Applied mathematics Books

Book Synopsisaeo This textbook is based on a course taught jointly by an economist and a mathematician making it a balanced and comprehensive introduction to mathematics in economics. aeo Mathematical techniques are always presented in the context of the economics problems they are used to solve.Trade Review"I wish Adam Ostaszewski good luck with this book. May it enjoy the success it deserves." Ken Binmore, University of Michigan "I believe Mathematics in Economics to be an excellent book, which is much needed in first year UK degree programmes. Its coverage of syllabus is better than its rivals and its treatment of the economics and the mathematics indicates that considerable rigour is needed to do things properly." Martin Cripps, University of Warwick "In this book the build-up in confidence is done gradually by means of carefully chosen examples." "Throughout the book the approach to mathematics is rigorous, and excellent use is made of graphs and other figures." "A valuable guide to the ways in which mathematics provides a basis for modern economics." Tony WhitfordTable of ContentsPart I:. 1. Sets and Numbers. 2. Matrices and Vectors. 3. Modelling Consumer Choice. 4. Discrete Variables. 5. Functions. 6. Equilibrium. 7. Eigenvalues and Eigenvectors. Part II:. 1. Limits and Their Uses. 2. Continuity and Its Uses. 3. Uses of the Derivative. 4. Continuous Compounding and Exponential Growth. 5. Partial Differentiation. 6. The Gradient. 7. Taylor's Theorem - An Approximation Tool. 8. Optimisation in Two Variables. 9. Economic Dynamics: Differential Equations.

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Book SynopsisHow do we make the field and laboratory coherent? How do we use statistics to help experimentation? How do we integrate modeling and statistics? This book answers these questions. It makes liberal use of computer programming for the generation of hypotheses, exploration of data, and the comparison of different models.Table of ContentsPreface: Beyond the Null Hypothesis1An Ecological Scenario and the Tools of the Ecological Detective32Alternative Views of the Scientific Method and of Modeling123Probability and Probability Models: Know Your Data394Incidental Catch in Fisheries: Seabirds in the New Zealand Squid Trawl Fishery945The Confrontation: Sum of Squares1066The Evolutionary Ecology of Insect Oviposition Behavior1187The Confrontation: Likelihood and Maximum Likelihood1318Conservation Biology of Wildebeest in the Serengeti1809The Confrontation: Bayesian Goodness of Fit20310Management of Hake Fisheries in Namibia Motivation23511The Confrontation: Understanding How the Best Fit Is Found263Appendix"The Method of Multiple Working Hypotheses"281References295Index309

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Book SynopsisCovers local search and its variants from both a theoretical and practical point of view. This book is suitable for students and researchers in discrete mathematics, computer science, operations research, industrial engineering, and management science.Trade Review"A truly remarkable and unique collection of work... Invaluable."--Informs "The world of local search has changed dramatically in the last decade and Aarts and Lenstra's book is a tribute to this development... A very useful source."--Optima

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Book SynopsisOffers an introduction to mathematical models in epidemiology and shows how they can be used to predict and control the geographic spread of major infectious diseases. This work explains the key concepts in infectious disease modeling, guides readers from simple mathematical models to more complex ones, and explores their strengths and weaknesses.Trade Review"Sattenspiel and Lloyd do a first-rate job of making a lot of material accessible to a broad audience. They focus on a handful of examples and provide comprehensive insights. I found this book to be tightly and cogently written, supplying a level of detail that will be really useful for advanced undergraduates, graduate students, and researchers. It is one I would certainly recommend."—Andrew P. Dobson, Princeton UniversityTable of ContentsPreface ix Chapter 1. Introduction 1 1.1 Mathematical Models and the Geographic Spread of Epidemics 5 1.2 Structure of this Book 11 Chapter 2. The Art of Epidemic Modeling: Concepts and Basic Structures 12 2.1 Essential Biological and Epidemiological Concepts 12 2.2 The Cornerstone of Many Epidemic Models | the SIR Model 16 2.3 Demography and Epidemic Models 23 2.4 More Complex Models 25 2.5 The Basic Reproductive Number Revisited 53 Chapter 3. Modeling the Geographic Spread of Inuenza Epidemics 58 3.1 A Brief Overview of the Biology of Inuenza 58 3.2 Population-based Inuenza Models 61 3.3 Individual-based Inuenza Models 77 3.4 So What Kind of Model Should One Use to Study Inuenza Transmission? 84 Chapter 4. Modeling Geographic Spread I: Population-based Approaches 86 4.1 Spatial Structure and Disease Transmission: Basic Themes 86 4.2 Spatial Modeling Frameworks 89 4.3 Metapopulation Models 90 4.4 Spatially Continuous Models 102 Chapter 5. Spatial Heterogeneity and Endemicity: The Case of Measles 117 5.1 The Persistence and Long-term Cycling of Measles 122 5.2 Spatial Heterogeneity, Synchrony, and the Spatial Spread of Measles 125 Chapter 6. Modeling Geographic Spread II: Individual-based Approaches 134 6.1 Historical Underpinnings of the Use of Networks in Epidemiology 137 6.2 The Nature of Networks 140 6.3 The Language of Network Analysis 142 6.4 Major Classes of Networks 150 6.5 The Inuence of Networks on the Dynamics of Epidemic Spread 159 6.6 Theoretical Analysis of Network Models 162 6.7 The Basic Reproductive Number in Network Models 168 6.8 Infection Control on Networks 171 6.9 Why Aren't There More Applications of Network Models for Spatial Spread? 173 Chapter 7. Spatial Models and the Control of Foot-and-Mouth Disease 176 7.1 Modeling the Geographic Spread of FMD 180 7.2 The Official Response to the Epidemic and Its Aftermath 185 Chapter 8. Maps, Projections, and GIS: Geographers' Approaches 191 8.1 Mapping Methods 191 8.2 Identifying Patterns of Disease Di_usion 195 8.3 Epidemic Projections 204 8.4 Detection of Disease Clustering 208 8.5 New and Potential Directions 211 Chapter 9. Revisiting SARS and Looking to the Future 215 9.1 Did Mathematical Modeling Help to Stop the 2003 SARS Epidemic? 215 9.2 Modeling the Geographic Spread of Past, Present, and Future Infectious Disease Epidemics: Lessons and Advice 223 Bibliography 237 Index 279

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Book SynopsisSuitable for students of all mathematics and art levels, this title focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. It encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.Trade Review"The book goes a long way trying to convey to its audience--through both theory and practice--professional techniques that could not fail but empower students to make accurate, sophisticated drawings. The book presents an elegant fusion of mathematical ideas and practical aspects of fine art."--Cut the Knot "[T]his is an excellent text that I will certainly consider using for a future class. The material on perspective is accessible, thorough and well-written, and the text is designed for a hands-on pedagogy that is well-suited to the intended audience. And as an elementary, but thorough, discussion of both the mathematics and practice of perspective drawing, it deserves a place in any collection of books on mathematics and the arts."--Blake Mellor, Journal of Mathematics and the Arts "The writing is extremely clear, the material is fresh, and the many excellent diagrams clarify the ideas under discussion. The authors use relevant artwork to illustrate the mathematical principles... The exercises are original and promote active learning... This is an excellent work for academic curricula and an outstanding resource for self-study in mathematical perspective, fractals, and the relationship between art and mathematics."--Choice "This is not a book to read passively and, indeed, you will want to read this book with a pencil in hand. The text is designed to be experienced first hand, sketching out examples whilst following the text, as well as doing the exercises at the end of each chapter that develop the material well... Prerequisites for this book are a minimum, effectively being an understanding of basic coordinate geometry. I would recommend this book to anyone who is interested in the interplay between mathematics and art."--George Matthews, Mathematics TodayTable of ContentsPreface vii Acknowledgments ix Chapter 1: Introduction to Perspective and Space Coordinates 1 Artist Vignette: Sherry Stone 9 Chapter 2: Perspective by the Numbers 13 Artist Vignette: Peter Galante 25 Chapter 3: Vanishing Points and Viewpoints 29 Artist Vignette: Jim Rose 39 Chapter 4: Rectangles in One-Point Perspective 43 What's My Line?: A Perspective Game 55 Chapter 5: Two-Point Perspective 59 Artist Vignette: Robert Bosch 77 Chapter 6: Three-Point Perspective and Beyond 85 Artist Vignette: Dick Termes 113 Chapter 7: Anamorphic Art 117 Viewpoints at the Movies: The Hitchcock Zoom 135 Plates follow page 138 Chapter 8: Introduction to Fractal Geometry 139 Artist Vignette: Teri Wagner 157 Chapter 9: Fractal Dimension 161 Artist Vignette: Kerry Mitchell 193 Answers to Selected Exercises 197 Appendix: Information for Instructors 215 Annotated References 223 Index 229

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Book SynopsisFrom rainbows, river meanders, and shadows to spider webs, honeycombs, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Trade ReviewWinner of the 2003 for Professional/Scholarly Award in Mathematics and Statistics, Association of American Publishers One of Choice's Outstanding Academic Titles for 2004 "Mathematics in Nature is an excellent resource for bringing a greater variety of patterns into the mathematical study of nature, as well as for teaching students to think about describing natural phenomena mathematically... [T]he breadth of patterns studied is phenomenal."--Will Wilson, American Scientist "John Adam has combined his interest in the great outdoors and applied mathematics to compile one surprising example after another of how mathematics can be used to explain natural phenomena. And what examples! ... [He] has done a great deal of reading and exposition, indulging his passions to create this compilation of mathematical models of natural phenomena, and the sheer number of examples he manages to cram into this book is testament to his efforts. There are other texts on the market which explore the connection between mathematics and nature ... but none this wide-ranging."--Steven Morics, MAA Online "Adam has laced his mathematical models with popular descriptions of the phenomena selected... Mathematics in Nature can accordingly be read for pleasure and instruction by the select laity who are not afraid of reading between the lines of equations."--Philip J. Davis, SIAM News "John Adam's quest is a very simple one: that is, to invite one to look around and observe the wonders of nature, both natural and biological; to ponder them; and to try to explain them at various levels with, for the most part, quite elementary mathematical concepts and techniques."--Brian D. Sleeman, Notices of the American Mathematical Association "Reading this book progressively creates a course in mathematical modeling built around familiar, tangible, human-scale examples, with a trajectory that takes readers from dimensional estimates through geometrical modeling, linear and nonlinear dynamics, to pattern formation."--Choice "John Adam's Mathematics in Nature illustrates how, in a friendly and lucid manner, mathematicians think about nature. Adam lets us see how mathematics is not only an ally, but is perhaps the very language that nature uses to express the beautiful... This is a book that will challenge while it intrigues and excites."--Stanley David Gedzelman, Weatherwise "Although Mathematics in Nature has not been written as a textbook, availability of such a manual shall help instructors who choose this delightful book for teaching a course in applied mathematics or mathematical modeling."--Yuri V. Rogovchenko, Zentralblatt Math "Spanning a range of mathematical levels, this book can be used as an undergraduate textbook, a source of high school math enrichment, or can be read for pleasure by folks with an appreciation of nature but without advanced mathematical background."--Southeastern NaturalistTable of ContentsPreface: The motivation for the book; Acknowledgments; Credits xiii Prologue: Why I Might Never Have Written This Book xxi CHAPTER ONE: The Confluence of Nature and Mathematical Modeling 1 CHAPTER TWO: Estimation: The Power of Arithmetic in Solving Fermi Problems 17 CHAPTER THREE: Shape, Size, and Similarity: The Problem of Scale 31 CHAPTER FOUR: Meteorological Optics I: Shadows, Crepuscular Rays, and Related Optical Phenomena 57 CHAPTER FIVE: Meteorological Optics II: A "Calculus I" Approach to Rainbows, Halos, and Glories 80 CHAPTER SIX: Clouds, Sand Dunes, and Hurricanes 118 CHAPTER SEVEN: (Linear) Waves of All Kinds 139 CHAPTER EIGHT: Stability 173 CHAPTER NINE: Bores and Nonlinear Waves 194 CHAPTER TEN: The Fibonacci Sequence and the Golden Ratio 213 CHAPTER ELEVEN: Bees, Honeycombs, Bubbles, and Mud Cracks 231 CHAPTER TWELVE: River Meanders, Branching Patterns, and Trees 254 CHAPTER THIRTEEN: Bird Flight 295 CHAPTER FOURTEEN: HowDid the Leopard Get Its Spots? 309 APPENDIX: Fractals: An Appetite Whetter... 336 BIBLIOGRAPHY 341 INDEX 357

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Book SynopsisMany problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It is of interest to applied mathematicians, and computer scientists.Trade Review"This book is succinct but essentially self-contained; it includes an appendix with background material as well as an extensive bibliography. The algorithmic techniques developed may be useful anytime a model leads to a mathematical optimization problem where the domain naturally is a manifold, particularly if the manifold is a matrix manifold. The book follows the usual definition-theorem-proof style but it is not intended for traditional course work so there are no exercises. A reader with limited exposure to manifold theory and differential geometry most likely will benefit from consulting standard texts on those subjects first."--Anders Linner, Mathematical Reviews "[T]his book is succinct but essentially self-contained; it includes an appendix with background material as well as an extensive bibliography. The algorithmic techniques developed may be useful anytime a model leads to a mathematical optimization problem where the domain naturally is a manifold, particularly if the manifold is a matrix manifold. The book follows the usual definition-theorem-proof style but it is not intended for traditional course work so there are no exercises. A reader with limited exposure to manifold theory and differential geometry most likely will benefit from consulting standard texts on those subjects first."--Anders Linner, American Mathematical Society "The book is very well and carefully written. Every chapter starts with a page-long introduction clearly outlining its goals and how they are achieved together with possible relations to other chapters. I find the material very well explained and supported with appropriate examples. It is a pleasure to work with such a book."--Nickolay T. Trendafilov, Foundations of Computational MathematicsTable of ContentsList of Algorithms xi Foreword, by Paul Van Dooren xiii Notation Conventions xv Chapter 1. Introduction 1 Chapter 2. Motivation and Applications 5 2.1 A case study: the eigenvalue problem 5 2.1.1 The eigenvalue problem as an optimization problem 7 2.1.2 Some benefits of an optimization framework 9 2.2 Research problems 10 2.2.1 Singular value problem 10 2.2.2 Matrix approximations 12 2.2.3 Independent component analysis 13 2.2.4 Pose estimation and motion recovery 14 2.3 Notes and references 16 Chapter 3. Matrix Manifolds: First-Order Geometry 17 3.1 Manifolds 18 3.1.1 Definitions: charts, atlases, manifolds 18 3.1.2 The topology of a manifold* 20 3.1.3 How to recognize a manifold 21 3.1.4 Vector spaces as manifolds 22 3.1.5 The manifolds Rn x p and Rn x p 22 3.1.6 Product manifolds 23 3.2 Differentiable functions 24 3.2.1 Immersions and submersions 24 3.3 Embedded submanifolds 25 3.3.1 General theory 25 3.3.2 The Stiefel manifold 26 3.4 Quotient manifolds 27 3.4.1 Theory of quotient manifolds 27 3.4.2 Functions on quotient manifolds 29 3.4.3 The real projective space RPn x 1 30 3.4.4 The Grassmann manifold Grass(p, n) 30 3.5 Tangent vectors and differential maps 32 3.5.1 Tangent vectors 33 3.5.2 Tangent vectors to a vector space 35 3.5.3 Tangent bundle 36 3.5.4 Vector fields 36 3.5.5 Tangent vectors as derivations? 37 3.5.6 Differential of a mapping 38 3.5.7 Tangent vectors to embedded submanifolds 39 3.5.8 Tangent vectors to quotient manifolds 42 3.6 Riemannian metric, distance, and gradients 45 3.6.1 Riemannian submanifolds 47 3.6.2 Riemannian quotient manifolds 48 3.7 Notes and references 51 Chapter 4. Line-Search Algorithms on Manifolds 54 4.1 Retractions 54 4.1.1 Retractions on embedded submanifolds 56 4.1.2 Retractions on quotient manifolds 59 4.1.3 Retractions and local coordinates* 61 4.2 Line-search methods 62 4.3 Convergence analysis 63 4.3.1 Convergence on manifolds 63 4.3.2 A topological curiosity* 64 4.3.3 Convergence of line-search methods 65 4.4 Stability of fixed points 66 4.5 Speed of convergence 68 4.5.1 Order of convergence 68 4.5.2 Rate of convergence of line-search methods* 70 4.6 Rayleigh quotient minimization on the sphere 73 4.6.1 Cost function and gradient calculation 74 4.6.2 Critical points of the Rayleigh quotient 74 4.6.3 Armijo line search 76 4.6.4 Exact line search 78 4.6.5 Accelerated line search: locally optimal conjugate gradient 78 4.6.6 Links with the power method and inverse iteration 78 4.7 Refining eigenvector estimates 80 4.8 Brockett cost function on the Stiefel manifold 80 4.8.1 Cost function and search direction 80 4.8.2 Critical points 81 4.9 Rayleigh quotient minimization on the Grassmann manifold 83 4.9.1 Cost function and gradient calculation 83 4.9.2 Line-search algorithm 85 4.10 Notes and references 86 Chapter 5. Matrix Manifolds: Second-Order Geometry 91 5.1 Newton's method in Rn 91 5.2 Affine connections 93 5.3 Riemannian connection 96 5.3.1 Symmetric connections 96 5.3.2 Definition of the Riemannian connection 97 5.3.3 Riemannian connection on Riemannian submanifolds 98 5.3.4 Riemannian connection on quotient manifolds 100 5.4 Geodesics, exponential mapping, and parallel translation 101 5.5 Riemannian Hessian operator 104 5.6 Second covariant derivative* 108 5.7 Notes and references 110 Chapter 6. Newton's Method 111 6.1 Newton's method on manifolds 111 6.2 Riemannian Newton method for real-valued functions 113 6.3 Local convergence 114 6.3.1 Calculus approach to local convergence analysis 117 6.4 Rayleigh quotient algorithms 118 6.4.1 Rayleigh quotient on the sphere 118 6.4.2 Rayleigh quotient on the Grassmann manifold 120 6.4.3 Generalized eigenvalue problem 121 6.4.4 The nonsymmetric eigenvalue problem 125 6.4.5 Newton with subspace acceleration: Jacobi-Davidson 126 6.5 Analysis of Rayleigh quotient algorithms 128 6.5.1 Convergence analysis 128 6.5.2 Numerical implementation 129 6.6 Notes and references 131 Chapter 7. Trust-Region Methods 136 7.1 Models 137 7.1.1 Models in Rn 137 7.1.2 Models in general Euclidean spaces 137 7.1.3 Models on Riemannian manifolds 138 7.2 Trust-region methods 140 7.2.1 Trust-region methods in Rn 140 7.2.2 Trust-region methods on Riemannian manifolds 140 7.3 Computing a trust-region step 141 7.3.1 Computing a nearly exact solution 142 7.3.2 Improving on the Cauchy point 143 7.4 Convergence analysis 145 7.4.1 Global convergence 145 7.4.2 Local convergence 152 7.4.3 Discussion 158 7.5 Applications 159 7.5.1 Checklist 159 7.5.2 Symmetric eigenvalue decomposition 160 7.5.3 Computing an extreme eigenspace 161 7.6 Notes and references 165 Chapter 8. A Constellation of Superlinear Algorithms 168 8.1 Vector transport 168 8.1.1 Vector transport and affine connections 170 8.1.2 Vector transport by differentiated retraction 172 8.1.3 Vector transport on Riemannian submanifolds 174 8.1.4 Vector transport on quotient manifolds 174 8.2 Approximate Newton methods 175 8.2.1 Finite difference approximations 176 8.2.2 Secant methods 178 8.3 Conjugate gradients 180 8.3.1 Application: Rayleigh quotient minimization 183 8.4 Least-square methods 184 8.4.1 Gauss-Newton methods 186 8.4.2 Levenberg-Marquardt methods 187 8.5 Notes and references 188 A. Elements of Linear Algebra, Topology, and Calculus 189 A.1 Linear algebra 189 A.2 Topology 191 A.3 Functions 193 A.4 Asymptotic notation 194 A.5 Derivatives 195 A.6 Taylor's formula 198 Bibliography 201 Index 221

