Applied mathematics Books
Penguin Books Ltd Love Triangle
Book SynopsisA #1 SUNDAY TIMES BESTSELLER Explore the life-changing magic of trigonometry with Matt Parker, stand-up mathematician and No. 1 bestselling author of Humble Pi Why can no two people ever see the same rainbow? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? Why does the wake behind a duck always form an angle of exactly 39 degrees? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle. In Love Triangle, stand-up comedian, ex-maths teacher and Sunday Times number one bestselling author Matt Parker is on a mission to prove why we should all show a lot more love for triangles, along with the useful trigonometry and geometry they enable. To make his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich into three equal parts, and measure tall bu
£19.90
Scribner Book Company Math of Life and Death
Book Synopsis
£16.19
Princeton University Press Feedback Systems
Book Synopsis
£70.40
Yale University Press Causal Inference
Book SynopsisAn accessible and contemporary introduction to the methods for determining cause and effect in the social sciencesTrade Review“A new guide to methods for determining cause and effect in the social sciences. In summarising, systematising and prioritising methodological tools for researchers, this book will be of use to all social scientists looking to validate their quantitative findings.”—Dr Simeon Mitropolitski, LSE Review of Books "Cunningham's brilliant book is that rare statistical treatise written for students and practitioners alike. Engaging language and vivid examples bring the tools of causal inference to a broad audience. Read the book, absorb its lessons, and you'll develop the skills you need to credibly assess whether a statistics class, a public policy, or a new business practice truly makes a difference."–Justin Wolfers, University of Michigan "Accessible and engaging. An excellent introduction to the statistics of causal inference."–Alberto Abadie, MIT “Learning about causal effects is the main goal of most empirical research in economics. In this engaging book, Scott Cunningham provides an accessible introduction to this area, full of wisdom and wit and with detailed coding examples for practitioners.”--Guido Imbens, coauthor of Causal Inference "This book will probably shock economics instructors with the clarity, insights, and tools that modern graphical models introduce to the teaching of econometrics. The benefits will outlast the shock."--Judea Pearl, University of California, Los Angeles “Causation versus correlation has been the basis of arguments—economic and otherwise—since the beginning of time. Causal Inference: The Mixtape uses legit real-world examples that I found genuinely thought-provoking. It’s rare that a book prompts readers to expand their outlook; this one did for me.”—Marvin Young (Young MC)
£27.50
John Wiley & Sons Inc EvidenceBased Technical Analysis
Book SynopsisEvidence-Based Technical Analysis examines how you can apply the scientific method, and recently developed statistical tests, to determine the true effectiveness of technical trading signals. Throughout the book, expert David Aronson provides you with comprehensive coverage of this new methodology, which is specifically designed for evaluating the performance of rules/signals that are discovered by data mining.Trade Review"…his book is well written and contains a great deal of information that is of value…." (The Technical Analyst, May/June 2007)Table of ContentsAcknowledgments. About the Author. Introduction. PART I Methodological, Psychological, Philosophical, and Statistical Foundations. CHAPTER 1 Objective Rules and Their Evaluation. CHAPTER 2 The Illusory Validity of Subjective Technical Analysis. CHAPTER 3 The Scientific Method and Technical Analysis. CHAPTER 4 Statistical Analysis. CHAPTER 5 Hypothesis Tests and Confidence Intervals. CHAPTER 6 Data-Mining Bias: The Fool’s Gold of Objective TA. CHAPTER 7 Theories of Nonrandom Price Motion. PART II Case Study: Signal Rules for the S&P 500 Index. CHAPTER 8 Case Study of Rule Data Mining for the S&P 500. CHAPTER 9 Case Study Results and the Future of TA. APPENDIX Proof That Detrending Is Equivalent to Benchmarking Based on Position Bias. Notes. Index.
