 7.4 Statistical Software Packages for Conducting Meta‐Analyses 155 7.5 Summary 155 Section 4 Reporting, Understanding, and Communicating Research Findings 157 8 Disseminating Your Research Findings 159 8.1 Preparing a Research Report 159 8.2 Presenting Your Findings at a Conference 167 8.3 Summary 168 9 Concluding Remarks 169 9.1 Why is it Important to Understand Research Design and Analysis as a Consumer? 169 9.2 Research Ethics and Responsibilities of Journalists 175 9.3 Responsibilities of Researchers 177 9.4 Conclusion 178 Appendix A Data Sets and Databases 179 Appendix B Statistical Analysis Packages 195 Appendix C Helpful Statistics Resources 217 Glossary 221 References 233 Index 243

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Book SynopsisPractice your way to a higher grade in Calculus! Calculus is a hands-on skill. You've gotta use it or lose it. And the best way to get the practice you need to develop your mathematical talents is Calculus: 1001 Practice Problems For Dummies. The perfect companion to Calculus For Dummiesand your class this book offers readers challenging practice problems with step-by-step and detailed answer explanations and narrative walkthroughs. You'll get free access to all 1,001 practice problems online so you can create your own study sets for extra-focused learning. Readers will also find: A useful course supplement and resource for students in high school and college taking Calculus IFree, one-year access to all practice problems online, for on-the-go study and practiceAn excellent preparatory resource for faster-paced college classes Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) is an essential resource for high school and college students looking for more practice and extra help with this challenging math subject. Calculus: 1001 Practice Problems For Dummies (9781119883654) was previously published as 1,001 Calculus Practice Problems For Dummies (9781118496718). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.Table of ContentsIntroduction 1 Part 1: The Questions 5 Chapter 1: Algebra Review 7 Chapter 2: Trigonometry Review 17 Chapter 3: Limits and Rates of Change 29 Chapter 4: Derivative Basics 43 Chapter 5: The Product, Quotient, and Chain Rules 49 Chapter 6: Exponential and Logarithmic Functions and Tangent Lines 55 Chapter 7: Implicit Differentiation 59 Chapter 8: Applications of Derivatives 63 Chapter 9: Areas and Riemann Sums 75 Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem 79 Chapter 11: Applications of Integration 87 Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L’Hôpital’s Rule 101 Chapter 13: U-Substitution and Integration by Parts 109 Chapter 14: Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions 115 Chapter 15: Improper Integrals and More Approximating Techniques 123 Part 2: The Answers 127 Chapter 16: Answers and Explanations 129 Index 581

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Book SynopsisTable of ContentsIntroduction 1 Part 1: Making Friends with the Calculator 5 Chapter 1: Starting with the Basics 7 Chapter 2: Doing Basic Arithmetic 25 Chapter 3: Dealing with Fractions 35 Chapter 4: Solving Equations 41 Part 2: Taking Your Calculator Relationship to the Next Level 53 Chapter 5: Working with Complex Numbers 55 Chapter 6: Understanding the Math Menu and Submenus 61 Chapter 7: The Angle and Test Menus 69 Chapter 8: Creating and Editing Matrices 79 Part 3: Graphing and Analyzing Functions 89 Chapter 9: Graphing Functions 91 Chapter 10: Exploring Functions 111 Chapter 11: Evaluating Functions 127 Chapter 12: Graphing Inequalities 143 Chapter 13: Graphing Parametric Equations 155 Chapter 14: Graphing Polar Equations 163 Part 4: Working with Probability and Statistics 173 Chapter 15: Probability 175 Chapter 16: Dealing with Statistical Data 183 Chapter 17: Analyzing Statistical Data 193 Part 5: Doing More with Your Calculator 209 Chapter 18: Communicating with a PC Using TI Connect CE Software 211 Chapter 19: Communicating Between Calculators 221 Chapter 20: Fun with Images 227 Chapter 21: Managing Memory 231 Part 6: The Part of Tens 237 Chapter 22: Ten Essential Skills 239 Chapter 23: Ten Common Errors 243 Chapter 24: Ten Common Error Messages 249 Part 7: Appendices 253 Appendix A: Creating Calculator Programs 255 Appendix B: Controlling Program Input and Output 259 Appendix C: Controlling Program Flow 269 Appendix D: Introducing Python Programming 281 Appendix E: Mastering the Basics of Python Programming 287 Index 293