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Book SynopsisExplores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. This book provides a range of exercises, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory.Trade Review"This book will serve as a solid and invaluable reference."--Byung-Jun Yoon, Quarterly Review of BiologyTable of ContentsPreface xi PART 1. PRELIMINARIES 1 Chapter 1. Introduction to Probability and Random Variables 3 1.1 Introduction to Random Variables 3 1.1.1 Motivation 3 1.1.2 Definition of a Random Variable and Probability 4 1.1.3 Function of a Random Variable, Expected Value 8 1.1.4 Total Variation Distance 12 1.2 Multiple Random Variables 17 1.2.1 Joint and Marginal Distributions 17 1.2.2 Independence and Conditional Distributions 18 1.2.3 Bayes' Rule 27 1.2.4 MAP and Maximum Likelihood Estimates 29 1.3 Random Variables Assuming Infinitely Many Values 32 1.3.1 Some Preliminaries 32 1.3.2 Markov and Chebycheff Inequalities 35 1.3.3 Hoeffding's Inequality 38 1.3.4 Monte Carlo Simulation 41 1.3.5 Introduction to Cramer's Theorem 43 Chapter 2. Introduction to Information Theory 45 2.1 Convex and Concave Functions 45 2.2 Entropy 52 2.2.1 Definition of Entropy 52 2.2.2 Properties of the Entropy Function 53 2.2.3 Conditional Entropy 54 2.2.4 Uniqueness of the Entropy Function 58 2.3 Relative Entropy and the Kullback-Leibler Divergence 61 Chapter 3. Nonnegative Matrices 71 3.1 Canonical Form for Nonnegative Matrices 71 3.1.1 Basic Version of the Canonical Form 71 3.1.2 Irreducible Matrices 76 3.1.3 Final Version of Canonical Form 78 3.1.4 Irreducibility, Aperiodicity, and Primitivity 80 3.1.5 Canonical Form for Periodic Irreducible Matrices 86 3.2 Perron-Frobenius Theory 89 3.2.1 Perron-Frobenius Theorem for Primitive Matrices 90 3.2.2 Perron-Frobenius Theorem for Irreducible Matrices 95 PART 2. HIDDEN MARKOV PROCESSES 99 Chapter 4. Markov Processes 101 4.1 Basic Definitions 101 4.1.1 The Markov Property and the State Transition Matrix 101 4.1.2 Estimating the State Transition Matrix 107 4.2 Dynamics of Stationary Markov Chains 111 4.2.1 Recurrent and Transient States 111 4.2.2 Hitting Probabilities and Mean Hitting Times 114 4.3 Ergodicity of Markov Chains 122 Chapter 5. Introduction to Large Deviation Theory 129 5.1 Problem Formulation 129 5.2 Large Deviation Property for I.I.D. Samples: Sanov's Theorem 134 5.3 Large Deviation Property for Markov Chains 140 5.3.1 Stationary Distributions 141 5.3.2 Entropy and Relative Entropy Rates 143 5.3.3 The Rate Function for Doubleton Frequencies 148 5.3.4 The Rate Function for Singleton Frequencies 158 Chapter 6. Hidden Markov Processes: Basic Properties 164 6.1 Equivalence of Various Hidden Markov Models 164 6.1.1 Three Different-Looking Models 164 6.1.2 Equivalence between the Three Models 166 6.2 Computation of Likelihoods 169 6.2.1 Computation of Likelihoods of Output Sequences 170 6.2.2 The Viterbi Algorithm 172 6.2.3 The Baum-Welch Algorithm 174 Chapter 7. Hidden Markov Processes: The Complete Realization Problem 177 7.1 Finite Hankel Rank: A Universal Necessary Condition 178 7.2 Nonsuffciency of the Finite Hankel Rank Condition 180 7.3 An Abstract Necessary and Suffcient Condition 190 7.4 Existence of Regular Quasi-Realizations 195 7.5 Spectral Properties of Alpha-Mixing Processes 205 7.6 Ultra-Mixing Processes 207 7.7 A Sufficient Condition for the Existence of HMMs 211 PART 3. APPLICATIONS TO BIOLOGY 223 Chapter 8. Some Applications to Computational Biology 225 8.1 Some Basic Biology 226 8.1.1 The Genome 226 8.1.2 The Genetic Code 232 8.2 Optimal Gapped Sequence Alignment 235 8.2.1 Problem Formulation 236 8.2.2 Solution via Dynamic Programming 237 8.3 Gene Finding 240 8.3.1 Genes and the Gene-Finding Problem 240 8.3.2 The GLIMMER Family of Algorithms 243 8.3.3 The GENSCAN Algorithm 246 8.4 Protein Classification 247 8.4.1 Proteins and the Protein Classification Problem 247 8.4.2 Protein Classification Using Profile Hidden Markov Models 249 Chapter 9. BLAST Theory 255 9.1 BLAST Theory: Statements of Main Results 255 9.1.1 Problem Formulations 255 9.1.2 The Moment Generating Function 257 9.1.3 Statement of Main Results 259 9.1.4 Application of Main Results 263 9.2 BLAST Theory: Proofs of Main Results 264 Bibliography 273 Index 285

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Book SynopsisCovers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations. Suitable for advanced undergraduates and beginning graduate students in the sciences, engineering, and mathematics, this book takes a modern approach that bridges the gap between linear and nonlinear systems.Trade Review"This book takes a unique modern approach that bridges the gap between linear and nonlinear systems... Clear formulated definitions and theorems, correct proofs and many interesting examples and exercises make this textbook very attractive."--Ferenc Szenkovits, MathematicaTable of ContentsList of Figures xi Preface xiii Chapter 1: Introduction 1 1.1 Open Loop Control 1 1.2 The Feedback Stabilization Problem 2 1.3 Chapter and Appendix Descriptions 5 1.4 Notes and References 11 Chapter 2: Mathematical Background 12 2.1 Analysis Preliminaries 12 2.2 Linear Algebra and Matrix Algebra 12 2.3 Matrix Analysis 17 2.4 Ordinary Differential Equations 30 2.4.1 Phase Plane Examples: Linear and Nonlinear 35 2.5 Exercises 44 2.6 Notes and References 48 Chapter 3: Linear Systems and Stability 49 3.1 The Matrix Exponential 49 3.2 The Primary Decomposition and Solutions of LTI Systems 53 3.3 Jordan Form and Matrix Exponentials 57 3.3.1 Jordan Form of Two-Dimensional Systems 58 3.3.2 Jordan Form of n-Dimensional Systems 61 3.4 The Cayley-Hamilton Theorem 67 3.5 Linear Time Varying Systems 68 3.6 The Stability Definitions 71 3.6.1 Motivations and Stability Definitions 71 3.6.2 Lyapunov Theory for Linear Systems 73 3.7 Exercises 77 3.8 Notes and References 81 Chapter 4: Controllability of Linear Time Invariant Systems 82 4.1 Introduction 82 4.2 Linear Equivalence of Linear Systems 84 4.3 Controllability with Scalar Input 88 4.4 Eigenvalue Placement with Single Input 92 4.5 Controllability with Vector Input 94 4.6 Eigenvalue Placement with Vector Input 96 4.7 The PBH Controllability Test 99 4.8 Linear Time Varying Systems: An Example 103 4.9 Exercises 105 4.10 Notes and References 108 Chapter 5: Observability and Duality 109 5.1 Observability, Duality, and a Normal Form 109 5.2 Lyapunov Equations and Hurwitz Matrices 117 5.3 The PBH Observability Test 118 5.4 Exercises 121 5.5 Notes and References 123 Chapter 6: Stabilizability of LTI Systems 124 6.1 Stabilizing Feedbacks for Controllable Systems 124 6.2 Limitations on Eigenvalue Placement 128 6.3 The PBH Stabilizability Test 133 6.4 Exercises 134 6.5 Notes and References 136 Chapter 7: Detectability and Duality 138 7.1 An Example of an Observer System 138 7.2 Detectability, the PBH Test, and Duality 142 7.3 Observer-Based Dynamic Stabilization 145 7.4 Linear Dynamic Controllers and Stabilizers 147 7.5 LQR and the Algebraic Riccati Equation 152 7.6 Exercises 156 7.7 Notes and References 159 Chapter 8: Stability Theory 161 8.1 Lyapunov Theorems and Linearization 161 8.1.1 Lyapunov Theorems 162 8.1.2 Stabilization from the Jacobian Linearization 171 8.1.3 Brockett's Necessary Condition 172 8.1.4 Examples of Critical Problems 173 8.2 The Invariance Theorem 176 8.3 Basin of Attraction 181 8.4 Converse Lyapunov Theorems 183 8.5 Exercises 183 8.6 Notes and References 187 Chapter 9: Cascade Systems 189 9.1 The Theorem on Total Stability 189 9.1.1 Lyapunov Stability in Cascade Systems 192 9.2 Asymptotic Stability in Cascades 193 9.2.1 Examples of Planar Systems 193 9.2.2 Boundedness of Driven Trajectories 196 9.2.3 Local Asymptotic Stability 199 9.2.4 Boundedness and Global Asymptotic Stability 202 9.3 Cascades by Aggregation 204 9.4 Appendix: The Poincar'e-Bendixson Theorem 207 9.5 Exercises 207 9.6 Notes and References 211 Chapter 10: Center Manifold Theory 212 10.1 Introduction 212 10.1.1 An Example 212 10.1.2 Invariant Manifolds 213 10.1.3 Special Coordinates for Critical Problems 214 10.2 The Main Theorems 215 10.2.1 Definition and Existence of Center Manifolds 215 10.2.2 The Reduced Dynamics 218 10.2.3 Approximation of a Center Manifold 222 10.3 Two Applications 225 10.3.1 Adding an Integrator for Stabilization 226 10.3.2 LAS in Special Cascades: Center Manifold Argument 228 10.4 Exercises 229 10.5 Notes and References 231 Chapter 11: Zero Dynamics 233 11.1 The Relative Degree and Normal Form 233 11.2 The Zero Dynamics Subsystem 244 11.3 Zero Dynamics and Stabilization 248 11.4 Vector Relative Degree of MIMO Systems 251 11.5 Two Applications 254 11.5.1 Designing a Center Manifold 254 11.5.2 Zero Dynamics for Linear SISO Systems 257 11.6 Exercises 263 11.7 Notes and References 267 Chapter 12: Feedback Linearization of Single-Input Nonlinear Systems 268 12.1 Introduction 268 12.2 Input-State Linearization 270 12.2.1 Relative Degree n 271 12.2.2 Feedback Linearization and Relative Degree n 272 12.3 The Geometric Criterion 275 12.4 Linearizing Transformations 282 12.5 Exercises 285 12.6 Notes and References 287 Chapter 13: An Introduction to Damping Control 289 13.1 Stabilization by Damping Control 289 13.2 Contrasts with Linear Systems: Brackets, Controllability, Stabilizability 296 13.3 Exercises 299 13.4 Notes and References 300 Chapter 14: Passivity 302 14.1 Introduction to Passivity 302 14.1.1 Motivation and Examples 302 14.1.2 Definition of Passivity 304 14.2 The KYP Characterization of Passivity 306 14.3 Positive Definite Storage 309 14.4 Passivity and Feedback Stabilization 314 14.5 Feedback Passivity 318 14.5.1 Linear Systems 321 14.5.2 Nonlinear Systems 325 14.6 Exercises 327 14.7 Notes and References 330 Chapter 15: Partially Linear Cascade Systems 331 15.1 LAS from Partial-State Feedback 331 15.2 The Interconnection Term 333 15.3 Stabilization by Feedback Passivation 336 15.4 Integrator Backstepping 349 15.5 Exercises 355 15.6 Notes and References 357 Chapter 16: Input-to-State Stability 359 16.1 Preliminaries and Perspective 359 16.2 Stability Theorems via Comparison Functions 364 16.3 Input-to-State Stability 366 16.4 ISS in Cascade Systems 372 16.5 Exercises 374 16.6 Notes and References 376 Chapter 17: Some Further Reading 378 Appendix A: Notation: A Brief Key 381 Appendix B: Analysis in R and Rn 383 B.1 Completeness and Compactness 386 B.2 Differentiability and Lipschitz Continuity 393 Appendix C: Ordinary Differential Equations 393 C.1 Existence and Uniqueness of Solutions 393 C.2 Extension of Solutions 396 C.3 Continuous Dependence 399 Appendix D: Manifolds and the Preimage Theorem; Distributions and the Frobenius Theorem 403 D.1 Manifolds and the Preimage Theorem 403 D.2 Distributions and the Frobenius Theorem 410 Appendix E: Comparison Functions and a Comparison Lemma 420 E.1 Definitions and Basic Properties 420 E.2 Differential Inequality and Comparison Lemma 424 Appendix F: Hints and Solutions for Selected Exercises 430 Bibliography 443 Index 451