£63.00
Oxford University Press The Theory of Open Quantum Systems
Book SynopsisThis book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states.The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented.The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.Trade ReviewReview from previous edition ...a carefully-researched, thorough and well-presented text. * Contemporary Physics *...very clearly written and essentially self-contained... not only a very good and thorough introduction to the subject, but also a precious reference for researchers. * Foundations of Physics *'This book covers a large set of topics, normally not covered in standard physics curricula ... I recommend this book to physicists interested in widening their horizons in the directions covered by the book ... I do not know of any other source providing such a systematic and well written introduction into this area of research.' * Mathematical Reviews *Table of ContentsPREFACE; ACKNOWLEDGEMENTS; PART 1: PROBABILITY IN CLASSICAL AND QUANTUM PHYSICS; PART 2: DENSITY MATRIX THEORY; PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE; PART 4: NON-MARKOVIAN QUANTUM PROCESSES; PART 5: RELATIVISTIC QUANTUM PROCESSES
£65.55
Bloomsbury Publishing PLC Soccermatics
Book SynopsisSoccer is the most mathematical of sports--riddled with numbers, patterns, and shapes. How to make sense of them? The answer lies in mathematical modeling, a science with applications in a host of biological systems. Soccermatics brings the two together in a fascinating, mind-bending synthesis. What''s the connection between an ant colony and Total Football, Dutch-style? How is the Barcelona midfield linked geometrically? And how can we relate the mechanics of a Mexican Wave to the singing of cicadas in an Australian valley? Welcome to the world of mathematical modeling, expressed brilliantly by David Sumpter through the prism of soccer. Soccer is indeed more than a game and this book is packed with game theory. After reading it, you will forever watch the game with new eyes.Trade ReviewSumpter's deconstruction of formations proved why maths and football can't live without each other. It's every football nerd's dream. * FourFourTwo *A fascinating and entertaining dive into the mathematics of the beautiful game. * The Guardian *...Highly readable... * The Irish Times *...You will love this book. * The Tribune *This is football looked at in a very different way. David Sumpter is mining a rich and deep seam here in Soccermatics, one that will become an increasingly important part of the game. -- Pat Nevin, former Chelsea and Everton star and football media analystA fascinating study of the structures and patterns that underpin football matches, with revealing and surprising conclusions. -- Michael Cox, editor of Zonal Marking and Guardian SportsSoccermatics provides fresh insight into a game we've been watching all of our lives. But it's more than a book about football and is all the better for it. -- Adam Bate, football features writer for Sky SportsDavid Sumpter brings together his two passions, mathematics and football, in a highly original and entertaining way. The beautiful game illustrated through the beauty of mathematics. -- Philip Maini FRS, Professor of Mathematical Biology, University of OxfordTable of ContentsPreface: The Kick-off Part I: On the Pitch Chapter 1: I Never Predict Anything and I Never Will Chapter 2: How Slime Moulds Built Barcelona Chapter 3: Check My Flow Chapter 4: Statistical Brilliance Chapter 5: Zlatan Ibrah Rocket Science Part II: In the Dugout Chapter 6: Three Points for the Bird-brained Manager Chapter 7: The Tactical Map CHapter 8: Total Cyber Dynamo Chapter 9: The World in Motion Part III: From the Crowd Chapter 10: You'll Never Walk Alone Chapter 11: Bet Against the Masses Chapter 12: Putting My Money Where My Mouth Is Chapter 13: The Results Are In The Full-Time Whistle Notes Acknowledgements Index
£10.44
John Wiley & Sons Inc Basic Math PreAlgebra For Dummies Book Workbook