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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 SynopsisCatrin Radcliffe is a tutor of mathematics and statistics at Oxford Brookes University, UK.Table of ContentsIntroduction PART 1: GETTING STARTED 1. What does your assignment ask you to do? 2. How will you do it? 3. Defining your research question 4. Tips for designing your questionnaire 5. How to enter your data into a spreadsheet PART 2: UNDERSTANDING AND DESCRIBING YOUR DATA 6. What type of data do you have? 7. Descriptive statistics 8. What plot should you use? PART 3: HOW DO STATISTICAL TESTS WORK? 9. What is a statistical hypothesis? 10. Using probability distributions in statistical tests 11. Statistics, "errors" and interpretation PART 4: WHAT STATISTICAL TEST DO YOU NEED? 12. The statistics signpost 13. Statistical flowcharts 14. Case studies PART 5: THE STATISTICAL PROCESS 15. You the researcher 16. You the interpreter Symbols explained Useful resources References Index.

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Book SynopsisAimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.Table of ContentsSets, mappings, countability and choice. Metric spaces and normed spaces. Completeness and applications. Topological spaces and continuity. Compactness and sequential compactness. The Lebesgue measure on the Euclidean space. Measure theory on general spaces. The Lebesgue integration theory. The class of Lebesgue functional spaces. Inner product spaces and Hilbert spaces. Linear operators on normed spaces. Weak topologies on Banach spaces. Weak* topologies and compactness. Functional properties of the Lebesgue spaces. Solutions to the exercises.

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Book SynopsisTable of ContentsP. Prerequisites: Fundamental Concepts of Algebra P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation P.3 Radicals and Rational Exponents P.4 Polynomials Mid-Chapter Check Point P.5 Factoring Polynomials P.6 Rational Expressions SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER P TEST 1. Equations and Inequalities 1.1 Graphs and Graphing Utilities 1.2 Linear Equations and Rational Equations 1.3 Models and Applications 1.4 Complex Numbers 1.5 Quadratic Equations Mid-Chapter Check Point 1.6 Other Types of Equations 1.7 Linear Inequalities and Absolute Value Inequalities SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 1 TEST 2. Functions and Graphs 2.1 Basics of Functions and Their Graphs 2.2 More on Functions and Their Graphs 2.3 Linear Functions and Slope 2.4 More on Slope Mid-Chapter Check Point 2.5 Transformations of Functions 2.6 Combinations of Functions; Composite Functions 2.7 Inverse Functions 2.8 Distance and Midpoint Formulas; Circles SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 2 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2) 3. Polynomial and Rational Functions 3.1 Quadratic Functions 3.2 Polynomial Functions and Their Graphs 3.3 Dividing Polynomials; Remainder and Factor Theorems 3.4 Zeros of Polynomial Functions Mid-Chapter Check Point 3.5 Rational Functions and Their Graphs 3.6 Polynomial and Rational Inequalities 3.7 Modeling Using Variation SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 3 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3) 410 4. Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Properties of Logarithms Mid-Chapter Check Point 4.4 Exponential and Logarithmic Equations 4.5 Exponential Growth and Decay; Modeling Data SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 4 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4) 5. Systems of Equations and Inequalities 5.1 Systems of Linear Equations in Two Variables 5.2 Systems of Linear Equations in Three Variables 5.3 Partial Fractions 5.4 Systems of Nonlinear Equations in Two Variables Mid-Chapter Check Point 5.5 Systems of Inequalities 5.6 Linear Programming SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 5 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5) 6. Matrices and Determinants 6.1 Matrix Solutions to Linear Systems 6.2 Inconsistent and Dependent Systems and Their Applications 6.3 Matrix Operations and Their Applications Mid-Chapter Check Point 6.4 Multiplicative Inverses of Matrices and Matrix Equations 6.5 Determinants and Cramer's Rule SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 6 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-6) 7. Conic Sections 7.1 The Ellipse 7.2 The Hyperbola Mid-Chapter Check Point 7.3 The Parabola SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 7 TEST