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Book SynopsisOffers an introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation. This title includes research in the area of incomplete markets and unhedgeable risks, and a chapter on finite difference methods. It integrates detailed examples and MATLAB codes.Trade Review"Ales Černy's new edition of Mathematical Techniques in Finance is an excellent master's-level treatment of mathematical methods used in financial asset pricing. By updating the original edition with methods used in recent research, Černy has once again given us an up-to-date first-class textbook treatment of the subject."—Darrell Duffie, Stanford UniversityTable of ContentsPreface to the Second Edition xiii From the Preface to the First Edition xix Chapter 1: The Simplest Model of Financial Markets 1 1.1 One-Period Finite State Model 1 1.2 Securities and Their Payoffs 3 1.3 Securities as Vectors 3 1.4 Operations on Securities 4 1.5 The Matrix as a Collection of Securities 6 1.6 Transposition 6 1.7 Matrix Multiplication and Portfolios 8 1.8 Systems of Equations and Hedging 10 1.9 Linear Independence and Redundant Securities 12 1.10 The Structure of the Marketed Subspace 14 1.11 The Identity Matrix and Arrow-Debreu Securities 16 1.12 Matrix Inverse 17 1.13 Inverse Matrix and Replicating Portfolios 17 1.14 Complete Market Hedging Formula 19 1.15 Summary 20 1.16 Notes 21 1.17 Exercises 22 Chapter 2: Arbitrage and Pricing in the One-Period Model 25 2.1 Hedging with Redundant Securities and Incomplete Market 25 2.2 Finding the Best Approximate Hedge 29 2.3 Minimizing the Expected Squared Replication Error 32 2.4 Numerical Stability of Least Squares 34 2.5 Asset Prices, Returns and Portfolio Units 36 2.6 Arbitrage 38 2.7 No-Arbitrage Pricing 40 2.8 State Prices and the Arbitrage Theorem 41 2.9 State Prices and Asset Returns 44 2.10 Risk-Neutral Probabilities 45 2.11 State Prices and No-Arbitrage Pricing 46 2.12 Asset Pricing Duality 47 2.13 Summary 48 2.14 Notes 49 2.15 Appendix: Least Squares with QR Decomposition 49 2.16 Exercises 52 Chapter 3: Risk and Return in the One-Period Model 55 3.1 Utility Functions 56 3.2 Expected Utility Maximization 59 3.3 The Existence of Optimal Portfolios 61 3.4 Reporting Expected Utility in Terms of Money 62 3.5 Normalized Utility and Investment Potential 63 3.6 Quadratic Utility 67 3.7 The Sharpe Ratio 69 3.8 Arbitrage-Adjusted Sharpe Ratio 71 3.9 The Importance of Arbitrage Adjustment 75 3.10 Portfolio Choice with Near-Arbitrage Opportunities 77 3.11 Summary 79 3.12 Notes 81 3.13 Exercises 82 Chapter 4: Numerical Techniques for Optimal Portfolio Selection in Incomplete Markets 84 4.1 Sensitivity Analysis of Portfolio Decisions with the CRRA Utility 84 4.2 Newton's Algorithm for Optimal Investment with CRRA Utility 88 4.3 Optimal CRRA Investment Using Empirical Return Distribution 90 4.4 HARA Portfolio Optimizer 94 4.5 HARA Portfolio Optimization with Several Risky Assets 96 4.6 Quadratic Utility Maximization with Multiple Assets 99 4.7 Summary 102 4.8 Notes 102 4.9 Exercises 102 Chapter 5: Pricing in Dynamically Complete Markets 104 5.1 Options and Portfolio Insurance 104 5.2 Option Pricing 105 5.3 Dynamic Replicating Trading Strategy 108 5.4 Risk-Neutral Probabilities in a Multi-Period Model 116 5.5 The Law of Iterated Expectations 119 5.6 Summary 121 5.7 Notes 121 5.8 Exercises 121 Chapter 6: Towards Continuous Time 125 6.1 IID Returns, and the Term Structure of Volatility 125 6.2 Towards Brownian Motion 127 6.3 Towards a Poisson Jump Process 136 6.4 Central Limit Theorem and Infinitely Divisible Distributions 142 6.5 Summary 143 6.6 Notes 145 6.7 Exercises 145 Chapter 7: Fast Fourier Transform 147 7.1 Introduction to Complex Numbers and the Fourier Transform 147 7.2 Discrete Fourier Transform (DFT) 152 7.3 Fourier Transforms in Finance 153 7.4 Fast Pricing via the Fast Fourier Transform (FFT) 158 7.5 Further Applications of FFTs in Finance 162 7.6 Notes 166 7.7 Appendix 167 7.8 Exercises 169 Chapter 8: Information Management 170 8.1 Information: Too Much of a Good Thing? 170 8.2 Model-Independent Properties of Conditional Expectation 174 8.3 Summary 178 8.4 Notes 179 8.5 Appendix: Probability Space 179 8.6 Exercises 183 Chapter 9: Martingales and Change of Measure in Finance 187 9.1 Discounted Asset Prices Are Martingales 187 9.2 Dynamic Arbitrage Theorem 192 9.3 Change of Measure 193 9.4 Dynamic Optimal Portfolio Selection in a Complete Market 198 9.5 Summary 206 9.6 Notes 208 9.7 Exercises 208 Chapter 10: Brownian Motion and Ito Formulae 213 10.1 Continuous-Time Brownian Motion 213 10.2 Stochastic Integration and Ito Processes 218 10.3 Important Ito Processes 220 10.4 Function of a Stochastic Process: the Ito Formula 222 10.5 Applications of the Ito Formula 223 10.6 Multivariate Ito Formula 225 10.7 Ito Processes as Martingales 228 10.8 Appendix: Proof of the Ito Formula 229 10.9 Summary 229 10.10 Notes 230 10.11 Exercises 231 Chapter 11: Continuous-Time Finance 233 11.1 Summary of Useful Results 233 11.2 Risk-Neutral Pricing 234 11.3 The Girsanov Theorem 237 11.4 Risk-Neutral Pricing and Absence of Arbitrage 241 11.5 Automatic Generation of PDEs and the Feynman-Kac Formula 246 11.6 Overview of Numerical Methods 250 11.7 Summary 251 11.8 Notes 252 11.9 Appendix: Decomposition of Asset Returns into Uncorrelated Components 252 11.10 Exercises 255 Chapter 12: Finite-Difference Methods 261 12.1 Interpretation of PDEs 261 12.2 The Explicit Method 263 12.3 Instability 264 12.4 Markov Chains and Local Consistency 266 12.5 Improving Convergence by Richardson's Extrapolation 268 12.6 Oscillatory Convergence Due to Grid Positioning 269 12.7 Fully Implicit Scheme 270 12.8 Crank-Nicolson Scheme 273 12.9 Summary 274 12.10 Notes 276 12.11 Appendix: Efficient Gaussian Elimination for Tridiagonal Matrices 276 12.12 Appendix: Richardson's Extrapolation 277 12.13 Exercises 277 Chapter 13: Dynamic Option Hedging and Pricing in Incomplete Markets 280 13.1 The Risk in Option Hedging Strategies 280 13.2 Incomplete Market Option Price Bounds 299 13.3 Towards Continuous Time 304 13.4 Derivation of Optimal Hedging Strategy 309 13.5 Summary 318 13.6 Notes 319 13.7 Appendix: Expected Squared Hedging Error in the Black-Scholes Model 320 13.8 Exercises 322 Appendix A Calculus 326 A.1 Notation 326 A.2 Differentiation 329 A.3 Real Function of Several Real Variables 332 A.4 Power Series Approximations 334 A.5 Optimization 336 A.6 Integration 338 A.7 Exercises 344 Appendix B Probability 348 B.1 Probability Space 348 B.2 Conditional Probability 348 B.3 Marginal and Joint Distribution 351 B.4 Stochastic Independence 352 B.5 Expectation Operator 354 B.6 Properties of Expectation 355 B.7 Mean and Variance 356 B.8 Covariance and Correlation 357 B.9 Continuous Random Variables 360 B.10 Normal Distribution 364 B.11 Quantiles 370 B.12 Relationships among Standard Statistical Distributions 371 B.13 Notes 372 B.14 Exercises 372 References 381 Index 385

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Book SynopsisIntroduces the distributed control of robotic networks. This book presents a set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity. It analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation.Trade Review"This book covers its subject very thoroughly. The framework the authors have established is very elegant and, if it catches on, this book could be the primary reference for this approach. I don't know of any other book that covers this set of topics."—Richard M. Murray, California Institute of Technology"The authors do an excellent job of clearly describing the problems and presenting rigorous, provably correct algorithms with complexity bounds for each problem. The authors also do a fantastic job of providing the mathematical insight necessary for such complex problems."—Ali Jadbabaie, University of Pennsylvania"The order of presentation makes much sense, and the book thoroughly covers what it sets out to cover. The algorithms and results are presented using a clear mathematical and computer science formalism, which allows a uniform presentation. The formalism used and the way of presenting the algorithms may be helpful for structuring the presentation of new algorithms in the future."—Vincent Blondel, Université catholique de LouvainTable of ContentsPreface ix Chapter 1. An introduction to distributed algorithms 1 1.1 Elementary concepts and notation 1 1.2 Matrix theory 6 1.3 Dynamical systems and stability theory 12 1.4 Graph theory 20 1.5 Distributed algorithms on synchronous networks 37 1.6 Linear distributed algorithms 52 1.7 Notes 66 1.8 Proofs 69 1.9 Exercises 85 Chapter 2. Geometric models and optimization 95 2.1 Basic geometric notions 95 2.2 Proximity graphs 104 2.3 Geometric optimization problems and multicenter functions 111 2.4 Notes 124 2.5 Proofs 125 2.6 Exercises 133 Chapter 3. Robotic network models and complexity notions 139 3.1 A model for synchronous robotic networks 139 3.2 Robotic networks with relative sensing 151 3.3 Coordination tasks and complexity notions 158 3.4 Complexity of direction agreement and equidistance 165 3.5 Notes 166 3.6 Proofs 169 3.7 Exercises 176 Chapter 4. Connectivity maintenance and rendezvous 179 4.1 Problem statement 180 4.2 Connectivity maintenance algorithms 182 4.3 Rendezvous algorithms 191 4.4 Simulation results 200 4.5 Notes 201 4.6 Proofs 204 4.7 Exercises 215 Chapter 5. Deployment 219 5.1 Problem statement 220 5.2 Deployment algorithms 222 5.3 Simulation results 233 5.4 Notes 237 5.5 Proofs 239 5.6 Exercises 245 Chapter 6. Boundary estimation and tracking 247 6.1 Event-driven asynchronous robotic networks 248 6.2 Problem statement 252 6.3 Estimate update and cyclic balancing law 256 6.4 Simulation results 266 6.5 Notes 268 6.6 Proofs 270 6.7 Exercises 275 Bibliography 279 Algorithm Index 305 Subject Index 307 Symbol Index 313

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Book SynopsisIntroduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters. This book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree.Trade Review"The text is easy to read due to ubiquitous remarks, examples and explanations before and after the rigorous mathematical derivations. There are plenty of numerical simulations and figures that illustrate the control designs and compare them to each other. This book is recommended for everybody interested in control systems, system identification for PDEs, or just PDEs in general. From students to researchers, and from engineers to mathematicians everybody can find interesting new results in it."--Andras Balogh, Mathematical ReviewsTable of ContentsPreface ix Chapter 1. Introduction 1 1.1 Parabolic and Hyperbolic PDE Systems 1 1.2 The Roles of PDE Plant Instability, Actuator Location, Uncertainty Structure, Relative Degree, and Functional Parameters 2 1.3 Class of Parabolic PDE Systems 3 1.4 Backstepping 4 1.5 Explicitly Parametrized Controllers 5 1.6 Adaptive Control 5 1.7 Overview of the Literature on Adaptive Control for Parabolic PDEs 6 1.8 Inverse Optimality 7 1.9 Organization of the Book 7 1.10 Notation 9 PART I: NONADAPTIVE CONTROLLERS 11 Chapter 2. State Feedback 13 2.1 Problem Formulation 13 2.2 Backstepping Transformation and PDE for Its Kernel 14 2.3 Converting the PDE into an Integral Equation 17 2.4 Analysis of the Integral Equation by Successive Approximation Series 19 2.5 Stability of the Closed-Loop System 22 2.6 Dirichlet Uncontrolled End 24 2.7 Neumann Actuation 26 2.8 Simulation 27 2.9 Discussion 27 2.10 Notes and References 33 Chapter 3. Closed-Form Controllers 35 3.1 The Reaction-Diffusion Equation 35 3.2 A Family of Plants with Spatially Varying Reactivity 38 3.3 Solid Propellant Rocket Model 40 3.4 Plants with Spatially Varying Diffusivity 42 3.5 The Time-Varying Reaction Equation 45 3.6 More Complex Systems 50 3.7 2D and 3D Systems 52 3.8 Notes and References 54 Chapter 4. Observers 55 4.1 Observer Design for the Anti-Collocated Setup 55 4.2 Plants with Dirichlet Uncontrolled End and Neumann Measurements 58 4.3 Observer Design for the Collocated Setup 59 4.4 Notes and References 61 Chapter 5. Output Feedback 63 5.1 Anti-Collocated Setup 63 5.2 Collocated Setup 65 5.3 Closed-Form Compensators 67 5.4 Frequency Domain Compensator 71 5.5 Notes and References 72 Chapter 6. Control of Complex-Valued PDEs 73 6.1 State-Feedback Design for the Schrodinger Equation 73 6.2 Observer Design for the Schrodinger Equation 76 6.3 Output-Feedback Compensator for the Schrodinger Equation 79 6.4 The Ginzburg-Landau Equation 81 6.5 State Feedback for the Ginzburg-Landau Equation 83 6.6 Observer Design for the Ginzburg-Landau Equation 98 6.7 Output Feedback for the Ginzburg-Landau Equation 101 6.8 Simulations with the Nonlinear Ginzburg-Landau Equation 104 6.9 Notes and References 107 PART II: ADAPTIVE SCHEMES 109 Chapter 7. Systematization of Approaches to Adaptive Boundary Stabilization of PDEs 111 7.1 Categorization of Adaptive Controllers and Identifiers 111 7.2 Benchmark Systems 113 7.3 Controllers 114 7.4 Lyapunov Design 115 7.5 Certainty Equivalence Designs 117 7.6 Trade-offs between the Designs 121 7.7 Stability 122 7.8 Notes and References 124 Chapter 8. Lyapunov-Based Designs 125 8.1 Plant with Unknown Reaction Coefficient 125 8.2 Proof of Theorem 8.1 128 8.3 Well-Posedness of the Closed-Loop System 132 8.4 Parametric Robustness 134 8.5 An Alternative Approach 135 8.6 Other Benchmark Problems 136 8.7 Systems with Unknown Diffusion and Advection Coefficients 142 8.8 Simulation Results 147 8.9 Notes and References 149 Chapter 9. Certainty Equivalence Design with Passive Identifiers 150 9.1 Benchmark Plant 150 9.2 3D Reaction-Advection-Diffusion Plant 154 9.3 Proof of Theorem 9.2 157 9.4 Simulations 163 9.5 Notes and References 164 Chapter 10. Certainty Equivalence Design with Swapping Identifiers 166 10.1 Reaction-Advection-Diffusion Plant 166 10.2 Proof of Theorem 10.1 169 10.3 Simulations 175 10.4 Notes and References 175 Chapter 11. State Feedback for PDEs with Spatially Varying Coefficients 176 11.1 Problem Statement 176 11.2 Nominal Control Design 177 11.3 Robustness to Error in Gain Kernel 179 11.4 Lyapunov Design 185 11.5 Lyapunov Design for Plants with Unknown Advection and Diffusion Parameters 190 11.6 Passivity-Based Design 191 11.7 Simulations 195 11.8 Notes and References 197 Chapter 12. Closed-Form Adaptive Output-Feedback Contollers 198 12.1 Lyapunov Design--Plant with Unknown Parameter in the Domain 199 12.2 Lyapunov Design--Plant with Unknown Parameter in the 205 Boundary Condition 12.3 Swapping Design--Plant with Unknown Parameter in the Domain 210 12.4 Swapping Design--Plant with Unknown Parameter in the Boundary Condition 216 12.5 Simulations 223 12.6 Notes and References 225 Chapter 13. Output Feedback for PDEs with Spatially Varying Coefficients 226 13.1 Reaction-Advection-Diffusion Plant 226 13.2 Transformation to Observer Canonical Form 227 13.3 Nominal Controller 228 13.4 Filters 230 13.5 Frequency Domain Compensator with Frozen Parameters 232 13.6 Update Laws 233 13.7 Stability 235 13.8 Trajectory Tracking 242 13.9 The Ginzburg-Landau Equation 244 13.10 Identifier for the Ginzburg-Landau Equation 246 13.11 Stability of Adaptive Scheme for the Ginzburg-Landau Equation 248 13.12 Simulations 255 13.13 Notes and References 255 Chapter 14. Inverse Optimal Control 261 14.1 Nonadaptive Inverse Optimal Control 262 14.2 Reducing Control Effort through Adaptation 265 14.3 Dirichlet Actuation 267 14.4 Design Example 267 14.5 Comparison with the LQR Approach 268 14.6 Inverse Optimal Adaptive Control 271 14.7 Stability and Inverse Optimality of the Adaptive Scheme 273 14.8 Notes and References 275 Appendix A. Adaptive Backstepping for Nonlinear ODEs--The Basics 277 A.1 Nonadaptive Backstepping--The Known Parameter Case 277 A.2 Tuning Functions Design 279 A.3 Modular Design 289 A.4 Output Feedback Designs 297 A.5 Extensions 303 Appendix B. Poincare and Agmon Inequalities 305 Appendix C. Bessel Functions 307 C.1 Bessel Function Jn 307 C.2 Modified Bessel Function In 307 Appendix D. Barbalat's and Other Lemmas for Proving Adaptive Regulation 310 Appendix E. Basic Parabolic PDEs and Their Exact Solutions 313 E.1 Reaction-Diffusion Equation with Dirichlet Boundary Conditions 313 E.2 Reaction-Diffusion Equation with Neumann Boundary Conditions 315 E.3 Reaction-Diffusion Equation with Mixed Boundary Conditions 315 References 317 Index 327

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Book SynopsisDescribes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. This book provides the mathematical background and explains the theory.Table of ContentsPreface xi PART 1. THEORY 1 Chapter 1. Introduction 3 Chapter 2. Orthogonal Polynomials 8 2.1 Definition of Orthogonal Polynomials 8 2.2 Three-Term Recurrences 10 2.3 Properties of Zeros 14 2.4 Historical Remarks 15 2.5 Examples of Orthogonal Polynomials 15 2.6 Variable-Signed Weight Functions 20 2.7 Matrix Orthogonal Polynomials 21 Chapter 3. Properties of Tridiagonal Matrices 24 3.1 Similarity 24 3.2 Cholesky Factorizations of a Tridiagonal Matrix 25 3.3 Eigenvalues and Eigenvectors 27 3.4 Elements of the Inverse 29 3.5 The QD Algorithm 32 Chapter 4. The Lanczos and Conjugate Gradient Algorithms 39 4.1 The Lanczos Algorithm 39 4.2 The Nonsymmetric Lanczos Algorithm 43 4.3 The Golub-Kahan Bidiagonalization Algorithms 45 4.4 The Block Lanczos Algorithm 47 4.5 The Conjugate Gradient Algorithm 49 Chapter 5. Computation of the Jacobi Matrices 55 5.1 The Stieltjes Procedure 55 5.2 Computing the Coefficients from the Moments 56 5.3 The Modified Chebyshev Algorithm 58 5.4 The Modified Chebyshev Algorithm for Indefinite Weight Functions 61 5.5 Relations between the Lanczos and Chebyshev Semi-Iterative Algorithms 62 5.6 Inverse Eigenvalue Problems 66 5.7 Modifications of Weight Functions 72 Chapter 6. Gauss Quadrature 84 6.1 Quadrature Rules 84 6.2 The Gauss Quadrature Rules 86 6.3 The Anti-Gauss Quadrature Rule 92 6.4 The Gauss-Kronrod Quadrature Rule 95 6.5 The Nonsymmetric Gauss Quadrature Rules 99 6.6 The Block Gauss Quadrature Rules 102 Chapter 7. Bounds for Bilinear Forms uT f(A)v 112 7.1 Introduction 112 7.2 The Case u = v 113 7.3 The Case u <> v 114 7.4 The Block Case 115 7.5 Other Algorithms for u <> v 115 Chapter 8. Extensions to Nonsymmetric Matrices 117 8.1 Rules Based on the Nonsymmetric Lanczos Algorithm 118 8.2 Rules Based on the Arnoldi Algorithm 119 Chapter 9. Solving Secular Equations 122 9.1 Examples of Secular Equations 122 9.2 Secular Equation Solvers 129 9.3 Numerical Experiments 134 PART 2. APPLICATIONS 137 Chapter 10. Examples of Gauss Quadrature Rules 139 10.1 The Golub and Welsch Approach 139 10.2 Comparisons with Tables 140 10.3 Using the Full QR Algorithm 141 10.4 Another Implementation of QR 143 10.5 Using the QL Algorithm 144 10.6 Gauss-Radau Quadrature Rules 144 10.7 Gauss-Lobatto Quadrature Rules 146 10.8 Anti-Gauss Quadrature Rule 148 10.9 Gauss-Kronrod Quadrature Rule 148 10.10 Computation of Integrals 149 10.11 Modification Algorithms 155 10.12 Inverse Eigenvalue Problems 156 Chapter 11. Bounds and Estimates for Elements of Functions of Matrices 162 11.1 Introduction 162 11.2 Analytic Bounds for the Elements of the Inverse 163 11.3 Analytic Bounds for Elements of Other Functions 166 11.4 Computing Bounds for Elements of f(A) 167 11.5 Solving Ax = c and Looking at d T/x 167 11.6 Estimates of tr(A-1) and det(A) 168 11.7 Krylov Subspace Spectral Methods 172 11.8 Numerical Experiments 173 Chapter 12. Estimates of Norms of Errors in the Conjugate Gradient Algorithm 200 12.1 Estimates of Norms of Errors in Solving Linear Systems 200 12.2 Formulas for the A-Norm of the Error 202 12.3 Estimates of the A-Norm of the Error 203 12.4 Other Approaches 209 12.5 Formulas for the l2 Norm of the Error 210 12.6 Estimates of the l2 Norm of the Error 211 12.7 Relation to Finite Element Problems 212 12.8 Numerical Experiments 214 Chapter 13. Least Squares Problems 227 13.1 Introduction to Least Squares 227 13.2 Least Squares Data Fitting 230 13.3 Numerical Experiments 237 13.4 Numerical Experiments for the Backward Error 253 Chapter 14. Total Least Squares 256 14.1 Introduction to Total Least Squares 256 14.2 Scaled Total Least Squares 259 14.3 Total Least Squares Secular Equation Solvers 261 Chapter 15. Discrete Ill-Posed Problems 280 15.1 Introduction to Ill-Posed Problems 280 15.2 Iterative Methods for Ill-Posed Problems 295 15.3 Test Problems 298 15.4 Study of the GCV Function 300 15.5 Optimization of Finding the GCV Minimum 305 15.6 Study of the L-Curve 313 15.7 Comparison of Methods for Computing the Regularization Parameter 325 Bibliography 335 Index 361