Book SynopsisTable of ContentsBasic Math and Pre-Algebra For Dummies, 2nd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: Playing the Numbers Game 7 CHAPTER 2: It’s All in the Fingers: Numbers and Digits 23 CHAPTER 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29 Part 2: Getting a Handle on Whole Numbers 47 CHAPTER 4: Putting the Big Four Operations to Work 49 CHAPTER 5: A Question of Values: Evaluating Arithmetic Expressions 63 CHAPTER 6: Say What? Turning Words into Numbers 75 CHAPTER 7: Divisibility 87 CHAPTER 8: Fabulous Factors and Marvelous Multiples 95 Part 3: Parts of the Whole: Fractions, Decimals, and Percents 109 CHAPTER 9: Fooling with Fractions 111 CHAPTER 10: Parting Ways: Fractions and the Big Four Operations 125 CHAPTER 11: Dallying with Decimals 149 CHAPTER 12: Playing with Percents 171 CHAPTER 13: Word Problems with Fractions, Decimals, and Percents 183 Part 4: Picturing and Measuring — Graphs, Measures, Stats, and Sets 195 CHAPTER 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197 CHAPTER 15: How Much Have You Got? Weights and Measures 205 CHAPTER 16: Picture This: Basic Geometry 217 CHAPTER 17: Seeing Is Believing: Graphing as a Visual Tool 239 CHAPTER 18: Solving Geometry and Measurement Word Problems 247 CHAPTER 19: Figuring Your Chances: Statistics and Probability 259 CHAPTER 20: Setting Things Up with Basic Set Theory 271 Part 5: The X-Files: Introduction to Algebra 279 CHAPTER 21: Enter Mr X: Algebra and Algebraic Expressions 281 CHAPTER 22: Unmasking Mr X: Algebraic Equations 299 CHAPTER 23: Putting Mr X to Work: Algebra Word Problems 311 Part 6: The Part of Tens 321 CHAPTER 24: Ten Little Math Demons That Trip People Up 323 CHAPTER 25: Ten Important Number Sets to Know 329 Index 337 Basic Math and Pre-Algebra Workbook For Dummies, 3rd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: We've Got Your Numbers 7 CHAPTER 2: Smooth Operators: Working with the Big Four Operations 23 CHAPTER 3: Getting Down with Negative Numbers 37 CHAPTER 4: It's Just an Expression 49 CHAPTER 5: Dividing Attention: Divisibility, Factors, and Multiples 69 Part 2: Slicing Things Up: Fractions, Decimals, and Percents 89 CHAPTER 6: Fractions Are a Piece of Cake 91 CHAPTER 7: Fractions and the Big Four 109 CHAPTER 8: Getting to the Point with Decimals 143 CHAPTER 9: Playing the Percentages 165 Part 3: A Giant Step Forward: Intermediate Topics 177 CHAPTER 10: Seeking a Higher Power through Scientific Notation 179 CHAPTER 11: Weighty Questions on Weights and Measures 189 CHAPTER 12: Shaping Up with Geometry 203 CHAPTER 13: Getting Graphic: Xy-Graphs 223 Part 4: The X Factor: Introducing Algebra 235 CHAPTER 14: Expressing Yourself with Algebraic Expressions 237 CHAPTER 15: Finding the Right Balance: Solving Algebraic Equations 259 Part 5: The Part of Tens 277 CHAPTER 16: Ten Alternative Numeral and Number Systems 279 CHAPTER 17: Ten Curious Types of Numbers 287 Index 293
£21.84
Penguin Books Ltd Things to Make and Do in the Fourth Dimension
Book Synopsis''Maths at its most playful and multifarious'' Jordan EllenbergMatt Parker, author of the No.1 bestseller Humble Pi, takes us on a riotous journey through the possibilities of numbers Mathematician Matt Parker uses bizarre Klein Bottles, unimaginably small pizza slices, knots no one can untie and computers built from dominoes to reveal some of the most exotic and fascinating ideas in mathematics. Starting with simple numbers and algebra, this book goes on to deal with inconceivably big numbers in more dimensions than you ever knew existed. And always with something for you to make or do along the way. ''The book oozes with sheer joy'' New Scientist''Matt Parker is some sort of unholy fusion of a prankster, wizard and brilliant nerd - clever, funny and ever so slightly naughty'' Adam Rutherford, author of Creation''Matt Parker never got the memo about maths being boring ... he seeks to reconnect us to the numbers around us'' Simon Usborne, Independent''Essential reading'' ObserverTrade ReviewAn unusual, in-depth but highly accessible popular-maths book by a member of the London Mathematical Society who also has a sideline in stand-up