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Book SynopsisTable of Contents1. A Review of Basic Concepts (Optional) 1.1 Statistics and Data 1.2 Populations, Samples, and Random Sampling 1.3 Describing Qualitative Data 1.4 Describing Quantitative Data Graphically 1.5 Describing Quantitative Data Numerically 1.6 The Normal Probability Distribution 1.7 Sampling Distributions and the Central Limit Theorem 1.8 Estimating a Population Mean 1.9 Testing a Hypothesis About a Population Mean 1.10 Inferences About the Difference Between Two Population Means 1.11 Comparing Two Population Variances 2. Introduction to Regression Analysis 2.1 Modeling a Response 2.2 Overview of Regression Analysis 2.3 Regression Applications 2.4 Collecting the Data for Regression 3. Simple Linear Regression 3.1 Introduction 3.2 The Straight-Line Probabilistic Model 3.3 Fitting the Model: The Method of Least Squares 3.4 Model Assumptions 3.5 An Estimator of s2 3.6 Assessing the Utility of the Model: Making Inferences About the Slope ß1 3.7 The Coefficient of Correlation 3.8 The Coefficient of Determination 3.9 Using the Model for Estimation and Prediction 3.10 A Complete Example 3.11 Regression Through the Origin (Optional) Case Study 1: Legal Advertising--Does It Pay? 4. Multiple Regression Models 4.1 General Form of a Multiple Regression Model 4.2 Model Assumptions 4.3 A First-Order Model with Quantitative Predictors 4.4 Fitting the Model: The Method of Least Squares 4.5 Estimation of s2, the Variance of e 4.6 Testing the Utility of a Model: The Analysis of Variance F-Test 4.7 Inferences About the Individual ß Parameters 4.8 Multiple Coefficients of Determination: R2 and R2adj 4.9 Using the Model for Estimation and Prediction 4.10 An Interaction Model with Quantitative Predictors 4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor 4.12 More Complex Multiple Regression Models (Optional) 4.13 A Test for Comparing Nested Models 4.14 A Complete Example Case Study 2: Modeling the Sale Prices of Residential Properties in Four Neighborhoods 5. Principles of Model Building 5.1 Introduction: Why Model Building is Important 5.2 The Two Types of Independent Variables: Quantitative and Qualitative 5.3 Models with a Single Quantitative Independent Variable 5.4 First-Order Models with Two or More Quantitative Independent Variables 5.5 Second-Order Models with Two or More Quantitative Independent Variables 5.6 Coding Quantitative Independent Variables (Optional) 5.7 Models with One Qualitative Independent Variable 5.8 Models with Two Qualitative Independent Variables 5.9 Models with Three or More Qualitative Independent Variables 5.10 Models with Both Quantitative and Qualitative Independent Variables 5.11 External Model Validation 6. Variable Screening Methods 6.1 Introduction: Why Use a Variable-Screening Method? 6.2 Stepwise Regression 6.3 All-Possible-Regressions Selection Procedure 6.4 Caveats Case Study 3: Deregulation of the Intrastate Trucking Industry 7. Some Regression Pitfalls 7.1 Introduction 7.2 Observational Data Versus Designed Experiments 7.3 Parameter Estimability and Interpretation 7.4 Multicollinearity 7.5 Extrapolation: Predicting Outside the Experimental Region 7.6 Variable Transformations 8. Residual Analysis 8.1 Introduction 8.2 Plotting Residuals 8.3 Detecting Lack of Fit 8.4 Detecting Unequal Variances 8.5 Checking the Normality Assumption 8.6 Detecting Out