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Book SynopsisFeatures simple treatment of uncertain linear programming. This book also presents an analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach.Trade Review"Robust optimization is an active area of research that is likely to find many practical applications in the future. This book is an authoritative reference that will be very useful to researchers working in this area. Furthermore, the book has been structured so that the first part could easily be used as the text for a graduate level course in robust optimization."--Brian Borchers, MAA Reviews "[T]his reference book gives an excellent and stimulating account of the classical and advanced results in the field, and should be consulted by all researchers and practitioners."--Joseph Frederic Bonnans, Zentralblatt MATHTable of ContentsPreface ix PART I. ROBUST LINEAR OPTIMIZATION 1 Chapter 1. Uncertain Linear Optimization Problems and their Robust Counterparts 3 1.1 Data Uncertainty in Linear Optimization 3 1.2 Uncertain Linear Problems and their Robust Counterparts 7 1.3 Tractability of Robust Counterparts 16 1.4 Non-Affne Perturbations 23 1.5 Exercises 25 1.6 Notes and Remarks 25 Chapter 2. Robust Counterpart Approximations of Scalar Chance Constraints 27 2.1 How to Specify an Uncertainty Set 27 2.2 Chance Constraints and their Safe Tractable Approximations 28 2.3 Safe Tractable Approximations of Scalar Chance Constraints: Basic Examples 31 2.4 Extensions 44 2.5 Exercises 60 2.6 Notes and Remarks 64 Chapter 3. Globalized Robust Counterparts of Uncertain LO Problems 67 3.1 Globalized Robust Counterpart | Motivation and Definition 67 3.2 Computational Tractability of GRC 69 3.3 Example: Synthesis of Antenna Arrays 70 3.4 Exercises 79 3.5 Notes and Remarks 79 Chapter 4. More on Safe Tractable Approximations of Scalar Chance Constraints 81 4.1 Robust Counterpart Representation of a Safe Convex Approximation to a Scalar Chance Constraint 81 4.2 Bernstein Approximation of a Chance Constraint 83 4.3 From Bernstein Approximation to Conditional Value at Risk and Back 90 4.4 Majorization 105 4.5 Beyond the Case of Independent Linear Perturbations 109 4.6 Exercises 136 4.7 Notes and Remarks 145 PART II. ROBUST CONIC OPTIMIZATION 147 Chapter 5. Uncertain Conic Optimization: The Concepts 149 5.1 Uncertain Conic Optimization: Preliminaries 149 5.2 Robust Counterpart of Uncertain Conic Problem: Tractability 151 5.3 Safe Tractable Approximations of RCs of Uncertain Conic Inequalities 153 5.4 Exercises 156 5.5 Notes and Remarks 157 Chapter 6. Uncertain Conic Quadratic Problems with Tractable RCs 159 6.1 A Generic Solvable Case: Scenario Uncertainty 159 6.2 Solvable Case I: Simple Interval Uncertainty 160 6.3 Solvable Case II: Unstructured Norm-Bounded Uncertainty 161 6.4 Solvable Case III: Convex Quadratic Inequality with Un-structured Norm-Bounded Uncertainty 165 6.5 Solvable Case IV: CQI with Simple Ellipsoidal Uncertainty 167 6.6 Illustration: Robust Linear Estimation 173 6.7 Exercises 178 6.8 Notes and Remarks 178 Chapter 7. Approximating RCs of Uncertain Conic Quadratic Problems 179 7.1 Structured Norm-Bounded Uncertainty 179 7.2 The Case of \-Ellipsoidal Uncertainty 195 7.3 Exercises 201 7.4 Notes and Remarks 201 Chapter 8. Uncertain Semidefinite Problems with Tractable RCs 203 8.1 Uncertain Semidefinite Problems 203 8.2 Tractability of RCs of Uncertain Semidefinite Problems 204 8.3 Exercises 222 8.4 Notes and Remarks 222 Chapter 9. Approximating RCs of Uncertain Semide-nite Problems 225 9.1 Tight Tractable Approximations of RCs of Uncertain SDPs with Structured Norm-Bounded Uncertainty 225 9.2 Exercises 232 9.3 Notes and Remarks 234 Chapter 10. Approximating Chance Constrained CQIs and LMIs 235 10.1 Chance Constrained LMIs 235 10.2 The Approximation Scheme 240 10.3 Gaussian Majorization 252 10.4 Chance Constrained LMIs: Special Cases 255 10.5 Notes and Remarks 276 Chapter 11. Globalized Robust Counterparts of Uncertain Conic Problems 279 11.1 Globalized Robust Counterparts of Uncertain Conic Problems: De-nition 279 11.2 Safe Tractable Approximations of GRCs 281 11.3 GRC of Uncertain Constraint: Decomposition 282 11.4 Tractability of GRCs 284 11.5 Illustration: Robust Analysis of Nonexpansive Dynamical Systems 292 Chapter 12. Robust Classification and Estimation 301 12.1 Robust Support Vector Machines 301 12.2 Robust Classification and Regression 309 12.3 Affine Uncertainty Models 325 12.4 Random Affine Uncertainty Models 331 12.5 Exercises 336 12.6 Notes and remarks 337 PART III. ROBUST MULTI-STAGE OPTIMIZATION 339 Chapter 13. Robust Markov Decision Processes 341 13.1 Markov Decision Processes 341 13.2 The Robust MDP Problems 345 13.3 The Robust Bellman Recursion on Finite Horizon 347 13.4 Notes and Remarks 352 Chapter 14. Robust Adjustable Multistage Optimization 355 14.1 Adjustable Robust Optimization: Motivation 355 14.2 Adjustable Robust Counterpart 357 14.3 Affinely Adjustable Robust Counterparts 368 14.4 Adjustable Robust Optimization and Synthesis of Linear Controllers 392 14.5 Exercises 408 14.6 Notes and Remarks 411 PART IV. SELECTED APPLICATIONS 415 Chapter 15. Selected Applications 417 15.1 Robust Linear Regression and Manufacturing of TV Tubes 417 15.2 Inventory Management with Flexible Commitment Contracts 421 15.3 Controlling a Multi-Echelon Multi-Period Supply Chain 432 Appendix A. Notation and Prerequisites 447 A.1 Notation 447 A.2 Conic Programming 448 A.3 Efficient Solvability of Convex Programming 460 Appendix B. Some Auxiliary Proofs 469 B.1 Proofs for Chapter 4 469 B.2 S-Lemma 481 B.3 Approximate S-Lemma 483 B.4 Matrix Cube Theorem 489 B.5 Proofs for Chapter 10 506 Appendix C. Solutions to Selected Exercises 511 C.1 Chapter 1 511 C.2 Chapter 2 511 C.3 Chapter 3 513 C.4 Chapter 4 513 C.5 Chapter 5 516 C.6 Chapter 6 519 C.7 Chapter 7 520 C.8 Chapter 8 521 C.9 Chapter 9 523 C.10 Chapter 12 525 C.11 Chapter 14 527 Bibliography 531 Index 539

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Book SynopsisEmphasizing the theory behind the computation, this book provides a self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software. It presents the mathematical foundations of numerical analysis. It introduces many advanced concepts in modern analysis.Trade Review"[Numerical Analysis] is a solid narrative of mathematical aspects of numerical analysis with an 'inquiry-based' learning method... There are more than 350 frequently challenging exercises that will interest both beginning students and readers with strong mathematical backgrounds."--Choice "A student who picks up this book and works through it systematically will learn a lot of interesting and important mathematics."--David S. Watkins, SIAM Review "Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks."--World Book IndustryTable of ContentsPreface xi Chapter 1. Numerical Algorithms 1 1.1 Finding roots 2 1.2 Analyzing Heron's algorithm 5 1.3 Where to start 6 1.4 An unstable algorithm 8 1.5 General roots: effects of floating-point 9 1.6 Exercises 11 1.7 Solutions 13 Chapter 2. Nonlinear Equations 15 2.1 Fixed-point iteration 16 2.2 Particular methods 20 2.3 Complex roots 25 2.4 Error propagation 26 2.5 More reading 27 2.6 Exercises 27 2.7 Solutions 30 Chapter 3. Linear Systems 35 3.1 Gaussian elimination 36 3.2 Factorization 38 3.3 Triangular matrices 42 3.4 Pivoting 44 3.5 More reading 47 3.6 Exercises 47 3.7 Solutions 50 Chapter 4. Direct Solvers 51 4.1 Direct factorization 51 4.2 Caution about factorization 56 4.3 Banded matrices 58 4.4 More reading 60 4.5 Exercises 60 4.6 Solutions 63 Chapter 5. Vector Spaces 65 5.1 Normed vector spaces 66 5.2 Proving the triangle inequality 69 5.3 Relations between norms 71 5.4 Inner-product spaces 72 5.5 More reading 76 5.6 Exercises 77 5.7 Solutions 79 Chapter 6. Operators 81 6.1 Operators 82 6.2 Schur decomposition 84 6.3 Convergent matrices 89 6.4 Powers of matrices 89 6.5 Exercises 92 6.6 Solutions 95 Chapter 7. Nonlinear Systems 97 7.1 Functional iteration for systems 98 7.2 Newton's method 103 7.3 Limiting behavior of Newton's method 108 7.4 Mixing solvers 110 7.5 More reading 111 7.6 Exercises 111 7.7 Solutions 114 Chapter 8. Iterative Methods 115 8.1 Stationary iterative methods 116 8.2 General splittings 117 8.3 Necessary conditions for convergence 123 8.4 More reading 128 8.5 Exercises 128 8.6 Solutions 131 Chapter 9. Conjugate Gradients 133 9.1 Minimization methods 133 9.2 Conjugate Gradient iteration 137 9.3 Optimal approximation of CG 141 9.4 Comparing iterative solvers 147 9.5 More reading 147 9.6 Exercises 148 9.7 Solutions 149 Chapter 10. Polynomial Interpolation 151 10.1 Local approximation: Taylor's theorem 151 10.2 Distributed approximation: interpolation 152 10.3 Norms in infinite-dimensional spaces 157 10.4 More reading 160 10.5 Exercises 160 10.6 Solutions 163 Chapter 11. Chebyshev and Hermite Interpolation 167 11.1 Error term ! 167 11.2 Chebyshev basis functions 170 11.3 Lebesgue function 171 11.4 Generalized interpolation 173 11.5 More reading 177 11.6 Exercises 178 11.7 Solutions 180 Chapter 12. Approximation Theory 183 12.1 Best approximation by polynomials 183 12.2 Weierstrass and Bernstein 187 12.3 Least squares 191 12.4 Piecewise polynomial approximation 193 12.5 Adaptive approximation 195 12.6 More reading 196 12.7 Exercises 196 12.8 Solutions 199 Chapter 13. Numerical Quadrature 203 13.1 Interpolatory quadrature 203 13.2 Peano kernel theorem 209 13.3 Gregorie-Euler-Maclaurin formulas 212 13.4 Other quadrature rules 219 13.5 More reading 221 13.6 Exercises 221 13.7 Solutions 224 Chapter 14. Eigenvalue Problems 225 14.1 Eigenvalue examples 225 14.2 Gershgorin's theorem 227 14.3 Solving separately 232 14.4 How not to eigen 233 14.5 Reduction to Hessenberg form 234 14.6 More reading 237 14.7 Exercises 238 14.8 Solutions 240 Chapter 15. Eigenvalue Algorithms 241 15.1 Power method 241 15.2 Inverse iteration 250 15.3 Singular value decomposition 252 15.4 Comparing factorizations 253 15.5 More reading 254 15.6 Exercises 254 15.7 Solutions 256 Chapter 16. Ordinary Differential Equations 257 16.1 Basic theory of ODEs 257 16.2 Existence and uniqueness of solutions 258 16.3 Basic discretization methods 262 16.4 Convergence of discretization methods 266 16.5 More reading 269 16.6 Exercises 269 16.7 Solutions 271 Chapter 17. Higher-order ODE Discretization Methods 275 17.1 Higher-order discretization 276 17.2 Convergence conditions 281 17.3 Backward differentiation formulas 287 17.4 More reading 288 17.5 Exercises 289 17.6 Solutions 291 Chapter 18. Floating Point 293 18.1 Floating-point arithmetic 293 18.2 Errors in solving systems 301 18.3 More reading 305 18.4 Exercises 305 18.5 Solutions 308 Chapter 19. Notation 309 Bibliography 311 Index 323