comedy -- Books of the Year * Economist *Matt Parker is some sort of unholy fusion of a prankster, wizard and brilliant nerd - clever, funny and ever so slightly naughty -- Adam Rutherford, author of CREATIONEssential reading * Observer *Matt Parker is a lovely, funny, big, dork -- Ben GoldacreShows off maths at its most playful and multifarious, ranging from classics like knot theory and ruler-and-compass constructions to more whimsical topics like the topology of beer logos and error-correcting scarves -- Jordan Ellenberg, author of HOW NOT TO BE WRONGThis is the best book on recreational mathematics since Martin Gardner's My Best Mathematical and Logic Puzzles -- Harold D. Shane, Mathematics Emeritus, Baruch Coll., CUNY * Library Journal *
£12.34
Princeton University Press The Princeton Companion to Applied Mathematics
Book SynopsisThis is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; coversTrade Review"The treasures [in the Princeton Companion to Applied Mathematics] go on and on."--Lloyd N. Trefethen, SIAM Review "[An] impressive volume... It has been a major project that eventually resulted in this amazing product."--Adhemar Bultheel, European Mathematical Society "Safe to say there is something for everyone in The Princeton Companion to Applied Mathematics."--Alan Stevens, Mathematics Today "[A] valuable addition to the mathematics library of any university or research institution."--Library Journal "Higham and his associate editors ... have produced an admirably readable and informative volume, which anyone interested in applied mathematics would be well advised to consult or--better still--to own!"--James Case, SIAM News "A unique work full of beautiful and interesting mathematics. It is surely a valuable resource for exposing young mathematicians to possible areas of applied mathematics for research and further study. Without a doubt PCAM is an important contribution to the mathematical literature."--Jason M. Graham, MathSciNet "[A]n excellent reference that successfully compiles into a readable and engaging form the broad range of topics that an applied mathematician might encounter in their career... As a reader, I find myself flipping through the pages and becoming engaged in new and interesting ideas from the world of applied math."--Joanna Bieri, MAA Reviews "A handy one-volume reference for applied mathematics that cuts across several disciplines within an academic framework."--Lesley S.J. Farmer, Reference ReviewsTable of Contents*Frontmatter, pg. i*Contents, pg. v*Preface, pg. ix*Contributors, pg. xiii*Part I. Introduction to Applied Mathematics, pg. 1*Part II. Concepts, pg. 81*Part III. Equations, Laws, and Functions of Applied Mathematics, pg. 135*Part IV. Areas of Applied Mathematics, pg. 173*Part V. Modeling, pg. 591*Part VI. Example Problems, pg. 733*Part VII. Application Areas, pg. 783*Part VIII. Final Perspectives, pg. 897*Index, pg. 963
£73.60
John Wiley & Sons Inc Advanced Engineering Mathematics International
Book SynopsisThe tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems.Table of ContentsPART A Ordinary Differential Equations (ODEs) 1 CHAPTER 1 First-Order ODEs 2 1.1 Basic Concepts. Modeling 2 1.2 Geometric Meaning of y ƒ(x, y). Direction Fields, Euler’s Method 9 1.3 Separable ODEs. Modeling 12 1.4 Exact ODEs. Integrating Factors 20 1.5 Linear ODEs. Bernoulli Equation. Population Dynamics 27 1.6 Orthogonal Trajectories. Optional 36 1.7 Existence and Uniqueness of Solutions for Initial Value Problems 38 CHAPTER 2 Second-Order Linear ODEs 46 2.1 Homogeneous Linear ODEs of Second Order 46 2.2 Homogeneous Linear ODEs with Constant Coefficients 53 2.3 Differential Operators. Optional 60 2.4 Modeling of Free Oscillations of a Mass–Spring System 62 2.5 Euler–Cauchy Equations 71 2.6 Existence and Uniqueness of Solutions. Wronskian 74 2.7 Nonhomogeneous ODEs 79 2.8 Modeling: Forced Oscillations. Resonance 85 2.9 Modeling: Electric Circuits 93 2.10 Solution by Variation of Parameters 99 CHAPTER 3 Higher Order Linear ODEs 105 3.1 Homogeneous Linear ODEs 105 3.2 Homogeneous Linear ODEs with