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Book SynopsisMarvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999.Table of ContentsR. Functions, Graphs, and Models R.1 Graphs and Equations R.2 Functions and Models R.3 Finding Domain and Range R.4 Slope and Linear Functions R.5 Nonlinear Functions and Models R.6 Mathematical Modeling and Curve Fitting Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Average Price of a Movie Ticket 1. Differentiation 1.1 Limits: A Numerical and Graphical Approach 1.2 Algebraic Limits and Continuity 1.3 Average Rates of Change 1.4 Differentiation Using Limits of Difference Quotients 1.5 The Power and Sum—Difference Rules 1.6 The Product and Quotient Rules 1.7 The Chain Rule 1.8 Higher-Order Derivatives Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Path of a Baseball: The Tale of the Tape 2. Applications of Differentiation 2.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 2.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 2.3 Graph Sketching: Asymptotes and Rational Functions 2.4 Using Derivatives to Find Absolute Maximum and Minimum Values 2.5 Maximum—Minimum Problems; Business, Economics, and General Applications 2.6 Marginals and Differentials 2.7 Elasticity of Demand 2.8 Implicit Differentiation and Related Rates Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Maximum Sustainable Harvest 3. Exponential and Logarithmic Functions 3.1 Exponential Functions 3.2 Logarithmic Functions 3.3 Applications: Uninhibited and Limited Growth Models 3.4 Applications: Decay 3.5 The Derivatives of ax and loga x 3.6 A Business Application: Amortization Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–The Business of Motion Picture Revenue and DVD Release 4. Integration 4.1 Antidifferentiation 4.2 Antiderivatives as Areas 4.3 Area and Definite Integrals 4.4 Properties of Definite Integrals 4.5 Integration Techniques: Substitution 4.6 Integration Techniques: Integration by Parts 4.7 Integration Techniques: Tables Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Business: Distribution of Wealth 5. Applications of Integration 5.1 Consumer Surplus and Producer Surplus 5.2 Integrating Growth and Decay Models 5.3 Improper Integrals 5.4 Probability 5.5 Probability: Expected Value; The Normal Distribution 5.6 Volume 5.7 Differential Equations Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Curve Fitting and Volumes of Containers 6. Functions of Several Variables 6.1 Functions of Several Variables 6.2 Partial Derivatives 6.3 Maximum—Minimum Problems 6.4 An Application: The Least-Squares Technique 6.5 Constrained Optimization 6.6 Double Integrals Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Minimizing Employees’ Travel Time in a Building Cumulative Revi

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Book SynopsisTable of Contents R. Algebra Reference R-1 Polynomials R-2 Factoring R-3 Rational Expressions R-4 Equations R-5 Inequalities R-6 Exponents R-7 Radicals 1. Linear Functions 2. Nonlinear Functions 3. The Derivative 4. Calculating the Derivative 5. Graphs and the Derivative 6. Applications of the Derivative 7. Integration 8. Further Techniques and Applications of Integration 9. Multivariable Calculus 10. Differential Equations 11. Probability and Calculus 12. Sequences and Series 13. The Trigonometric Functions Tables Answers to Selected Exercises Photo Acknowledgements Index

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Book SynopsisThis package includes MyMathLab.   For freshman/sophomore, 2-semester (2-3 quarter) courses covering applied calculus for students in business, economics, social sciences, or life sciences.   Calculus with Applications, Eleventh Edition by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to help them learn the material, such as Warm-Up Exercises and added help text within examples.   This package includes MyMathLab, an online homework, tutorial, and assessment program designed to work with this text to personalize learning and improve results. With a wide range of inte

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Book SynopsisTable of Contents1. Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 2. Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 3. Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 4. Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 5. Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 7. Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 8. Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions

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Book SynopsisJoel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking. Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey art

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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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Book SynopsisIn recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves both as a starting point for researchers and graduate students in computer science, mathematics, and statistics trying to get into the field and as an invaluable reference for future research.Table of Contents1. The modern mathematics of deep learning Julius Berner, Philipp Grohs, Gitta Kutyniok and Philipp Petersen; 2. Generalization in deep learning Kenji Kawaguchi, Leslie Pack Kaelbling, and Yoshua Bengio; 3. Expressivity of deep neural networks Ingo Gühring, Mones Raslan and Gitta Kutyniok; 4. Optimization landscape of neural networks René Vidal, Zhihui Zhu and Benjamin D. Haeffele; 5. Explaining the decisions of convolutional and recurrent neural networks Wojciech Samek, Leila Arras, Ahmed Osman, Grégoire Montavon and Klaus-Robert Müller; 6. Stochastic feedforward neural networks: universal approximation Thomas Merkh and Guido Montúfar; 7. Deep learning as sparsity enforcing algorithms A. Aberdam and J. Sulam; 8. The scattering transform Joan Bruna; 9. Deep generative models and inverse problems Alexandros G. Dimakis; 10. A dynamical systems and optimal control approach to deep learning Weinan E, Jiequn Han and Qianxiao Li; 11. Bridging many-body quantum physics and deep learning via tensor networks Yoav Levine, Or Sharir, Nadav Cohen and Amnon Shashua.