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Book SynopsisOffers an introduction to steady flight and performance for fixed-wing aircraft from a twenty-first-century flight systems perspective. This title covers various aspect of flight performance, including maximum and minimum air speed, maximum climb rate, minimum turn radius, flight ceiling, maximum range, and maximum endurance.Trade Review"Steady Aircraft Flight and Performance is very well written, and it contains many useful figures and illustrations. The level of presentation is readily accessible to its intended audience—undergraduate students in aerospace engineering—and the numerous examples and problems help solidify the concepts presented in the book. MATLAB code is included for many problems, facilitating the transition from concepts to computation."—Robert F. Stengel, Princeton University"This book is right on the mark. McClamroch's theoretical developments are, as usual, very rigorous and detailed."—Eric Feron, Georgia Institute of TechnologyTable of ContentsLIST OF ILLUSTRATIONS xi LIST OF MATLAB M-FILES xv PREFACE AND ACKNOWLEDGMENTS xix Chapter 1: Aircraft Components and Subsystems 1 1.1 Aircraft Subsystems for Conventional Fixed-Wing Aircraft 1 1.2 Aerodynamic Control Surfaces 2 1.3 Aircraft Propulsion Systems 3 1.4 Aircraft Structural Systems 4 1.5 Air Data and Flight Instrumentation 5 1.6 Guidance, Navigation, and Control 5 1.7 Flight Control Computers 6 1.8 Communication Systems 6 1.9 Aircraft Pilots 6 1.10 Autonomous Aircraft 7 1.11 Interconnection and Integration of Flight Systems 7 Chapter 2: Fluid Mechanics and Aerodynamics 9 2.1 Fundamental Properties of Air 9 2.2 Standard Atmosphere Model 10 2.3 Aerodynamics Fundamentals 15 2.4 Aerodynamics of Flow over a Wing 18 2.5 Wing Geometry 19 2.6 Problems 21 Chapter 3: Aircraft Translational Kinematics, Attitude, Aerodynamic Forces and Moments 24 3.1 Cartesian Frames 25 3.2 Aircraft Translational Kinematics 26 3.3 Aircraft Attitude and the Translational Kinematics 29 3.4 Translational Kinematics for Flight in a Fixed Vertical Plane 30 3.5 Translational Kinematics for Flight in a Fixed Horizontal Plane 32 3.6 Small Angle Approximations 34 3.7 Coordinated Flight 34 3.8 Clarification of Bank Angles 35 3.9 Aerodynamic Forces 35 3.10 Aerodynamic Moments 39 3.11 Problems 41 Chapter 4: Propulsion Systems 47 4.1 Steady Thrust and Power Relations 47 4.2 Jet Engines 47 4.3 Propeller Driven by Internal Combustion Engine 50 4.4 Turboprop Engines 53 4.5 Throttle as a Pilot Input 53 4.6 Problems 53 Chapter 5: Prelude to Steady Flight Analysis 56 5.1 Aircraft Forces and Moments 57 5.2 Steady Flight Equations 58 5.3 Steady Longitudinal Flight 60 5.4 Steady Level Turning Flight 60 5.5 Flight Constraints 60 5.6 Aircraft Case Studies 61 5.7 Characteristics of an Executive Jet Aircraft 62 5.8 Characteristics of a Single Engine Propeller-Driven General Aviation Aircraft 63 5.9 Characteristics of an Uninhabited Aerial Vehicle (UAV) 64 5.10 Problems 66 Chapter 6: Aircraft Steady Gliding Longitudinal Flight 69 6.1 Steady Gliding Longitudinal Flight 69 6.2 Steady Gliding Longitudinal Flight Analysis 71 6.3 Minimum Glide Angle 74 6.4 Minimum Descent Rate 74 6.5 Maximum Glide Angle 75 6.6 Maximum Descent Rate 75 6.7 Steady Gliding Longitudinal Flight Envelopes 76 6.8 Steady Gliding Longitudinal Flight: Executive Jet Aircraft 76 6.9 Steady Gliding Longitudinal Flight: General Aviation Aircraft 81 6.10 Conclusions 85 6.11 Problems 86 Chapter 7: Aircraft Cruise in Steady Level Longitudinal Flight 90 7.1 Steady Level Longitudinal Flight 90 7.2 Steady Level Longitudinal Flight Analysis 94 7.3 Jet Aircraft Steady Level Longitudinal Flight Performance 99 7.4 General Aviation Aircraft Steady Level Longitudinal Flight Performance 100 7.5 Steady Level Longitudinal Flight: Executive Jet Aircraft 102 7.6 Steady Level Longitudinal Flight Envelopes: Executive Jet Aircraft 106 7.7 Steady Level Longitudinal Flight: General Aviation Aircraft 109 7.8 Steady Level Longitudinal Flight Envelopes: General Aviation Aircraft 113 7.9 Conclusions 116 7.10 Problems 116 Chapter 8: Aircraft Steady Longitudinal Flight 121 8.1 Steady Longitudinal Flight 121 8.2 Steady Longitudinal Flight Analysis 125 8.3 Jet Aircraft Steady Longitudinal Flight Performance 130 8.4 General Aviation Aircraft Steady Longitudinal Flight Performance 133 8.5 Steady Climbing Longitudinal Flight: Executive Jet Aircraft 136 8.6 Steady Descending Longitudinal Flight: Executive Jet Aircraft 143 8.7 Steady Longitudinal Flight Envelopes: Executive Jet Aircraft 149 8.8 Steady Climbing Longitudinal Flight: General Aviation Aircraft 150 8.9 Steady Descending Longitudinal Flight: General Aviation Aircraft 157 8.10 Steady longitudinal Flight Envelopes: General Aviation Aircraft 162 8.11 Conclusions 164 8.12 Problems 165 Chapter 9: Aircraft Steady Level Turning Flight 171 9.1 Turns by Side-Slipping 171 9.2 Steady Level Banked Turning Flight 171 9.3 Steady Level Banked Turning Flight Analysis 175 9.4 Jet Aircraft Steady Level Turning Flight Performance 180 9.5 General Aviation Aircraft Steady Level Turning Flight Performance 183 9.6 Steady Level Turning Flight: Executive Jet Aircraft 186 9.7 Steady Level Turning Flight Envelopes: Executive Jet Aircraft 195 9.8 Steady Level Turning Flight: General Aviation Aircraft 196 9.9 Steady Level Turning Flight Envelopes: General Aviation Aircraft 207 9.10 Conclusions 209 9.11 Problems 209 Chapter 10: Aircraft Steady Turning Flight 214 10.1 Steady Banked Turns 214 10.2 Steady Banked Turning Flight Analysis 218 10.3 Jet Aircraft Steady Turning Flight Performance 225 10.4 General Aviation Aircraft Steady Turning Flight Performance 229 10.5 Steady Climbing and Turning Flight: Executive Jet Aircraft 233 10.6 Steady Descending and Turning Flight: Executive Jet Aircraft 244 10.7 Steady Turning Flight Envelopes: Executive Jet Aircraft 253 10.8 Steady Climbing and Turning Flight: General Aviation Aircraft 255 10.9 Steady Descending and Turning Flight: General Aviation Aircraft 266 10.10 Steady Turning Flight Envelopes: General Aviation Aircraft 276 10.11 Conclusions 278 10.12 Problems 279 Chapter 11: Aircraft Range and Endurance in Steady Flight 285 11.1 Fuel Consumption 285 11.2 Steady Flight Background 286 11.3 Range and Endurance of a Jet Aircraft in Steady Level Longitudinal Flight 286 11.4 Range and Endurance of a General Aviation Aircraft in Steady Level Longitudinal Flight 291 11.5 Range and Endurance of a Jet Aircraft in a Steady Level Turn 297 11.6 Range and Endurance of a General Aviation Aircraft in a Steady Level Turn 298 11.7 Range and Endurance of a Jet Aircraft in a Steady Turn 299 11.8 Range and Endurance of a General Aviation Aircraft in a Steady Turn 300 11.9 Maximum Range and Maximum Endurance: Executive Jet Aircraft 301 11.10 Maximum Range and Maximum Endurance: General Aviation Aircraft 307 11.11 Conclusions 313 11.12 Problems 313 Chapter 12: Aircraft Maneuvers and Flight Planning 319 12.1 Static Flight Stability 319 12.2 Flight Maneuvers 321 12.3 Pilot Inputs That Achieve a Desired Flight Condition 324 12.4 Flight Plans Defined by a Sequence of Waypoints 325 12.5 A Flight Planning Problem: Executive Jet Aircraft 327 12.6 A Flight Planning Problem: General Aviation Aircraft 331 12.7 Conclusions 336 12.8 Problems 336 Chapter 13: From Steady Flight to Flight Dynamics 344 13.1 Flight Dynamics Assumptions 345 13.2 Differential Equations for the Translational Flight Dynamics 346 13.3 Including Engine Characteristics and Fuel Consumption 349 13.4 Differential Equations for Longitudinal Translational Flight Dynamics 351 13.5 Differential Equations for Takeoff and Landing 353 13.6 Steady Flight and the Translational Flight Dynamics 355 13.7 Dynamic Flight Stability 356 13.8 Computing Dynamic Flight Performance Measures and Flight Envelopes 357 13.9 Flight Simulations: Executive Jet Aircraft 359 13.10 Flight Simulations: General Aviation Aircraft 365 13.11 Conclusions 372 13.12 Problems 372 Appendix A The Standard Atmosphere Model 379 Appendix B End-of-Chapter Problems 382 B.1 Executive Jet Aircraft 382 B.2 Single Engine Propeller-Driven General Aviation Aircraft 383 B.3 Uninhabited Aerial Vehicle (UAV) 383 REFERENCES 385 INDEX 387

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Book SynopsisBenford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together maTrade Review"This book will prove to be both a valuable reference and a first source to turn to for whoever is interested in the mathematical genesis and empirical usefulness of Benford's law."--Walter Kramer, Statistical PapersTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. xiii*Preface, pg. xvii*Notation, pg. xxiii*Chapter One. A Quick Introduction to Benford's Law, pg. 3*Chapter Two. A Short Introduction to the Mathematical Theory of Benford's Law, pg. 23*Chapter Three. Fourier Analysis and Benford's Law, pg. 68*Chapter Four. Benford's Law Geometry, pg. 109*Chapter Five. Explicit Error Bounds via Total Variation, pg. 119*Chapter Six. Levy Processes and Benford's Law, pg. 135*Chapter Seven. Benford's Law as a Bridge between Statistics and Accounting, pg. 177*Chapter Eight. Detecting Fraud and Errors Using Benford's Law, pg. 191*Chapter Nine. Can Vote Counts' Digits and Benford's Law Diagnose Elections?, pg. 212*Chapter Ten. Complementing Benford's Law for Small N: A Local Bootstrap, pg. 223*Chapter Eleven. Measuring the Quality of European Statistics, pg. 235*Chapter Twelve. Benford's Law and Fraud in Economic Research, pg. 244*Chapter Thirteen. Testing for Strategic Manipulation of Economic and Financial Data, pg. 257*Chapter Fourteen. Psychology and Benford's Law, pg. 267*Chapter Fifteen. Managing Risk in Numbers Games, pg. 276*Chapter Sixteen. Benford's Law in the Natural Sciences, pg. 290*Chapter Seventeen. Generalizing Benford's Law, pg. 304*Chapter Eighteen. PV Modeling of Medical Imaging Systems, pg. 319*Chapter Nineteen. Application of Benford's Law to Images, pg. 338*Chapter Twenty. Exercises, pg. 373*Bibliography, pg. 402*Index, pg. 433

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Book SynopsisProvides key concepts and technologies underlying the dynamics, control, and guidance of fixed-wing unmanned aircraft, and enables students with an introductory-level background in controls or robotics to enter this important area. This title explores the essential underlying physics and sensors of unmanned air vehicles problems.Trade Review"It is very nicely written with a presentation style that engineers in industry will appreciate. Most of the mathematics involved is very straightforward and the results are presented in a very clear manner. This is a text that should be very useful to those working on unmanned aerial vehicles and may even be of interest to those working on unmanned land or marine vehicles."--Applied Control Technology ConsortiumTable of ContentsPreface xi Chapter 1 Introduction 1 1.1 System Architecture 1 1.2 Design Models 4 1.3 Design Project 6 Chapter 2 Coordinate Frames 8 2.1 RotationMatrices 9 2.2 MAV Coordinate Frames 12 2.3 Airspeed,Wind Speed, and Ground Speed 18 2.4 TheWind Triangle 20 2.5 Differentiation of a Vector 24 2.6 Chapter Summary 25 2.7 Design Project 27 Chapter 3 Kinematics and Dynamics 28 3.1 State Variables 28 3.2 Kinematics 30 3.3 Rigid-body Dynamics 31 3.4 Chapter Summary 37 3.5 Design Project 38 Chapter 4 Forces and Moments 39 4.1 Gravitational Forces 39 4.2 Aerodynamic Forces andMoments 40 4.3 Propulsion Forces andMoments 52 4.4 Atmospheric Disturbances 54 4.5 Chapter Summary 57 4.6 Design Project 58 Chapter 5 Linear Design Models 60 5.1 Summary of Nonlinear Equations of Motion 60 5.2 Coordinated Turn 64 5.3 Trim Conditions 65 5.4 Transfer Function Models 68 5.5 Linear State-space Models 77 5.6 Reduced-order Modes 87 5.7 Chapter Summary 91 5.8 Design Project 92 Chapter 6 Autopilot Design Using Successive Loop Closure 95 6.1 Successive Loop Closure 95 6.2 Saturation Constraints and Performance 97 6.3 Lateral-directional Autopilot 99 6.4 Longitudinal Autopilot 105 6.5 Digital Implementation of PID Loops 114 6.6 Chapter Summary 117 6.7 Design Project 118 Chapter 7 Sensors for MAVs 120 7.1 Accelerometers 120 7.2 Rate Gyros 124 7.3 Pressure Sensors 126 7.4 Digital Compasses 131 7.5 Global Positioning System 134 7.6 Chapter Summary 141 7.7 Design Project 141 Chapter 8 State Estimation 143 8.1 Benchmark Maneuver 143 8.2 Low-pass Filters 144 8.3 State Estimation by Inverting the Sensor Model 145 8.4 Dynamic-observer Theory 149 8.5 Derivation of the Continuous-discrete Kalman Filter 151 8.6 Attitude Estimation 156 8.7 GPS Smoothing 158 8.8 Chapter Summary 161 8.9 Design Project 162 Chapter 9 Design Models for Guidance 164 9.1 AutopilotModel 164 9.2 Kinematic Model of Controlled Flight 165 9.3 Kinematic Guidance Models 168 9.4 Dynamic Guidance Model 170 9.5 Chapter Summary 172 9.6 Design Project 173 Chapter 10 Straight-line and Orbit Following 174 10.1 Straight-line Path Following 175 10.2 Orbit Following 181 10.3 Chapter Summary 183 10.4 Design Project 185 Chapter 11 Path Manager 187 11.1 Transitions BetweenWaypoints 187 11.2 Dubins Paths 194 11.3 Chapter Summary 202 11.4 Design Project 204 Chapter 12 Path Planning 206 12.1 Point-to-Point Algorithms 207 12.2 Coverage Algorithms 220 12.3 Chapter Summary 223 12.4 Design Project 224 Chapter 13 Vision-guided Navigation 226 13.1 Gimbal and Camera Frames and Projective Geometry 226 13.2 Gimbal Pointing 229 13.3 Geolocation 231 13.4 Estimating Target Motion in the Image Plane 234 13.5 Time to Collision 238 13.6 Precision Landing 240 13.7 Chapter Summary 244 13.8 Design Project 245 APPENDIX A: Nomenclature and Notation 247 APPENDIX B: Quaternions 254 B.1 Quaternion Rotations 254 B.2 Aircraft Kinematic and Dynamic Equations 255 B.3 Conversion Between Euler Angles and Quaternions 259 APPENDIX C: Animations in Simulink 260 C.1 Handle Graphics inMatlab 260 C.2 Animation Example: Inverted Pendulum 261 C.3 Animation Example: Spacecraft Using Lines 263 C.4 Animation Example: Spacecraft Using Vertices and Faces 268 APPENDIX D: Modeling in Simulink Using S-Functions 270 D.1 Example: Second-order Differential Equation 270 APPENDIX E: Airframe Parameters 275 E.1 Zagi Flying Wing 275 E.2 Aerosonde UAV 276 APPENDIX F: Trim and Linearization in Simulink 277 F.1 Using the Simulink trim Command 277 F.2 Numerical Computation of Trim 278 F.3 Using the Simulink linmod Command to Generate a State-space Model 282 F.4 Numerical Computation of State-space Model 284 APPENDIX G: Essentials from Probability Theory 286 APPENDIX H: Sensor Parameters 288 H.1 Rate Gyros 288 H.2 Accelerometers 288 H.3 Pressure Sensors 289 H.4 Digital Compass/Magnetometer 289 H.5 GPS 290 Bibliography 291 Index 299

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Book SynopsisWhenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly - why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion - how is this possible? This title includes some of these counterintuitive mathematical occurrences.Trade Review"Havil once again explores a variety of mathematical results and problems that at first appear to be self-contradictory, or stated in such a way that no solution could exist. In each case, he then either sketches a proof of why the result is not contradictory, or explains the solution to the seemingly unsolvable problem ... Like a magician revealing secrets, Havil maintains this sense through most chapters, dropping the punch line at just the right moment."--J.T. Noonan, Choice "This sequel to the author's book Nonplussed! supplies another set of brain-stretching problems and ideas. Its subtitle is 'Surprising Solutions to Counterintuitive Conundrums'; the surprise often consisting of the fact that it is possible to obtain a solution at all! ... This is another excellent book by Havil, following in the Martin Gardner tradition."--Alan Stevens, Mathematics Today "Julian Havil has quietly joined the ranks of the very best writers of popular mathematics. His two volume set Impossible? and Nonplussed! Mathematical Proof of Implausible Ideas not only belong in every library, but in the hands of every young person interested in mathematics and especially in the hands of their teachers."--John J. Watkins, Mathematical Intelligencer "Impossible? is an immensely thought-provoking book. Even if you skim or skip the more complex abstract math, you may have a hard time letting these puzzles go, so strongly do they flout common sense. You'll just have to do your best to put them our of your mind when you need to get some sleep, but if the situation ever arises, be sure to take Monty up on his offer."--Ray Bert, Civil Engineering "I would highly recommend this book as a reference for the mathematician who likes recreational mathematics, or as a good read for the recreational enthusiast with a penchant for more rigor."--Blair Madore, MAA ReviewsTable of ContentsAcknowledgments xi Introduction 1 Chapter 1: It's Common Knowledge 3 Chapter 2: Simpson's Paradox 11 Chapter 3: The Impossible Problem 21 Chapter 4: Braess's Paradox 31 Chapter 5: The Power of Complex Numbers 39 Chapter 6: Bucking the Odds 50 Chapter 7: Cantor's Paradise 68 Chapter 8: Gamow-Stern Elevators 82 Chapter 9: The Toss of a Coin 88 Chapter 10: Wild-Card Poker 103 Chapter 11: Two Series 113 Chapter 12: Two Card Tricks 131 Chapter 13: The Spin of a Needle 146 Chapter 14: The Best Choice 165 Chapter 15: The Power of Powers 176 Chapter 16: Benford's Law 190 Chapter 17: Goodstein Sequences 201 Chapter 18: The Banach-Tarski Paradox 210 The Motifs 217 Appendix 221 Index 233

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Book SynopsisTrade ReviewWinner of the 2015 Louis J. Battan Author's Award, American Meteorological Society "Mathematicians Ian Roulstone and John Norbury demystify the maths behind meteorology. Trailblazers' work is vividly evoked, from eighteenth-century mathematician Leonhard Euler on hydrostatics to physicist Vilhelm Bjerknes's numerical weather prediction. The pace cranks up with twentieth-century advances such as Jule Gregory Charney's harnessing of the gargantuan ENIAC computer for his work in the 1940s and 1950s on forecasting pressure patterns."--Nature "[O]ne of the great strengths of the book is the way it picks apart the challenge of making predictions about a chaotic system, showing what improvements we might yet hope for and what factors confound them."--Philip Ball, Prospect "A welcome and authoritative account of the 20th-century contributions of mathematically sophisticated meteorologists such as Vilhelm Berknes (1862--1951), Carl-Gustav Rossby (1898--1957), Jule Charney (1917--1981), and Ed Lorenz (1917--2008)... Clearly, this book is informative and inspirational, leaving plenty of room for innovations by future generations of mathematicians and modelers."--James Rodger Fleming, MAA Reviews "This book gives a deep insight of the mathematics involved in the forecast of weather... The authors have done a brilliant work to collect a huge amount of historical information, as well as mathematical information, but keeping always a level in the explanations that makes the text accessible to undergraduate students in the first years, and even to people not so familiar with mathematics. All in all, this is a very interesting and enjoyable reading."--Vicente Munoz, European Mathematical Society "Shows how much modern weather forecasting depends on mathematics... A superior read."--Alexander Bogolomny, CTK Insights "Takes readers on a journey, starting with the initial vision of Bjerknes, and then leads them through the early unsuccessful hand-calculated attempts at forecasting the weather mathematically, progressing to the use of early electronic computers which, even though successful, could not produce a timely forecast. It concludes by describing the current methods of Numerical Weather Prediction ... a book that will appeal to the intelligent 'popular science' enthusiast without disengaging the more theoretically-versed reader."--David-John Gibbs, Weather "UK mathematicians Roulstone and Norbury provide a lively account of the evolution of numerical weather prediction, focusing on the individuals involved in advancing measurement of atmospheric properties and the implementation of numerical methods to describe and predict atmospheric processes... This unique historical narrative will interest scholars of the history and philosophy of science."--Choice "Roulstone and Norbury do well within the constraints of this species of book. The story they tell is far from exhausted. I hope they write a sequel!"--John P. Boyd, Mathematical Reviews "[A] fascinating account of science's admirable but ultimately inadequate attempts to get to grips with the natural environment upon which we depend for life itself, but which is equally capable of visiting death and destruction upon us."--Jonathan Gornall, The National "[T]he authors have done well to create a book that will appeal to the intelligent 'popular science' enthusiast without disengaging the more theoretically-versed reader."--David-John Gibbs, Weather "Accessible and timely, Invisible in the Storm explains the crucial role of mathematics in understanding the ever-changing weather."--Nina Shokina, Zentralblatt MATH "[T]his is a well-written book giving a generally clear and accessible account of how weather forecasts are prepared. The historical detail enlivens the narrative and makes for an enjoyable read. The authors have considerable knowledge and expertise, and the book is scientifically sound. It can be warmly recommended to anyone who wishes to understand, in broad terms, how modern weather forecasts are made and how we may use models of the atmosphere to anticipate changes in the earth's climate."--Peter Lynch, Notices of the AMS "This very readable book provides an excellent insight into the history of forecasting the weather, with a considerable, but not too challenging, mathematical bent."--Colin J W Czapiewski, Actuary "Invisible in the Storm: The Role of Mathematics in Understanding Weather explores how mathematics and meteorology come together to improve weather and climate prediction, taking readers on a fascinating journey through the work of trailblazing scientists over the past 100 years."--University of Surrey website "I really enjoyed reading the book and I would recommend it to specialists who want to get an overview of the history of numerical weather prediction. I think it is also well worth reading for anyone who wishes to understand the developments in the science of meteorology that has led to the present level of forecast skill."--Erland Kallen, ECMWF Newsletter "Roulstone and Norbury have done an outstanding job and provide readers a fine bibliography to continue their education on this fascinating topic."--Robert E. O'malley, Jr., SIAM Review "Accessible and timely, Invisible in the Storm explains the crucial role of mathematics in understanding the ever-changing weather."--World Book Industry "[T]his is a well-written book giving a generally clear and accessible account of how weather forecasts are prepared. The historical detail enlivens the narrative and makes for an enjoyable read. The authors have considerable knowledge and expertise, and the book is scientifically sound. It can be warmly recommended to anyone who wishes to understand, in broad terms, how modern weather forecasts are made, and how we may use models of the atmosphere to anticipate changes in the Earth's climate."--Peter Lynch, Irish Math Society Bulletin "This book is highly readable and gives a bird's eye view of development of meteorology... It is strongly recommended to practitioners of meteorology and those interested in understanding this complex subject."--Ravi S. Nanjundiah, Current Science "The authors have to be applauded for having succeeded in writing a very entertaining and accessible book... The book must be considered essential reading for anyone interested in the history and mathematics of weather prediction."--Sebastian Reich, Jahresbericht der DMV "I recommend Invisible in the Storm both to mathematics undergraduates and educators who are interested in applied mathematics, weather forecasting, or both."--Steven Boyce, Mathematics TeacherTable of ContentsPreface vii Prelude: New Beginnings 1 ONE The Fabric of a Vision 3 TWO From Lore to Laws 47 THREE Advances and Adversity 89 FOUR When the Wind Blows the Wind 125 Interlude: A Gordian Knot 149 FIVE Constraining the Possibilities 153 SIX The Metamorphosis of Meteorology 187 Color Insert follows page 230 SEVEN Math Gets the Picture 231 EIGHT Predicting in the Presence of Chaos 271 Postlude: Beyond the Butterfly 313 Glossary 317 Bibliography 319 Index 323