Constant Coefficients 111 3.3 Nonhomogeneous Linear ODEs 116 CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 124 4.0 For Reference: Basics of Matrices and Vectors 124 4.1 Systems of ODEs as Models in Engineering Applications 130 4.2 Basic Theory of Systems of ODEs. Wronskian 137 4.3 Constant-Coefficient Systems. Phase Plane Method 140 4.4 Criteria for Critical Points. Stability 148 4.5 Qualitative Methods for Nonlinear Systems 152 4.6 Nonhomogeneous Linear Systems of ODEs 160 CHAPTER 5 Series Solutions of ODEs. Special Functions 167 5.1 Power Series Method 167 5.2 Legendre's Equation. Legendre Polynomials Pn(x) 175 5.3 Extended Power Series Method: Frobenius Method 180 5.4 Bessel’s Equation. Bessel Functions (x) 187 5.5 Bessel Functions of the Y (x). General Solution 196 CHAPTER 6 Laplace Transforms 203 6.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) 204 6.2 Transforms of Derivatives and Integrals. ODEs 211 6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting) 217 6.4 Short Impulses. Dirac's Delta Function. Partial Fractions 225 6.5 Convolution. Integral Equations 232 6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients 238 6.7 Systems of ODEs 242 6.8 Laplace Transform: General Formulas 248 6.9 Table of Laplace Transforms 249 PART B Linear Algebra. Vector Calculus 255 CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 256 7.1 Matrices, Vectors: Addition and Scalar Multiplication 257 7.2 Matrix Multiplication 263 7.3 Linear Systems of Equations. Gauss Elimination 272 7.4 Linear Independence. Rank of a Matrix. Vector Space 282 7.5 Solutions of Linear Systems: Existence, Uniqueness 288 7.6 For Reference: Second- and Third-Order Determinants 291 7.7 Determinants. Cramer’s Rule 293 7.8 Inverse of a Matrix. Gauss–Jordan Elimination 301 7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. Optional 309 CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems 322 8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors 323 8.2 Some Applications of Eigenvalue Problems 329 8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices 334 8.4 Eigenbases. Diagonalization. Quadratic Forms 339 8.5 Complex Matrices and Forms. Optional 346 CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl 354 9.1 Vectors in 2-Space and 3-Space 354 9.2 Inner Product (Dot Product) 361 9.3 Vector Product (Cross Product) 368 9.4 Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives 375 9.5 Curves. Arc Length. Curvature. Torsion 381 9.6 Calculus Review: Functions of Several Variables. Optional 392 9.7 Gradient of a Scalar Field. Directional Derivative 395 9.8 Divergence of a Vector Field 403 9.9 Curl of a Vector Field 406 CHAPTER 10 Vector Integral Calculus. Integral Theorems 413 10.1 Line Integrals 413 10.2 Path Independence of Line Integrals 419 10.3 Calculus Review: Double Integrals. Optional 426 10.4 Green’s Theorem in the Plane 433 10.5 Surfaces for Surface Integrals 439 10.6 Surface Integrals 443 10.7 Triple Integrals. Divergence Theorem of Gauss 452 10.8 Further Applications of the Divergence Theorem 458 10.9 Stokes’s Theorem 463 PART C Fourier Analysis. Partial Differential Equations (PDEs) 473 CHAPTER 11 Fourier Analysis 474 11.1 Fourier Series 474 11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions 483 11.3 Forced Oscillations 492 11.4 Approximation by Trigonometric Polynomials 495 11.5 Sturm–Liouville Problems. Orthogonal Functions 498 11.6 Orthogonal Series. Generalized Fourier Series 504 11.7 Fourier Integral 510 11.8 Fourier Cosine and Sine Transforms 518 11.9 Fourier Transform. Discrete and Fast Fourier Transforms 522 11.10 Tables of Transforms 534 CHAPTER 12 Partial Differential Equations (PDEs) 540 12.1 Basic Concepts of PDEs 540 12.2 Modeling: Vibrating String, Wave Equation 543 12.3 Solution by Separating Variables. Use of Fourier Series 545 12.4 D’Alembert’s Solution of the Wave Equation. Characteristics 553 12.5 Modeling: Heat Flow from a Body in Space. Heat Equation 557 12.6 Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem 558 12.