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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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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 SynopsisTable of ContentsP. PREPARATION FOR CALCULUS. Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Review of Trigonometric Functions. Review Exercises. P.S. Problem Solving. 1. LIMITS AND THEIR PROPERTIES. A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits. Section Project: Graphs and Limits of Trigonometric Functions. Review Exercises. P.S. Problem Solving. 2. DIFFERENTIATION. The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Section Project: Optical Illusions. Related Rates. Review Exercises. P.S. Problem Solving. 3. APPLICATIONS OF DIFFERENTIATION. Extrema on an Interval. Rolle"s Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Section Project: Even Fourth-Degree Polynomials. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Section Project: Minimum Time. Newton"s Method. Differentials. Review Exercises. P.S. Problem Solving. 4. INTEGRATION. Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Section Project: Demonstrating the Fundamental Theorem. Integration by Substitution. Review Exercises. P.S. Problem Solving. 5. LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS. The Natural Logarithmic Function: Differentiation. The Natural Logarithmic Function: Integration. Inverse Functions. Exponential Functions: Differentiation and Integration. Bases Other than e and Applications. Section Project: Using Graphing Utilities to Estimate Slope. Indeterminate Forms and L'Hopital's Rule. Inverse Trigonometric Functions: Differentiation. Inverse Trigonometric Functions: Integration. Hyperbolic Functions. Section Project: Mercator Map. Review Exercises. P.S. Problem Solving. 6. DIFFERENTIAL EQUATIONS. Slope Fields and Euler"s Method. Growth and Decay. Separation of Variables and the Logistic Equation. First-Order Linear Differential Equations. Section Project: Weight Loss. Review Exercises. P.S. Problem Solving. 7. APPLICATIONS OF INTEGRATION. Area of a Region Between Two Curves. Volume: The Disk Method. Volume: The Shell Method. Section Project: Saturn. Arc Length and Surfaces of Revolution. Work. Section Project: Pyramid of Khufu. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force. Review Exercises. P.S. Problem Solving. 8. INTEGRATION TECHNIQUES AND IMPROPER INTEGRALS. Basic Integration Rules. Integration by Parts. Trigonometric Integrals. Section Project: The Wallis Product. Trigonometric Substitution. Partial Fractions. Numerical Integration. Integration by Tables and Other Integration Techniques. Improper Integrals. Review Exercises. P.S. Problem Solving. 9. INFINITE SERIES. Sequences. Series and Convergence. Section Project: Cantor"s Disappearing Table. The Integral Test and p-Series. Section Project: The Harmonic Series. Comparisons of Series. Alternating Series. The Ratio and Root Tests. Taylor Polynomials and Approximations. Power Series. Representation of Functions by Power Series. Taylor and Maclaurin Series. Review Exercises. P.S. Problem Solving. 10. CONICS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES. Conics and Calculus. Plane Curves and Parametric Equations. Section Project: Cycloids. Parametric Equations and Calculus. Polar Coordinates and Polar Graphs. Section Project: Cassini Oval. Area and Arc Length in Polar Coordinates. Polar Equations of Conics and Kepler"s Laws. Review Exercises. P.S. Problem Solving. 11. VECTORS AND THE GEOMETRY OF SPACE. Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space. Lines and Planes in Space. Section Project: Distances in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Review Exercises. P.S. Problem Solving. 12. VECTOR-VALUED FUNCTIONS. Vector-Valued Functions. Section Project: Witch of Agnesi. Differentiation and Integration of Vector-Valued Functions. Velocity and Acceleration. Tangent Vectors and Normal Vectors. Arc Length and Curvature. Review Exercises. P.S. Problem Solving. 13. FUNCTIONS OF SEVERAL VARIABLES. Introduction to Functions of Several Variables. Limits and Continuity. Partial Derivatives. Differentials. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines. Section Project: Wildflowers. Extrema of Functions of Two Variables. Applications of Extrema of Functions of Two Variables. Section Project: Building a Pipeline. Lagrange Multipliers. Review Exercises. P.S. Problem Solving. 14. MULTIPLE INTEGRATION. Iterated Integrals and Area in the Plane. Double Integrals and Volume. Change of Variables: Polar Coordinates. Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. Surface Area. Section Project: Surface Area in Polar Coordinates. Triple Integrals and Applications. Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. Change of Variables: Jacobians. Review Exercises. P.S. Problem Solving. 15. VECTOR ANALYSIS. Vector Fields. Line Integrals. Conservative Vector Fields and Independence of Path. Green"s Theorem. Section Project: Hyperbolic and Trigonometric Functions. Parametric Surfaces. Surface Integrals. Section Project: Hyperboloid of One Sheet. Divergence Theorem. Stokes" Theorem. Review Exercises. Section Project: The Planimeter. P.S. Problem Solving. 16. SECOND ORDER DIFFERENTIAL EQUATIONS* ONLINE. Exact First-Order Equations. Second-Order Homogeneous Linear Equations. Second-Order Nonhomogeneous Linear Equations. Section Project: Parachute Jump. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving. APPENDIX. A. Proofs of Selected Theorems. B. Integration Tables. C. Precalculus Review (Web). C.1. Real Numbers and the Real Number Line. C.2. The Cartesian Plane. D. Rotation and the General Second-Degree Equation (Web). E. Complex Numbers (Web). F. Business and Economic Applications (Web). G. Fitting Models to Data (Web).