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Book SynopsisDid you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? This title demonstrates how to use physical intuition to solve these and other math problems.Trade ReviewOne of Amazon.com science editors' Top 10 list for Science, Best for 2009 One of Choice's Outstanding Academic Titles for 2009 "The Mathematical Mechanic documents novel ways of viewing physics as a method of understanding mathematics. Levi uses physical arguments as tools to conjecture about mathematical concepts before providing rigorous proofs... The Mathematical Mechanic is an excellent display of creative, interdisciplinary problem-solving strategies. The author has explained complex concepts with simplicity, yet the mathematics is accurate."--Mathematics Teacher "A most interesting book... Many of the ideas in it could be used as motivational or illustrative examples to support the teaching of non-specialists, especially physicists and engineers. In conclusion--a thoroughly enjoyable and thought-provoking read."--Nigel Steele, London Mathematical Society Newsletter "The Mathematical Mechanic reverses the usual interaction of mathematics and physics... Careful study of Levi's book may train readers to think of physical companions to mathematical problems... Mathematicians will find The Mathematical Mechanic provides exercise in new ways of thinking. Instructors will find it contains material to supplement mathematics courses, helping physically-minded students approach mathematics and helping mathematically-minded students appreciate physics."--John D. Cook, MAA Reviews "Mark Levi reverses the old stereotype that math is merely a tool to aid physicists by showing that many questions in mathematics can be easily solved by interpreting them as physical problems... Some sections of the book require readers to brush up on their calculus but Levi's clear explanations, witty footnotes, and fascinating insights make the extra effort painless."--SEED Magazine "The book is chock-full of these seemingly magical physical thought experiments involving bicycle wheels, pistons, springs, soap films, pendulums, and electric circuits, with applications to geometry, maximization and minimization problems, inequalities, optics, integrals, and complex functions... I highly recommend it to anyone who is (even slightly) interested in physics, and appreciates mathematical elegance and cleverness. It would make a great gift for almost anyone, whether a high school student or university professor, armchair physicist or professional mathematician."--Boris Yorgey, The Math Less Traveled "The Mathematical Mechanic is a pleasant surprise."--E. Kincanon, Choice "This is a delightful and unusual book that is a welcome addition to the literature. Certainly, any calculus teacher and many others of us as well will want to have it on the shelf for ready reference. It not only will enhance our teaching experience but will also teach us (the instructors) something in the process."--Steven G. Krantz, UMAP JournalTable of Contents*FrontMatter, pg. i*Contents, pg. v*1 Introduction, pg. 1*2 The Pythagorean Theorem, pg. 9*3 Minima and Maxima, pg. 27*4 Inequalities by Electric Shorting, pg. 76*5 Center of Mass: Proofs and Solutions, pg. 84*6 Geometry and Motion, pg. 99*7 Computing Integrals Using Mechanics, pg. 109*8. The Euler-Lagrange Equation via Stretched Springs, pg. 115*9 Lenses, Telescopes, and Hamiltonian Mechanics, pg. 120*10 A Bicycle Wheel and the Gauss-Bonnet Theorem, pg. 133*11 Complex Variables Made Simple(r), pg. 148*Appendix. Physical Background, pg. 161*Bibliography, pg. 183*Index, pg. 185

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Book SynopsisFocuses on chessboard problems. From the Knight's Tour Problem and Queens Domination to their many variations, this work surveys the well-known problems in this surprisingly fertile area of recreational mathematics. Using visual language of graph theory, it guides the reader to the forefront of research in mathematics.Trade Review"This book is extremely well written and is, no doubt, the best exposition of the connection between the chessboard problems and recreational mathematics. The author surveys all the well-known problems about chess and the chessboard... The problems are treated in depth from their beginnings through to their status today."--Mohammed Aassila, MAA Review "Torus-shaped boards, three-dimensional boards, a shape called the Klein bottle--the simple checkerboard pattern proves to be creatively malleable when Watkins puts his mind to his hobbylike subject. Watkins' invitational tone ensures attention from the finite but enthusiastic audience for mathematical recreation."--Booklist "Watkins offers an excellent invitation to serious mathematics."--Choice "I would be happy to recommend this book to you... The book is an easy and entertaining read that shows numerous paths into various branches of discrete mathematics and graph theory."--Paul J. Campbell, Mathematics Magazine "This is not just about chess, but also the three centuries of 'recreational mathematics' that the game has inspired. From simple questions, such as whether it is possible for a knight to land on each square of the board on its path, Watkins wades into graph theory, the mathematics of three-dimensional chess and even chess on a torus."--Nature Physics "This book is stimulating and very well written. It is admirably clear... Definitely the book is highly recommended and is of much interest. This book is, no doubt, the newly best exposition of the interconnection between amusing recreational mathematics and the interesting chessboard problems. I feel sure that it will be of great use both to students of graph theory, geometry, topology and mathematics, in general, and captivate to scholars, instructors, chess enthusiasts, puzzle devotees, and to those intervening in amusing and recreational mathematics."--Francisco Jose Cano Sevilla, European Mathematical Society "A most enjoyable book that will surely offer new and original avenues for problem solvers of all kinds in need of new techniques, approaches or problems to solve."--Robert Bilinski, CruxTable of ContentsPreface ix Chapter One Introduction 1 Chapter Two Knight's Tours 25 Chapter Three The Knight's Tour Problem 39 Chapter Four Magic Squares 53 Chapter Five The Torus and the Cylinder 65 Chapter Six The Klein Bottle and Other Variations 79 Chapter Seven Domination 95 Chapter Eight Queens Domination 113 Chapter Nine Domination on Other Surfaces 139 Chapter Ten Independence 163 Chapter Eleven Other Surfaces, Other Variations 191 Chapter Twelve Eulerian Squares 213 Chapter Thirteen Polyominoes 223 References 247 Index 251

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Book SynopsisA collection of puzzles. Covering a range of fields, from geography and environmental studies to map- and flag-making, it uses basic algebra and geometry to solve problems. It is suitable for readers interested in sharpening their thinking and mathematical skills.Trade Review"[Banks displays] a playful imagination and love of the fantastic that one would not ordinarily associate with a mathematical engineer... Banks's style is entertaining but never condescending."--The Christian Science Monitor "Banks turns trivial questions into mind-expanding demonstrations of the magical powers of mathematics. Nor does he restrict himself to trivial questions: his shrewd analyses coax secrets out of such weighty topics as global population growth and the melting of polar ice caps... Not a math textbook which teaches readers how to solve set types of problems, this collection of puzzles does something far more important: it teaches us how to delight in unexpected challenges to our numerical imagination."--BooklistTable of ContentsPreface ix Acknowledgments xiii Chapter 1 Broad Stripes and Bright Stars 3 Chapter 2 More Stars, Honeycombs, and Snowflakes 13 Chapter 3 Slicing Things Like Pizzas and Watermelons 23 Chapter 4 Raindrops Keep Falling on My Head and Other Goodies 34 Chapter 5 Raindrops and Other Goodies Revisited 44 Chapter 6 Which Major Rivers Flow Uphill? 49 Chapter 7 A Brief Look at pi, e, and Some Other Famous Numbers 57 Chapter 8 Another Look at Some Famous Numbers 69 Chapter 9 Great Number Sequences: Prime, Fibonacci, and Hailstone 78 Chapter 10 A Fast Way to Escape 97 Chapter 11 How to Get Anywhere in About Forty-Two Minutes 105 Chapter 12 How Fast Should You Run in the Rain? 114 Chapter 13 Great Turtle Races: Pursuit Curves 123 Chapter 14 More Great Turtle Races: Logarithmic Spirals 131 Chapter 15 How Many People Have Ever Lived? 138 Chapter 16 The Great Explosion of 2023 146 Chapter 17 How to Make Fairly Nice Valentines 153 Chapter 18 Somewhere Over the Rainbow 163 Chapter 19 Making Mathematical Mountains 177 Chapter 20 How to Make Mountains out of Molehills 184 Chapter 21 Moving Continents from Here to There 196 Chapter 22 Cartography: How to Flatten Spheres 204 Chapter 23 Growth and Spreading and Mathematical Analogies 219 Chapter 24 How Long Is the Seam on a Baseball? 232 Chapter 25 Baseball Seams, Pipe Connections, and World Travels 247 Chapter 26 Lengths, Areas, and Volumes of All Kinds of Shapes 256 References 279 Index 285

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Book SynopsisWhat are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. This title challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations.Trade Review"Nahin's sophisticated puzzles, and their accompanying explanations, have a far better than even chance of fascinating and preoccupying the mathematically literate readership they seek."--Publisher's Weekly "An entertaining, thought-provoking collection of twenty-one puzzles...These puzzles invite the reader to think intuitively, mathematically, and creatively about the laws of probability as they apply in lighthearted, often counterintuitive ways to a diverse collection of practical and speculative situations."--Mathematics Teacher "By following Nahin's informal style it is possible to set [the examples] up quickly from first principles and slip them into courses on calculus, algebra, or scientific programming. They also offer a wealth of topics for undergraduate projects. Those duelling idiots are fighting over a goldmine."--Des Higham, MSOR ConnectionsTable of ContentsAcknowledgments ix Preface xi Introduction 3 The Problems 15 1. How to ask an Embarrassing question 15 2. When Idiots duel 16 3. Will the light Bulb glow? 22 4. Tho Underdog and the World Series 26 5. The Curious Case of the Snowy Birthdays 27 6. When Human Flesh Begins to Fail 34 7. Baseball Again, and Mortal Flesh Too 51 8. Ball Madness 56 9. Who Pays for the Coffee? 42 10. The Chess Champ versus the Gunslinger 45 11. A Different Slice of Probabilistic Pi 49 12. When Negativity is a No-No 50 15. The Power of Randomness 51 14. The Random Radio 52 15. An Inconceivable Difficulty 55 16. The Unsinkable Tub is Sinking! How to Find Her, Fast 57 17. A Walk in the Garden 58 18. Two Flies Stuck on a Piece of Flypaper--How Far Apart? 61 19.The Blind Spider and the Fly 62 20. Reliably Unreliable 68 21. When Theory Fails, There is always the Computer 71 The Solutions 81 Random Number Generators 176 "Some things Just Have to be Done By Hand!" 198 MATLAB Programs 202 Index 267 About the Author 271

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Book SynopsisWe all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory. This book gives us the complete history of this area of mathematics, from its classical analytical beginnings to the present day.Trade Review"In the 18th century, mathematicians began to tease apart how best to track down and intercept prey, inspired by pirate ships bearing down on merchant vessels. The mathematics is by no means trivial, and quickly becomes fiendish if the merchant ship takes evasive action. This is just one of the colorful problems in Paul Nahin's fascinating history of the mathematics of pursuit, in which he guides us masterfully through the maths itself--think lions and Christians, submarines and torpedoes, and the curvaceous flight of fighter aircraft."--New Scientist "This is a highly readable book that offers several colorful applications of differential equations and good examples of non-trivial integrals for calculus students. It would be a good source of examples for the classroom and or a starting point for an independent project."--Bill Satzer, MAA Review "This book contains a well-written, well-organized collection of solutions to twenty-one challenging calculus and differential equation problems that concern pursuit and evasion as well as the historical background of each problem type."--Mathematics Teacher "I am sure that this book will appeal to everyone who is interested in mathematics and game theory. Excellent work."--Prabhat Kumar Mahanti, Zentralblatt Math "Chases and Escapes is a wonderful collection of interesting and classic pursuit and evasion problems... If you are interested in in dogs chasing ducks, pirates chasing merchants, and submarines hiding, then this book is for you."--Mathematics TeacherTable of ContentsPreface to the Paperback Edition xiii What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It) xxvii Introduction 1 Chapter 1. The Classic Pursuit Problem 7 *1.1 Pierre Bouguer's Pirate Ship Analysis 7 *1.2 A Modern Twist on Bouguer 17 *1.3 Before Bouguer: The Tractrix 23 *1.4 The Myth of Leonardo da Vinci 27 *1.5 Apollonius Pursuit and Ramchundra's Intercept Problem 29 Chapter 2. Pursuit of (Mostly) Maneuvering Targets 41 *2.1 Hathaway's Dog-and-Duck Circular Pursuit Problem 41 *2.2 Computer Solution of Hathaway's Pursuit Problem 52 *2.3 Velocity and Acceleration Calculations for a Moving Body 64 *2.4 Houghton's Problem: A Circular Pursuit That Is Solvable in Closed Form 78 *2.5 Pursuit of Invisible Targets 85 *2.6 Proportional Navigation 93 Chapter 3. Cyclic Pursuit 106 *3.1 A Brief History of the n-Bug Problem, and Why It Is of Practical Interest 106 *3.2 The Symmetrical n-Bug Problem 110 *3.3 Morley's Nonsymmetrical 3-Bug Problem 116 Chapter 4. Seven Classic Evasion Problems 128 *4.1 The Lady-in-the-Lake Problem 128 *4.2 Isaacs's Guarding-the-Target Problem 138 *4.3 The Hiding Path Problem 143 *4.4 The Hidden Object Problem: Pursuit and Evasion as a Simple Two-Person, Zero-Sum Game of Attack-and-Defend 156 *4.5 The Discrete Search Game for a Stationary Evader -- Hunting for Hiding Submarines 168 *4.6 A Discrete Search Game with a Mobile Evader -- Isaacs's Princess-and-Monster Problem 174 *4.7 Rado's Lion-and-Man Problem and Besicovitch's Astonishing Solution 181 Appendix A Solution to the Challenge Problems of Section 1.1 187 Appendix B Solutions to the Challenge Problems of Section 1.2 190 Appendix C Solution to the Challenge Problem of Section 1.5 198 Appendix D Solution to the Challenge Problem of Section 2.2 202 Appendix E Solution to the Challenge Problem of Section 2.3 209 Appendix F Solution to the Challenge Problem of Section 2.5 214 Appendix G Solution to the Challenge Problem of Section 3.2 217 Appendix H Solution to the Challenge Problem of Section 4.3 219 Appendix I Solution to the Challenge Problem of Section 4.4 222 Appendix J Solution to the Challenge Problem of Section 4.7 224 Appendix K Guelman's Proof 229 Notes 235 Bibliography 245 Acknowledgments 249 Index 251