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms 568 12.8 Modeling: Membrane, Two-Dimensional Wave Equation 575 12.9 Rectangular Membrane. Double Fourier Series 577 12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series 585 12.11 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential 593 12.12 Solution of PDEs by Laplace Transforms 600 PART D Complex Analysis 607 CHAPTER 13 Complex Numbers and Functions. Complex Differentiation 608 13.1 Complex Numbers and Their Geometric Representation 608 13.2 Polar Form of Complex Numbers. Powers and Roots 613 13.3 Derivative. Analytic Function 619 13.4 Cauchy–Riemann Equations. Laplace’s Equation 625 13.5 Exponential Function 630 13.6 Trigonometric and Hyperbolic Functions. Euler's Formula 633 13.7 Logarithm. General Power. Principal Value 636 CHAPTER 14 Complex Integration 643 14.1 Line Integral in the Complex Plane 643 14.2 Cauchy's Integral Theorem 652 14.3 Cauchy's Integral Formula 660 14.4 Derivatives of Analytic Functions 664 CHAPTER 15 Power Series, Taylor Series 671 15.1 Sequences, Series, Convergence Tests 671 15.2 Power Series 680 15.3 Functions Given by Power Series 685 15.4 Taylor and Maclaurin Series 690 15.5 Uniform Convergence. Optional 698 CHAPTER 16 Laurent Series. Residue Integration 708 16.1 Laurent Series 708 16.2 Singularities and Zeros. Infinity 714 16.3 Residue Integration Method 719 16.4 Residue Integration of Real Integrals 725 CHAPTER 17 Conformal Mapping 735 17.1 Geometry of Analytic Functions: Conformal Mapping 736 17.2 Linear Fractional Transformations (Möbius Transformations) 741 17.3 Special Linear Fractional Transformations 745 17.4 Conformal Mapping by Other Functions 749 17.5 Riemann Surfaces. Optional 753 CHAPTER 18 Complex Analysis and Potential Theory 756 18.1 Electrostatic Fields 757 18.2 Use of Conformal Mapping. Modeling 761 18.3 Heat Problems 765 18.4 Fluid Flow 768 18.5 Poisson's Integral Formula for Potentials 774 18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem 778 PART E Numeric Analysis 785 Software 786 CHAPTER 19 Numerics in General 788 19.1 Introduction 788 19.2 Solution of Equations by Iteration 795 19.3 Interpolation 805 19.4 Spline Interpolation 817 19.5 Numeric Integration and Differentiation 824 CHAPTER 20 Numeric Linear Algebra 841 20.1 Linear Systems: Gauss Elimination 841 20.2 Linear Systems: LU-Factorization, Matrix Inversion 849 20.3 Linear Systems: Solution by Iteration 855 20.4 Linear Systems: Ill-Conditioning, Norms 861 20.5 Least Squares Method 869 20.6 Matrix Eigenvalue Problems: Introduction 873 20.7 Inclusion of Matrix Eigenvalues 876 20.8 Power Method for Eigenvalues 882 20.9 Tridiagonalization and QR-Factorization 885 CHAPTER 21 Numerics for ODEs and PDEs 897 21.1 Methods for First-Order ODEs 898 21.2 Multistep Methods 908 21.3 Methods for Systems and Higher Order ODEs 912 21.4 Methods for Elliptic PDEs 919 21.5 Neumann and Mixed Problems. Irregular Boundary 928 21.6 Methods for Parabolic PDEs 933 21.7 Method for Hyperbolic PDEs 939 PART F Optimization, Graphs 947 CHAPTER 22 Unconstrained Optimization. Linear Programming 948 22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent 949 22.2 Linear Programming 952 22.3 Simplex Method 956 22.4 Simplex Method: Difficulties 960 CHAPTER 23 Graphs. Combinatorial Optimization 967 23.1 Graphs and Digraphs 967 23.2 Shortest Path Problems. Complexity 972 23.3 Bellman's Principle. Dijkstra’s Algorithm 977 23.4 Shortest Spanning Trees: Greedy Algorithm 980 23.5 Shortest Spanning Trees: Prim’s Algorithm 984 23.6 Flows in Networks 987 23.7 Maximum Flow: Ford–Fulkerson Algorithm 993 23.8 Bipartite Graphs. Assignment Problems 996 APPENDIX 1 References A1 APPENDIX 2 Answers to Selected Problems A4 APPENDIX 3 Auxiliary Material A51 A3.1 Formulas for Special Functions A51 A3.2 Partial Derivatives A57 A3.3 Sequences and Series A60 A3.4 Grad, Div, Curl, 2 in Curvilinear Coordinates A62 APPENDIX 4 Additional Proofs A65 APPENDIX 5 Tables A85 INDEX I1 PHOTO CREDITS P1
£53.19
World Scientific Publishing Co Pte Ltd Beginner's Further Guide To Mathematical Logic, A
Book Synopsis'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.