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Book SynopsisYear after year, PRECALCULUS: FUNCTIONS AND GRAPHS leads the way in helping students like you succeed in their Precalculus courses. Its clear explanations and examples and exercises featuring a variety of real-life applications make the content understandable and relatable. This 13th edition of Swokowski and Cole's bestselling text is consistently praised for being at just the right level for Precalculus students. Perhaps most important, this book effectively prepares readers for further courses in mathematics.Table of Contents1. TOPICS FROM ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Equations. Complex Numbers. Inequalities. 2. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions of Degree Greater Than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation. 4. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. 5. TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of the Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. 6. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Additions and Subtraction of Formulas. Multiple-Angle Formulas. Product-To-Sum and Sum-To-Product Formulas. The Inverse Trigonometric Functions. 7. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre���s Theorem and nth Roots of Complex Numbers. 8. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More Than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. 9. SEQUENCES, SERIES, AND PROBABILITY. Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability. 10. TOPICS FROM ANALYTICAL GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. 11. LIMITS OF FUNCTIONS. Introductions to Limits. Definition of a Limit. Techniques for Finding Limits. Limits Involving Infinity. Appendix I: Common Graphs and Their Equations. Appendix II: A Summary of Graph Transformations. Appendix III: Graphs of the Trigonometric Functions and Their Inverses. Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle. Appendix V: Theorems on Limits.