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Book SynopsisAlthough we seldom think of it, our lives are played out in a world of numbers. Such common activities as throwing baseballs, skipping rope, growing flowers, playing football, measuring savings accounts, and many others are inherently mathematical. So are more speculative problems that are simply fun to ponder in themselves--such as the best way to score Olympic events. Here Robert Banks presents a wide range of musings, both practical and entertaining, that have intrigued him and others: How tall can one grow? Why do we get stuck in traffic? Which football player would have a better chance of breaking away--a small, speedy wide receiver or a huge, slow linebacker? Can California water shortages be alleviated by towing icebergs from Antarctica? What is the fastest the 100-meter dash will ever be run? The book''s twenty-four concise chapters, each centered on a real-world phenomenon, are presented in an informal and engaging manner. Banks shows how math and simple reasoning together may produce elegant models that explain everything from the federal debt to the proper technique for ski-jumping. This book, which requires of its readers only a basic understanding of high school or college math, is for anyone fascinated by the workings of mathematics in our everyday lives, as well as its applications to what may be imagined. All will be rewarded with a myriad of interesting problems and the know-how to solve them.Trade ReviewOne of Choice's Outstanding Academic Titles for 1999 "Robert Banks's study of everyday phenomena is infused with infectious enthusiasm."--Publishers Weekly "There is something here for every mathematically inclined reader. The aerodynamics of balls in sport, the spread of diseases, traffic flow, the effect of meteor impacts--[Banks] deals with these and much more in engaging, well-judged detail."--Robert Matthews, New Scientist "A fabulous exposition of adventures in applied mathematics. It's already one of my favourite books. It's so good I find it hard to lay aside."--B. L. Henry, Physicist "This book provides an entertaining look at some simple and interesting mathematical models for a range of topics... The choice of modeling subjects is imaginative... Every chapter is interesting, and the self-contained nature of each section of the book means that one can happily 'dip in and out' without losing the thread of the text."--Alistair Fitt, London Mathematical Society Newsletter "The book stands out because the examples are all treated as real-life examples with real data, and taking into account all the complications that are usually left out in academic examples: the earth is not a perfect sphere, a baseball is rough because of its stitches, it is thrown with spin, there is resistance of the air, and the resistance differs with the height, etc. Even though, there are a lot of formulas and numbers, the reading is pleasant and smooth."--A. Bultheel, European Mathematical SocietyTable of ContentsPreface ix Acknowledgments xiii Chapter 1 Units and Dimensions and Mach Numbers 3 Chapter 2 Alligator Eggs and the Federal Debt 15 Chapter 3 Controlling Growth and Perceiving Spread 24 Chapter 4 Little Things Falling from the Sky 31 Chapter 5 Big Things Falling from the Sky 42 Chapter 6 Towing and Melting Enormous Icebergs: Part I 54 Chapter 7 Towing and Melting Enormous Icebergs: Part II 68 Chapter 8 A Better Way to Score the Olympics 79 Chapter 9 How to Calculate the Economic Energy of a Nation 93 Chapter 10 How to Start Football Games, and Other Probably Good Ideas 10 Chapter 11 Gigantic Numbers and Extreme Exponents 121 Chapter 12 Ups and Downs of Professional Football 133 Chapter 13 A Tower, a Bridge, and a Beautiful Arch 150 Chapter 14 Jumping Ropes and Wind Turbines 168 Chapter 15 The Crisis of the Deficit: Gompertz to the Rescue 179 Chapter 16 How to Reduce the Population with Differential Equations 189 Chapter 17 Shot Puts, Basketballs, and Water Fountains 201 Chapter 18 Balls and Strikes and Home Runs 219 Chapter 19 Hooks and Slices and Holes in One 234 Chapter 20 Happy Landings in the Snow 243 Chapter 21 Water Waves and Falling Dominoes 254 Chapter 22 Something Shocking about Highway Traffic 270 Chapter 23 How Tall Will I Grow? 283 Chapter 24 How Fast Can Runners Run? 300 References 321 Index 327

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Book SynopsisComputational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. This book provides students with a versatile and accessible introduction to the subject.Trade Review"The first edition of this book had received very positive feedback and was warmly welcomed by the mathematical community. It is very good news for all us is that the second revised edition is even better!"--Svitlana P. Rogovchenko, Zentralblatt MATH Praise for the previous edition: "The heart of Introduction to Computational Science is a collection of modules. Each module is either a discussion of a general computational issue or an investigation of an application... [This book] has been carefully and thoughtfully written with students clearly in mind."--William J. Satzer, MAA Reviews Praise for the previous edition: "Introduction to Computational Science is useful for students and others who want to obtain some of the basic skills of the field. Its impressive collection of projects allows readers to quickly enjoy the power of modern computing as an essential tool in building scientific understanding."--Wouter van Joolingen, Physics Today Praise for the previous edition: "A masterpiece. I know of nothing comparable. I give it five stars."--James M. Cargal, UMAP Journal Praise for the previous edition: "This is an important book with a wonderful collection of examples, models, and references."--Robert M. Panoff, Shodor Education Foundation Praise for the previous edition: "This is a very good introduction to the field of computational science."--Peter Turner, Clarkson University "Despite its substantial weight, the book is extremely user friendly... There are many different courses that one could build with this book as foundation, and it is an indispensible resource for anyone seeking to bring modeling projects into their classes."--David M. Bressoud, UMAP Journal

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Book SynopsisA website's ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exTrade Review"[A] thorough exploration of the methods and applications of ranking for an audience ranging from computer scientists and engineers to high-school teachers to 'people interested in wagering on just about anything'."--Nature Physics "Who's #1 provides a fascinating tour through the world of rankings and is highly recommended."--Richard J. Wilders, MAA Reviews "[T]he book ... provide[s] an excellent, accessible, and stimulating discussion of the material it does cover. Overall, the book makes a valuable addition to the canon of rating and ranking."--David J. Hand, Journal of Applied Statistics "This book provides an interesting overview of ranking various sports teams, chess players, politicians, and the like in real-life circumstances, which typically involve serious constraints on the time available to find the optimal ranking."--Choice "The book could be used to supplement a course on linear algebra and/or numerical linear algebra... The book could also be used as the basis for a short topics course or undergraduate research project on ranking, or it could be used in a modeling class as an example of how mathematical modeling is done. In addition to describing the mathematics of ranking, the book is full of interesting tidbits that add to the pleasure of its reading."--James Keener, SIAM Review "When I started this book I knew very little about American football. I was little the wiser after finishing it, but I had an excellent understanding of various methods used in the obtaining of the ranking of teams and their interrelationships. Langville and Meyer are to be commended for this collection, and anyone who is more conversant with North American sports than I am will most certainly be stimulated by reading Who's #1?"--Andrew I. Dale, Notices of the AMS "Readers will find many interesting ideas as they grapple with the complexities of the science of rating and ranking."--Bob Horton, Mathematics Teacher "[T]his book is a call to consciousness on the relevance of rating and ranking as well as an enjoyable start-up guide from the point of view of algebraic methods."--Francisco Grimaldo Moreno, JASSS "This book is a great introduction to the field (including its constituent parts in linear algebra and data mining) and contains enough depth to be used as a supplemental book in a data mining course or as a jumping off point for an interested researcher... Overall this is a very nice, well written book that could be use in multiple ways by a wide variety of audiences."--Nicholas Mattei, SigAct News "The profit the scientometrics community can gain from this book is an indirect one: an attitude how to compile a systematic collection of potential methods, how to select carefully using theoretical tests and empirical examples and how to combine methods to get a comprehensive, multidimensional rating and ranking system. In this sense, it is a highly recommended reading for all readers of the journal Scientometrics."--Andras Schubert, Scientometrics "This book is an excellent read for everyone; readers might be sports enthusiasts, social choice theorists, mathematicians, computer scientists, engineers, and college and high school teachers. Teachers will find quite an easy way to extract material for a short module."--Valentina Dagiene, Zentralblatt MATHTable of ContentsPreface xiii Purpose xiii Audience xiii Prerequisites xiii Teaching from This Book xiv Acknowledgments xiv Chapter 1. Introduction to Ranking 1 Social Choice and Arrow's Impossibility Theorem 3 Arrow's Impossibility Theorem 4 Small Running Example 4 Chapter 2. Massey's Method 9 Initial Massey Rating Method 9 Massey's Main Idea 9 The Running Example Using the Massey Rating Method 11 Advanced Features of the Massey Rating Method 11 The Running Example: Advanced Massey Rating Method 12 Summary of the Massey Rating Method 13 Chapter 3. Colley's Method 21 The Running Example 23 Summary of the Colley Rating Method 24 Connection between Massey and Colley Methods 24 Chapter 4. Keener's Method 29 Strength and Rating Stipulations 29 Selecting Strength Attributes 29 Laplace's Rule of Succession 30 To Skew or Not to Skew? 31 Normalization 32 Chicken or Egg? 33 Ratings 33 Strength 33 The Keystone Equation 34 Constraints 35 Perron-Frobenius 36 Important Properties 37 Computing the Ratings Vector 37 Forcing Irreducibility and Primitivity 39 Summary 40 The 2009-2010 NFL Season 42 Jim Keener vs. Bill James 45 Back to the Future 48 Can Keener Make You Rich? 49 Conclusion 50 Chapter 5. Elo's System 53 Elegant Wisdom 55 The K-Factor 55 The Logistic Parameter ? 56 Constant Sums 56 Elo in the NFL 57 Hindsight Accuracy 58 Foresight Accuracy 59 Incorporating Game Scores 59 Hindsight and Foresight with ? = 1000, K = 32, H = 15 60 Using Variable K-Factors with NFL Scores 60 Hindsight and Foresight Using Scores and Variable K-Factors 62 Game-by-Game Analysis 62 Conclusion 64 Chapter 6. The Markov Method 67 The Markov Method 67 Voting with Losses 68 Losers Vote with Point Differentials 69 Winners and Losers Vote with Points 70 Beyond Game Scores 71 Handling Undefeated Teams 73 Summary of the Markov Rating Method 75 Connection between the Markov and Massey Methods 76 Chapter 7. The Offense-Defense Rating Method 79 OD Objective 79 OD Premise 79 But Which Comes First? 80 Alternating Refinement Process 81 The Divorce 81 Combining the OD Ratings 82 Our Recurring Example 82 Scoring vs. Yardage 83 The 2009-2010 NFL OD Ratings 84 Mathematical Analysis of the OD Method 87 Diagonals 88 Sinkhorn-Knopp 89 OD Matrices 89 The OD Ratings and Sinkhorn-Knopp 90 Cheating a Bit 91 Chapter 8. Ranking by Reordering Methods 97 Rank Differentials 98 The Running Example 99 Solving the Optimization Problem 101 The Relaxed Problem 103 An Evolutionary Approach 103 Advanced Rank-Differential Models 105 Summary of the Rank-Differential Method 106 Properties of the Rank-Differential Method 106 Rating Differentials 107 The Running Example 109 Solving the Reordering Problem 110 Summary of the Rating-Differential Method 111 Chapter 9. Point Spreads 113 What It Is (and Isn't) 113 The Vig (or Juice) 114 Why Not Just Offer Odds? 114 How Spread Betting Works 114 Beating the Spread 115 Over/Under Betting 115 Why Is It Difficult for Ratings to Predict Spreads? 116 Using Spreads to Build Ratings (to Predict Spreads?) 117 NFL 2009-2010 Spread Ratings 120 Some Shootouts 121 Other Pair-wise Comparisons 124 Conclusion 125 Chapter 10. User Preference Ratings 127 Direct Comparisons 129 Direct Comparisons, Preference Graphs, and Markov Chains 130 Centroids vs. Markov Chains 132 Conclusion 133 Chapter 11. Handling Ties 135 Input Ties vs. Output Ties 136 Incorporating Ties 136 The Colley Method 136 The Massey Method 137 The Markov Method 137 The OD, Keener, and Elo Methods 138 Theoretical Results from Perturbation Analysis 139 Results from Real Datasets 140 Ranking Movies 140 Ranking NHL Hockey Teams 141 Induced Ties 142 Summary 144 Chapter 12. Incorporating Weights 147 Four Basic Weighting Schemes 147 Weighted Massey 149 Weighted Colley 150 Weighted Keener 150 Weighted Elo 150 Weighted Markov 150 Weighted OD 151 Weighted Differential Methods 151 Chapter 13. "What If ..." Scenarios and Sensitivity 155 The Impact of a Rank-One Update 155 Sensitivity 156 Chapter 14. Rank Aggregation-Part 1 159 Arrow's Criteria Revisited 160 Rank-Aggregation Methods 163 Borda Count 165 Average Rank 166 Simulated Game Data 167 Graph Theory Method of Rank Aggregation 172 A Refinement Step after Rank Aggregation 175 Rating Aggregation 176 Producing Rating Vectors from Rating Aggregation-Matrices 178 Summary of Aggregation Methods 181 Chapter 15. Rank Aggregation-Part 2 183 The Running Example 185 Solving the BILP 186 Multiple Optimal Solutions for the BILP 187 The LP Relaxation of the BILP 188 Constraint Relaxation 190 Sensitivity Analysis 191 Bounding 191 Summary of the Rank-Aggregation (by Optimization) Method 193 Revisiting the Rating-Differential Method 194 Rating Differential vs. Rank Aggregation 194 The Running Example 196 Chapter 16. Methods of Comparison 201 Qualitative Deviation between Two Ranked Lists 201 Kendall's Tau 203 Kendall's Tau on Full Lists 204 Kendall's Tau on Partial Lists 205 Spearman's Weighted Footrule on Full Lists 206 Spearman's Weighted Footrule on Partial Lists 207 Partial Lists of Varying Length 210 Yardsticks: Comparing to a Known Standard 211 Yardsticks: Comparing to an Aggregated List 211 Retroactive Scoring 212 Future Predictions 212 Learning Curve 214 Distance to Hillside Form 214 Chapter 17. Data 217 Massey's Sports Data Server 217 Pomeroy's College Basketball Data 218 Scraping Your Own Data 218 Creating Pair-wise Comparison Matrices 220 Chapter 18. Epilogue 223 Analytic Hierarchy Process (AHP) 223 The Redmond Method 223 The Park-Newman Method 224 Logistic Regression/Markov Chain Method (LRMC) 224 Hochbaum Methods 224 Monte Carlo Simulations 224 Hard Core Statistical Analysis 225 And So Many Others 225 Glossary 231 Bibliography 235 Index 241

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Book SynopsisThis book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law'Trade Review"This is a marvelous and excellent introduction."--Adhemar Bultheel, European Mathematical Society Bulletin "A must-read for novices and experts alike. It can be used for a graduate-level topics course or as a reference text for researchers in the field. The exposition is outstanding, with hundreds of carefully chosen examples, figures and diagrams to illustrate the theory. For those who are up for a challenge, the book contains several open problems as well. An Introduction to Benford's Law will surely be the go-to text on the subject for years to come."--Pieter C. Allaart, Mathematical ReviewsTable of ContentsPreface vii 1 Introduction 1 1.1 History 3 1.2 Empirical evidence 4 1.3 Early explanations 6 1.4 Mathematical framework 7 2 Significant Digits and the Significand 11 2.1 Significant digits 11 2.2 The significand 12 2.3 The significand sigma-algebra 14 3 The Benford Property 22 3.1 Benford sequences 23 3.2 Benford functions 28 3.3 Benford distributions and random variables 29 4 The Uniform Distribution and Benford's Law 43 4.1 Uniform distribution characterization of Benford's law 43 4.2 Uniform distribution of sequences and functions 46 4.3 Uniform distribution of random variables 54 5 Scale-, Base-, and Sum-Invariance 63 5.1 The scale-invariance property 63 5.2 The base-invariance property 74 5.3 The sum-invariance property 80 6 Real-valued Deterministic Processes 90 6.1 Iteration of functions 90 6.2 Sequences with polynomial growth 93 6.3 Sequences with exponential growth 97 6.4 Sequences with super-exponential growth 101 6.5 An application to Newton's method 111 6.6 Time-varying systems 116 6.7 Chaotic systems: Two examples 124 6.8 Differential equations 127 7 Multi-dimensional Linear Processes 135 7.1 Linear processes, observables, and difference equations 135 7.2 Nonnegative matrices 139 7.3 General matrices 145 7.4 An application to Markov chains 162 7.5 Linear difference equations 165 7.6 Linear differential equations 170 8 Real-valued Random Processes 180 8.1 Convergence of random variables to Benford's law 180 8.2 Powers, products, and sums of random variables 182 8.3 Mixtures of distributions 202 8.4 Random maps 213 9 Finitely Additive Probability and Benford's Law 216 9.1 Finitely additive probabilities 217 9.2 Finitely additive Benford probabilities 219 10 Applications of Benford's Law 223 10.1 Fraud detection 224 10.2 Detection of natural phenomena 225 10.3 Diagnostics and design 226 10.4 Computations and Computer Science 228 10.5 Pedagogical tool 230 List of Symbols 231 Bibliography 234 Index 245

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Book SynopsisTrade ReviewAmerican Association for the Advancement of Science's Books for General Audiences and Young Adults One of American Association for the Advancement of Science's Books for General Audiences and Young Adults 2014 "Fernandez's witty, delightful approach makes for a winning introduction to the wonderland of math behind the scenes of everyday life."--Publishers Weekly "Written in a bright conversational tone, [Everyday Calculus] wonderfully integrates calculus into everyday life."--Guardian "Fernandez is a delightfully quirky writer and his bookEveryday Calculusis lighthearted and compelling."--New York Journal of Books "The author earnestly and excitedly seeks to make the principles of calculus near and natural, without the intimidation of a five-pound textbook dense with equations... Fernandez invites the reader along on this work day and telegraphs an enthusiasm for seeing calculus, with hints of differential equations, presented to him. This excitement will communicate itself to the math enthusiast becoming acquainted with calculus through the author's style, which is both lively and confident."--Tom Schulte, MAA Reviews "Written in a bright conversational tone, this book wonderfully integrates calculus into everyday life."--GrrrlScientist "[T]he book is perfect for a reader who really wants to know what mathematics are governing our lives and who wants to learn and understand or polish up his rusty knowledge of these mathematics."--A. Bultheel, European Mathematical Society "A delightful read. [Everyday Calculus] will make you laugh and capture your imagination... [A] triumph in the pursuit of the lofty goal of comprehending the world."--San Francisco Book Review "Fernandez presents a broad array of ordinary events like REM sleep, drinking coffee, commuting to work, setting aside money for retirement, catching a cold, enjoying tandoori chicken, and watching a movie... [T]hen ties each aspect to pertinent mathematics... As the subtitle of the book suggests, the thrust is more one of 'discovering the hidden math all around us' rather than showing 'how mathematics is used,' which provides an honest and very pleasurable journey."--Choice "The book offers in clear and concise fashion much of the material found in a traditional calculus textbook, but presents it beginning with a real world observation and then developing the mathematics needed to understand the observation."--AAAS "A very captivating read, and certainly contains something for everyone... [E]asy to drop into for individual chapters, or to read when you have a couple hours spare. [Everyday Calculus] will certainly open the eyes of any reader who wishes to appreciate the mathematics and calculus which surrounds us."--Mathematics TodayTable of ContentsPreface ix Calculus Topics Discussed by Chapter xi CHAPTER 1 Wake Up and Smell the Functions 1 What's Trig Got to Do with Your Morning? 2 How a Rational Function Defeated Thomas Edison, and Why Induction Powers the World 5 The Logarithms Hidden in the Air 10 The Frequency of Trig Functions 14 Galileo's Parabolic Thinking 17 CHAPTER 2 Breakfast at Newton's 21 Introducing Calculus, the CNBC Way 21 Coffee Has Its Limits 25 A Multivitamin a Day Keeps the Doctor Away 30 Derivatives Are about Change 34 CHAPTER 3 Driven by Derivatives 35 Why Do We Survive Rainy Days? 36 Politics in Derivatives, or Derivatives in Politics? 39 What the Unemployment Rate Teaches Us about the Curvature of Graphs 41 America's Ballooning Population 44 Feeling Derivatives 46 The Calculus of Time Travel 47 CHAPTER 4 Connected by Calculus 51 E-Mails, Texts, Tweets, Ah! 51 The Calculus of Colds 53 What Does Sustainability Have to Do with Catching a Cold? 56 What Does Your Retirement Income Have to Do with Traffic? 58 The Calculus of the Sweet Tooth 61 CHAPTER 5 Take a Derivative and You'll Feel Better 65 I "Heart" Differentials 65 How Life (and Nature) Uses Calculus 67 The Costly Downside of Calculus 73 The Optimal Drive Back Home 75 Catching Speeders Efficiently with Calculus 77 CHAPTER 6 Adding Things Up, the Calculus Way 81 The Little Engine That Could ... Integrate 82 The Fundamental Theorem of Calculus 90 Using Integrals to Estimate Wait Times 93 CHAPTER 7 Derivatives Integrals: The Dream Team 97 Integration at Work-Tandoori Chicken 98 Finding the Best Seat in the House 101 Keeping the T Running with Calculus 104 Look Up to Look Back in Time 108 The Ultimate Fate of the Universe 109 The Age of the Universe 113 Epilogue 116 Appendix A Functions and Graphs 119 Appendices 1-7 125 Notes 147 Index 149