£19.00
Elsevier - Health Sciences Division MATLAB
Book SynopsisTable of ContentsPart 1 Introduction to Programming Using MATLAB 1. Introduction to MATLAB 2. Vectors and Matrices 3. Introduction to MATLAB Programming 4. Selection Statements 5. Loop Statements and Vectorizing Code 6. MATLAB Programs 7. Text Manipulation 8. Data Structures Part 2 Advanced Topics for Problem Solving with MATLAB 9. Data Transfer 10. Advanced Functions 11. Introduction to Object-Oriented Programming and Graphics 12. Advanced Plotting Techniques 13. Sights and Sounds 14. Advanced Mathematics 15. Introduction to Machine Learning
£46.76
Jenny Stanford Publishing Quantum Physics and Life: How We Interact with
Book SynopsisThis book reveals glimpses of how the quantum physics of atoms and molecules influences, and even controls, the way our cells function and how we and our fellow animals interact with our environment. Simply put, how birds fly and why grass grows.Certainly, biochemistry and molecular biology are the foundations for the biology of living cells, but there is more—quantum coherence and entanglement influencing the functioning of proteins and enzymes, and strictly speaking, without the quantum phenomena we wouldn’t even be here.In the end, however, this book is based on the solid ground of science, presenting the many fascinating phenomena of how quantum physics makes life possible without any unwarranted mystification.Table of Contents1. Life and Quantum Physics 2. Our World Is Just a Small Part of the Whole 3. The Gecko and Life Upside Down 4. The Quantized World 5. Evolution: About the Origin of Life 6. From the Big Bang to Black Holes 7. As Time Goes By: The Arrow of Time 8. The Art of Finding Your Way Back Home 9. The Vision in New Light 10. Photosynthesis and the Golf Putt 11. The Respiratory Chain Sustains Our Lives 12. A Sense of Smell 13. DNA Repair: A Matter of Survival and Development 14. Quantum Physics in Diagnostics and Therapy 15. Not More Mysterious Than Necessary 16. Consciousness: The Greatest Mystery 17. A Glance at the Future of Quantum and Life
£25.64
Taylor & Francis Inc Atomization and Sprays
Book SynopsisThe second edition of this long-time bestseller provides a framework for designing and understanding sprays for a wide array of engineering applications. The text contains correlations and design tools that can be easily understood and used in relating the design of atomizers to the resulting spray behavior. Written to be accessible to readers with a modest technical background, the emphasis is on application rather than in-depth theory. Numerous examples are provided to serve as starting points for using the information in the book. Overall, this is a thoroughly updated edition that still retains the practical focus and readability of the original work by Arthur Lefebvre.Trade Review"The book covers important topics with tremendous applications in industrial and medical applications. This second edition keep the best sections of the first edition while all other sections and chapters are completely rewritten or updated. All developments in simulation and measurement techniques of atomization and spraying are included. One most important and helpful addition for instructors and students is the new solved examples, which ease the use of endless empirical relations and figures in design of sophisticated modules like combustion chambers."— Ahmed F El-Sayed, Zagazig University, Egypt"The book is very comprehensive and provides the necessary details to gain an understanding of atomization processes and how they are best applied. The book is an excellent resource for anyone working with atomization processes or materials that have been produced by atomization."— Timothy J. Eden, The Pennsylvania State University, USA"The book covers important topics with tremendous applications in industrial and medical applications. This second edition keep the best sections of the first edition while all other sections and chapters are completely rewritten or updated. All developments in simulation and measurement techniques of atomization and spraying are included. One most important and helpful addition for instructors and students is the new solved examples, which ease the use of endless empirical relations and figures in design of sophisticated modules like combustion chambers."