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Book SynopsisTable of ContentsPART I: MECHANICS. 1. Physics and Measurement. 2. Motion in One Dimension. 3. Vectors. 4. Motion in Two Dimensions. 5. The Laws of Motion. 6. Circular Motion and Other Applications of Newton's Laws. 7. Energy of a System. 8. Conservation of Energy. 9. Linear Momentum and Collisions. 10. Rotation of a Rigid Object About a Fixed Axis. 11. Angular Momentum. 12. Static Equilibrium and Elasticity. 13. Universal Gravitation. 14. Fluid Mechanics. PART II: OSCILLATIONS AND MECHANICAL WAVES. 15. Oscillatory Motion. 16. Wave Motion. 17. Superposition and Standing Waves. PART III: THERMODYNAMICS. 18. Temperature. 19. The First Law of Thermodynamics. 20. The Kinetic Theory of Gases. 21. Heat Engines, Entropy, and the Second Law of Thermodynamics. Part IV: ELECTRICITY AND MAGNETISM. 22. Electric Fields. 23. Continuous Charge Distributions and Gauss's Law. 24. Electric Potential. 25. Capacitance and Dielectrics. 26. Current and Resistance. 27. Direct-Current Circuits. 28. Magnetic Fields. 29. Sources of the Magnetic Field. 30. Faraday's Law. 31. Inductance. 32. Alternating-Current Circuits. 33. Electromagnetic Waves. PART V: LIGHT AND OPTICS. 34. The Nature of Light and the Principles of Ray Optics 35. Image Formation. 36. Wave Optics. 37. Diffraction Patterns and Polarization. PART VI: MODERN PHYSICS. 38. Relativity. APPENDICES. A. Tables. B. Mathematics Review. C. Periodic Table of the Elements. D. SI Units. Answers to Quick Quizzes and Odd-Numbered Problems. Index.

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Book SynopsisSuitable for anyone working with problems of linear and nonlinear least squares fitting, this book includes an overview of computational methods together with their properties and advantages. It also includes topics from statistical regression analysis that help readers to understand and evaluate the computed solutions.Trade ReviewLeast Square Data fitting with Applications is a book that will be of great practical use to anyone whose work involves the analysis of data and its modeling. It offers a great deal of information that can be a s valuable in the lecture theater as in the lab or office. Mathematics TodayTable of ContentsPrefaceSymbols and AcronymsChapter 1. The Linear Data Fitting Problem1.1. Parameter estimation, data approximation1.2. Formulation of the data fitting problem1.3. Maximum likelihood estimation1.4. The residuals and their properties1.5. Robust regressionChapter 2. The Linear Least Squares Problem2.1. Linear least squares problem formulation2.2. The QR factorization and its role2.3. Permuted QR factorizationChapter 3. Analysis of Least Squares Problems3.1. The pseudoinverse3.2. The singular value decomposition3.3. Generalized singular value decomposition3.4. Condition number and column scaling3.5. Perturbation analysisChapter 4. Direct Methods for Full-Rank Problems4.1. Normal equations4.2. LU factorization4.3. QR factorization4.4. Modifying least squares problems4.5. Iterative refinement4.6. Stability and condition number estimation4.7. Comparison of the methodsChapter 5. Direct Methods for Rank-Deficient Problems5.1. Numerical rank5.2. Peters-Wilkinson LU factorization5.3. QR factorization with column permutations5.4. UTV and VSV decompositions5.5. Bidiagonalization5.6. SVD computationsChapter 6. Methods for Large-Scale Problems6.1. Iterative versus direct methods6.2. Classical stationary methods6.3. Non-stationary methods, Krylov methods6.4. Practicalities: preconditioning and stopping criteria6.5. Block methodsChapter 7. Additional Topics in Least Squares7.1. Constrained linear least squares problems7.2. Missing data problems7.3. Total least squares (TLS)7.4. Convex optimization7.5. Compressed sensingChapter 8. Nonlinear Least Squares Problems8.1. Introduction8.2. Unconstrained problems8.3. Optimality conditions for constrained problems8.4. Separable nonlinear least squares problems8.5. Multiobjective optimizationChapter 9. Algorithms for Solving Nonlinear LSQ Problems9.1. Newton's method9.2. The Gauss-Newton method9.3. The Levenberg-Marquardt method9.4. Additional considerations and software9.5. Iteratively reweighted LSQ algorithms for robust data fitting problems9.6. Variable projection algorithm9.7. Block methods for large-scale problemsChapter 10. Ill-Conditioned Problems10.1. Characterization10.2. Regularization methods10.3. Parameter selection techniques10.4. Extensions of Tikhonov regularization10.5. Ill-conditioned NLLSQ problemsChapter 11. Linear Least Squares Applications11.1. Splines in approximation11.2. Global temperatures data fitting11.3. Geological surface modelingChapter 12. Nonlinear Least Squares Applications12.1. Neural networks training12.2. Response surfaces, surrogates or proxies12.3. Optimal design of a supersonic aircraft12.4. NMR spectroscopy12.5. Piezoelectric crystal identification12.6. Travel time inversion of seismic dataAppendix A: Sensitivity AnalysisA.1. Floating-point arithmeticA.2. Stability, conditioning and accuracyAppendix B: Linear Algebra BackgroundB.1. NormsB.2. Condition numberB.3. OrthogonalityB.4. Some additional matrix propertiesAppendix C: Advanced Calculus BackgroundC.1. Convergence ratesC.2. Multivariable calculusAppendix D: StatisticsD.1. DefinitionsD.2. Hypothesis testingReferencesIndex