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Book SynopsisTrade Review“This remarkable book studies thermodynamics within the framework of dynamical systems theory. A major contribution by any standard, it is a gem in the tiara of books being written by one of the most prolific, deep-thinking, and insightful researchers working today.”—Frank Lewis, University of Texas, Arlington“Haddad develops an original mathematical framework for thermodynamics deeply rooted in modern systems theory, threading postulates and analyses of a science that has evolved from the seemingly mundane quest for efficiency in steam engines to the flow of time and the workings of the cosmos and life itself. He succeeds in presenting an all-encompassing treatise, from the early works of Carnot and Clausius to the insights of relativity and the conundrum of the time arrow, in a lucid exposition that systematically details a rigorous base for future generations of scientists and theorists.”—Tryphon Georgiou, University of California, Irvine"By applying ideas and techniques from compartmental systems theory, Haddad’s treatise places thermodynamics on a solid foundation for the twenty-first century."—Dennis Bernstein, University of Michigan"This effective blend of thermodynamics and the theory of dynamical systems provides a unified, coherent, and mathematically accurate framework that is currently missing in the literature. This is a significant contribution to several fields spanning dynamical systems, mathematics, physics, chemistry, and more. It will provide the underlying foundation for additional research and conceptual understanding of physical phenomena."—Kyriakos G. Vamvoudakis, Georgia Institute of Technology

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Book SynopsisTrade Review"A major achievement. The breadth and depth of this brilliant book, from rich ethnography to elaborate agent-based models, are awe inspiring and standard setting."—Scott E. Page, author of The Diversity Bonus: How Great Teams Pay Off in the Knowledge Economy"This exceptional book is chock-full of ideas that can inspire a new generation of researchers in the study of human societies using the framework of complex systems."—Mark Moritz, Ohio State University

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Book SynopsisTrade Review"A major achievement. The breadth and depth of this brilliant book, from rich ethnography to elaborate agent-based models, are awe inspiring and standard setting."—Scott E. Page, author of The Diversity Bonus: How Great Teams Pay Off in the Knowledge Economy"This exceptional book is chock-full of ideas that can inspire a new generation of researchers in the study of human societies using the framework of complex systems."—Mark Moritz, Ohio State University

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Book SynopsisTrade Review"For graduate students and researchers who are interested in high-dimensional statistics and its interplay with convex optimization, this book will serve as an invaluable resource."---Debashis Ghosh, International Statistical Review

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Book Synopsis

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Book Synopsis

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Book SynopsisTrade Review"[PDE Control of String-Actuated Motion] is what the metaphor applied mathematics is all about. In this field, there is often a gap between pretension and reality, a mismatch between mathematical rigor and engineering objectives. This book is a nice counterexample!"---Guenter Leugering, SIAM Review

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Book SynopsisTrade Review"A pleasure to read. . . . Newton himself would have been charmed by this book."---Steven G. Krantz, UMAP Journal"The Mathematical Mechanic documents novel ways of viewing physics as a method of understanding mathematics. Levi uses physical arguments as tools to conjecture about mathematical concepts before providing rigorous proofs. . . . The Mathematical Mechanic is an excellent display of creative, interdisciplinary problem-solving strategies. The author has explained complex concepts with simplicity, yet the mathematics is accurate." * Mathematics Teacher *"A most interesting book. . . . Many of the ideas in it could be used as motivational or illustrative examples to support the teaching of non-specialists, especially physicists and engineers. In conclusion--a thoroughly enjoyable and thought-provoking read."---Nigel Steele, London Mathematical Society Newsletter"The Mathematical Mechanic reverses the usual interaction of mathematics and physics. . . . Careful study of Levi's book may train readers to think of physical companions to mathematical problems. . . . Mathematicians will find The Mathematical Mechanic provides exercise in new ways of thinking. Instructors will find it contains material to supplement mathematics courses, helping physically-minded students approach mathematics and helping mathematically-minded students appreciate physics."---John D. Cook, MAA Reviews"Mark Levi reverses the old stereotype that math is merely a tool to aid physicists by showing that many questions in mathematics can be easily solved by interpreting them as physical problems. . . . Some sections of the book require readers to brush up on their calculus but Levi's clear explanations, witty footnotes, and fascinating insights make the extra effort painless." * SEED Magazine *"The book is chock-full of these seemingly magical physical thought experiments involving bicycle wheels, pistons, springs, soap films, pendulums, and electric circuits, with applications to geometry, maximization and minimization problems, inequalities, optics, integrals, and complex functions. . . . I highly recommend it to anyone who is (even slightly) interested in physics, and appreciates mathematical elegance and cleverness. It would make a great gift for almost anyone, whether a high school student or university professor, armchair physicist or professional mathematician."---Boris Yorgey, The Math Less Traveled"The Mathematical Mechanic is a pleasant surprise."---E. Kincanon, Choice

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Book Synopsis

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Book Synopsis

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Book SynopsisTrade ReviewHayduk is equally at ease explaining the simplest and most advanced applications of the program... Hayduk has written more than just a solid text for use in advanced graduate courses on statistical modeling. Those with a firm mathematical background who wish to learn about the approach, or those who know a little about the program and want to know more, will find this an excellent reference. American Journal of Sociology This is a fine book for providing persons who have a basic knowledge of regression and matrix algebra with a detailed understanding of LISREL. It is strong on explanation, on clarity, and on breadth of coverage. Contemporary PsychologyTable of ContentsPrefaceAcknowledgmentsChapter 1. Getting Started1.1 Means, variances, and covariance1.2 Thinking about covariances, variances, and means1.3 Expectations and equations1.4 Structural equation modelsChapter 2. Traditional Basics2.1 Fitting a line into a scatterplot2.2 Regression in the context of Chapter 12.3 Multiple regression2.4 Colinearity2.5 Interaction2.6 Nonlinearity Chapter 3. The New Basics3.1 A touch of matrix algebra3.2 Derivatives in a few easy pagesChapter 4. In the Beginning4.1 A new way of thinking. latent versus measured variables in causal modes4.2 LISREL is Greek to me!4.3 A real model. smoking behavior and antismoking acts4.4 A model implies a sigma ()4.5 Scaling and reliability4.6 Restrictions on model specificationChapter 5. Estimating Structural Coefficients with Maximum Likelihood Estimation5.1 Maximum likelihood estimation5.2 Making approximate S5.3 Identification and colinearity5.4 On simplifying models5.5 In closingChapter 6. Hitting Paydirt6.1 Chi-square6.2 Residuals6.3 Fitting better than the competition6.4 Significance of structural coefficients6.5 Partial derivatives and their uses6.6 Standardized solutionsChapter 7. Becoming a LISRELITE. Some Tricks of the Trade and Learning to Play7.1 Four simple replacements7.2 Moving into and rethinking the distinction between exogenous/endogenous7.3 Multiple indicators7.4 Nonlinearity among the concepts7.5 Interaction among the conceptsChapter 8. Interpreting It All8.1 The Basics8.2 General matrix formulas8.3 Two extensions of effect decompositions8.4 On developing equivalent models (effect recomposition)8.5 Interpreting the smoking model with an inserted loop8.6 SummaryChapter 9. More and Better9.1 Stacked models for multiple groups9.2 Modeling meansChapter 10. Odds and Endings10.1 Old Beta10.2 LISREL in SPSSX and pairwise matrices10.3Some data-related issues 10.4 Locating what is wrong in a program10.5 Alternative estimation strategies10.6 A guide to the literature10.7 The end AppendicesAppendix A. Summation NotationAppendix B. LISREL Output for the Smoking ModelAppendix C. LISREL Output with Multiple IndicatorsAppendix D. The Moment Matrix Fit FunctionBibliographyIndex

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Book SynopsisStudents will find this book a useful aid to learning the unfamiliar mathematical aspects of stochastic processes while applying them to physical processes that he or she has already encountered.Trade ReviewStudents will love this book. It tells them without fuss how to do simple and useful numerical calculations, with just enough background to understand what they are doing... a refreshingly brief and unconvoluted work. -- Vinay Ambegaokar American Journal of Physics The book is very clearly set out and very easy to read. Undergraduate students and those wishing to learn about stochastic processes for the first time would enjoy the clear pedagogic presentation. -- B.I. Henry The Physicist [ An Introduction to Stochastic Processes in Physics] presents fundamental ideas with admirable clarity and concision. The author presents in about 100 pages enough material for the student to appreciate the very different natures of stochastic and sure processes and to solve simple but important problems involving noise. Any physicist wondering what noise is about would be well advised to pack Lemons' books for their next train journey. -- Professor S.M. Barnett Contemporary Physics Self-contained and provides adequate insight into stochastic processes in physics. It is quite readable and will be useful to students interested in learning about stochastic processes and their relevance in understanding the physical phenomena. It also provides teachers a good approach to communicate the essence of the subject to students. -- Suresh V. Lawande Mathematical ReviewsTable of ContentsContents: Preface and Acknowledgments Chapter 1: Random Variables Chapter 2: Expected Values Chapter 3: Random Steps Chapter 4: Continuous Random Variables Chapter 5: Normal Variable Theorems Chapter 6: Einstein's Brownian Motion Chapter 7: Ornstein-Uhlenbeck Processes Chapter 8: Langevin's Brownian Motion Chapter 9: Other Physical Processes Chapter 10: Fluctuations without Dissipation Appendix A: "On the Theory of Brownian Motion," by Paul Langevin, translated by Anthony Gythiel Appendix B: Kinetic Equations Answers to Problems References Index

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Book SynopsisWhether you drive a Pacer or a Porsche, The Isaac Newton School of Driving offers better-and better-informed-driving through physics.Trade ReviewParker grew up a mechanic's son and is as comfortable discussing gear sets and weight transfer as he is explaining the formula for determining the force of drag on a vehicle at any given speed. You don't need to be an engineer to read and enjoy Parker's often entertaining book that covers everything from the basics of engines and electronics to crashes and congestion. And after learning about Wd=Fh/R, you will likely be a better driver. RATING: Three and 1/2 [out of four] helmets. -- Larry Edsall Autoweek 2004 Parker's entertaining book is not a heavy tome replete with complex mathematical formulas-nothing more complex than high school physics. What The Isaac Newton School of Driving answers is the annoying complaint every teacher or parent hears from a teenager: 'I'll never use all this (insert expletive) in real life!'. -- Terry Jackson AMI Auto World Magazine Contains examples of practical technology that would certainly enhance and extend many courses... written in a lighthearted manner that is successful and appealing. -- Hal Harris 21 C: Scanning the Future A comprehensive look at the fundamental elements of the driving experience... The author enlivens many difficult concepts with clear, comfortable explanations... Whether a reader is looking for simple applications or the physics of high performance racing vehicles, this book will make any reader pause and think about the science of their car and driving. -- Charles James National Science Teachers Association Recommends Barry Parker has written an intriguing book... The Isaac Newton School of Driving has a definite flair and keeps the reader interested. -- Henry J. P. Smith Industrial Physicist 2004 The discussions are clear and the physics is correct. Choice 2004Table of ContentsContents:Chapter 1 Introduction Chapter 2 The Open Road: Basic Physics of Driving Chapter 3 All Revved Up: The Internal Combustion Engine Chapter 4 When Sparks Fly: The Electrical System Chapter 5 "Give 'em a Brake": Slowing Down Chapter 6 Springs and Gears: The Suspension System and the Transmission Chapter 7 What a Drag: Aerodynamic Design Chapter 8 A Crash Course: The Physics of Collisions Chapter 9 Checkered Flags: The Physics of Auto Racing Chapter 10 Rush Hour: Traffic and Chaos Chapter 11 The Road Ahead: Cars of the Future Chapter 12 Epilogue: The Final Flag

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Book SynopsisAs we evolve from unquantified ignorance to an imperfect but everpresent state of measured awareness, Henshaw gives us a critical perspective from which we can measure upthe measurements that have come to affect our lives so greatly.Trade ReviewAcademic but accessible to the general reader. Scitech Book News 2006 Well written, entertaining, and informative. -- Luiz Henrique de Figueiredo MAA Reviews 2006 Henshaw has a remarkable ability to explain complex mathematics in a manner accessible to general readers. -- Judy Randle Tulsa World 2006 Clear and well written. -- Terry Ishihara Science Books and Films 2006 The book is fun to read... Recommended. Choice 2007 Best of 2006. Library Journal 2007 It is easy to read, and Henshaw has a pleasant style of throwing himself into the action. PsycCRITIQUES 2007Table of ContentsPrefaceAcknowledgments1. Of Love and Luminescene: What, Why, and How Things Get Measured2. Doing the Math: Scales, Standards, and Some Beautiful Measurements3. The Ratings Game: ''Overall'' Measurements and Rankings4. Measurement in Business: What Gets Measured Gets Done5. Games of Inches: Sports and Measurement6. Measuring the Mind: Intelligence, Biology, and Education7. Man: The Measure of All Things8. It's Not Just the Heat, it's the Humidity: Global Warming and Environmental Measurement9. Garbage In, Garbage Out: The Computer and Measurement10. How Funny Is That? Knowledge Without Measurement?11. Faith, Hope, and Love: The Future of Measuremen—and of KnowledgetReferencesIndex

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Book SynopsisThe book features end-of-chapter practice problems, an appendix of worked problems, a glossary of terms, and an annotated bibliography.Trade ReviewMere Thermodynamics is a good learning tool for students, and it's an interesting and thought-provoking book for educators and professionals. American Journal of Physics This book is a little gem. Lemons has a lightness of touch that belies the weight of thought he has given to this subject and how to present it in a non trivial way to a beginner. No awkward corner is avoided or ignored, and the whole piece is touched by enthusiasm, clarity, a central awareness of its relevance to the real world. -- Peter Sammut Physics Education Lucidly written and enjoyable to read... An interesting and informative supplement to other textbooks. Times Higher Education SupplementTable of ContentsPreface1. Definitions1.1. Thermodynamics1.2. System1.3. Boundary, Environment, and Interactions1.4. States and State Variables1.5. Equations of State1.6. Work1.7. HeatProblems2. Equilibrium2.1. Equilibrium2.2. Zeroth Law of Thermodynamics2.3. Empirical Temperature2.4. Traditional Temperature Scales2.5. Equilibrium ProcessesProblems3. Heat3.1. Quantifying Heat3.2. Calorimetry3.3. What is Heat?Problems4. The First Law4.1. Count Rumford4.2. Joule's Experiments4.3. The First Law of Thermodynamics4.4. Thermodynamic Cycles4.5. Cycle AdjustmentProblems5. The Second Law5.1. Sadi Carnot5.2. Statements of the Second Law5.3. Equivalence and Inequivalence5.4. Reversible Heat Engines5.5. Refrigerators and Heat PumpsProblems6. The First and Second Laws6.1. Rudolph Clausius6.2. Thermodynamic Temperature6.3. Clausius's TheoremProblems7. Entropy7.1. The Meaning of Reversibility7.2. Entropy7.3. Entropy Generation in Irreversible Processes7.4. The Entropy Generator7.5. Entropy Corollaries7.6. Thermodynamic Arrow of TimeProblems8. Fluid Variables8.1. What Is a Fluid?8.2. Reversible Work8.3. Fundamental Constraint8.4. Enthalpy8.5. Helmholtz and Gibbs Free Energies8.6. Partial Derivative Rules8.4. Thermodynamic Coeffi cients8.8. Heat CapacitiesProblems9. Simple Fluid Systems9.1. The Ideal Gas9.2. Room-Temperature Elastic Solid9.3. Cavity RadiationProblems10. Nonfluid Systems10.1. Nonfluid Variables10.2. The Theoretician's Rubber Band10.3. Paramagnetism10.4. Surfaces10.5. Chemical Potential10.6. Multivariate SystemsProblems11. Equilibrium and Stability11.1. Mechanical and Thermal Systems11.2. Principle of Maximum Entropy11.3. Other Stability Criteria11.4. Intrinsic Stability of a FluidProblems12. Two-Phase Systems12.1. Phase Diagrams12.2. Van der Waals Equation of State12.3. Two-Phase Transition12.4. Maxwell Construction12.5. Clausius-Clapeyron Equation12.6. Critical PointProblems13. The Third Law13.1. The Principle of Thomsen and Berthelot13.2. Entropy Change13.3. Unattainability13.4. Absolute EntropyProblemsAppendixesA. Physical Constants and Standard DefinitionsB. Catalog of 21 Simple CyclesC. Glossary of TermsD. Selected Worked ProblemsE. Answers to ProblemsAnnotated BibliographyIndex

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