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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 SynopsisIt is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.Trade ReviewThis book is well written and has sufficient rigor to allow students to use it for independent study. Choice An introductory Tensor Calculus for Physics book is a most welcome addition... Professor Neuenschwander's book fills the gap in robust fashion. American Journal of PhysicsTable of ContentsPrefaceAcknowledgmentsChapter 1. Tensors Need Context1.1. Why Aren't Tensors Defined by What They Are?1.2. Euclidean Vectors, without Coordinates1.3. Derivatives of Euclidean Vectors with Respect to a Scalar1.4. The Euclidean Gradient1.5. Euclidean Vectors, with Coordinates1.6. Euclidean Vector Operations with and without Coordinates1.7. Transformation Coefficients as Partial Derivatives1.8. What Is a Theory of Relativity?1.9. Vectors Represented as Matrices1.10. Discussion Questions and ExercisesChapter 2. Two-Index Tensors2.1. The Electric Susceptibility Tensor2.2. The Inertia Tensor2.3. The Electric Quadrupole Tensor2.4. The Electromagnetic Stress Tensor2.5. Transformations of Two-Index Tensors2.6. Finding Eigenvectors and Eigenvalues2.7. Two-Index Tensor Components as Products of Vector Components2.8. More Than Two Indices2.9. Integration Measures and Tensor Densities2.10. Discussion Questions and ExercisesChapter 3. The Metric Tensor3.1. The Distinction between Distance and Coordinate Displacement3.2. Relative Motion3.3. Upper and Lower Indices3.4. Converting between Vectors and Duals3.5. Contravariant, Covariant, and "Ordinary" Vectors3.6. Tensor Algebra3.7. Tensor Densities Revisited3.8. Discussion Questions and ExercisesChapter 4. Derivatives of Tensors4.1. Signs of Trouble4.2. The Affine Connection4.3. The Newtonian Limit4.4. Transformation of the Affine Connection4.5. The Covariant Derivative4.6. Relation of the Affine Connection to the Metric Tensor4.7. Divergence, Curl, and Laplacian with Covariant Derivatives4.8. Disccussion Questions and ExercisesChapter 5. Curvature5.1. What Is Curvature?5.2. The Riemann Tensor5.3. Measuring Curvature5.4. Linearity in the Second Derivative5.5. Discussion Questions and ExercisesChapter 6. Covariance Applications6.1. Covariant Electrodynamics6.2. General Covariance and Gravitation6.3. Discussion Questions and ExercisesChapter 7. Tensors and Manifolds7.1. Tangent Spaces, Charts, and Manifolds7.2. Metrics on Manifolds and Their Tangent Spaces7.3. Dual Basis Vectors7.4. Derivatives of Basis Vectors and the Affine Connection7.5. Discussion Questions and ExercisesChapter 8. Getting Acquainted with Differential Forms8.1. Tensors as Multilinear Forms8.2. 1-Forms and Their Extensions8.3. Exterior Products and Differential Forms8.4. The Exterior Derivative8.5. An Application to Physics: Maxwell's Equations8.6. Integrals of Differential Forms8.7. Discussion Questions and ExercisesAppendix A: Common Coordinate SystemsAppendix B: Theorem of AlternativesAppendix C: Abstract Vector SpacesBibliographyIndex

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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 SynopsisI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.Trade Review"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews) Table of ContentsI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index

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