— Ahmed F El-Sayed, Zagazig University, Egypt"The book is very comprehensive and provides the necessary details to gain an understanding of atomization processes and how they are best applied. The book is an excellent resource for anyone working with atomization processes or materials that have been produced by atomization."— Timothy J. Eden, The Pennsylvania State University, USATable of ContentsPreface General Considerations Introduction Atomization Atomizers Factors Influencing Atomization Spray Characteristics Applications Glossary References Basic Processes in Atomization Introduction Static Drop Formation Breakup of Drops Disintegration of Liquid Jets Disintegration of Liquid Sheets Summary Nomenclature References Drop Size Distributions of Sprays Introduction Graphical Representation of Drop Size Distributions Mathematical Distribution Functions Empirical Distribution Functions Mean Diameters Representative Diameters Drop Size Dispersion Concluding Remarks Nomenclature References Atomizers Introduction Atomizer Requirements Pressure Atomizers Rotary Atomizers Air-Assist Atomizers Airblast Atomizers Effervescent Atomizers Electrostatic Atomizers Ultrasonic Atomizers Whistle Atomizers References Flow in Atomizers Introduction Flow Number Plain-Orifice Atomizer Pressure-Swirl Atomizer Rotary Atomizer Airblast Atomizer Nomenclature References Atomizer Performance Introduction Plain-Orifice Atomizer Pressure-Swirl Atomizers Rotary Atomizers Air-Assist Atomizers Airblast Atomizers Effervescent Atomizer Electrostatic Atomizers Ultrasonic Atomizers Nomenclature References External Spray Characteristics Introduction Spray Properties Penetration Spray Cone Angle Circumferential Liquid Distribution Airblast Atomizers Drop Drag Coefficients Nomenclature References Drop Evaporation Introduction Steady-State Evaporation Unsteady-State Analysis Drop Lifetime Convective Effects on Evaporation Calculation of Effective Evaporation Constant Influence of Evaporation on Drop Size Distribution Drop Burning Multicomponent Fuel Drops Nomenclature References Spray Size and Patternation MethodsIntroduction Factors Influencing Drop Size Measurement Mechanical Methods Electrical Methods Optical Methods Concluding Remarks References Author Index Subject Index
£166.25
John Wiley & Sons Inc Statistical Models and Methods for Lifetime Data
Book SynopsisPraise for the First Edition An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . . -Choice This is an important book, which will appeal to statisticians working on survival analysis problems. -Biometrics A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook. -Statistics in Medicine The statistical analysis of lifetime or response time data is a key tool in engineering, medicine, and many other scientific and technological areas. This book provides a unified treatment of the models and statistical methods used to analyze lifetime data. Equally useful as a reference for individuals interested in the analysis of lifetime data and as a text for advanced students, Statistical Models and Methods for Lifetime Data, SecoTrade Review“...a welcome addition to the literature on survival analysis...for a unified and thorough reference of classical theory and models, this book is an excellent choice.” (Journal of the American Statistical Association, March 2004) "This book is a role-model for other who are planning to write books…every statistician and applied researcher ought to have this book in their collection." (Journal of Statistical Computation and Simulation, October 2003) "...expanded and updated with recent research...a valuable reference...this book...merits a place on the bookshelf of anyone concerned with the analysis of lifetime data from any field. (Technometrics, Vol. 45, No. 3, August 2003) "...updated version of the popular text...this excellent book will serve as either a reference or a graduate-level textbook." (Short Book Reviews, Vol. 23, No. 2, August 2003) "...excellent...provides a wealth of information for those familiar with the area." (Pharmaceutical Research, Vol. 20, No. 9, September 2003) "...the author's aim is to cover lifetime data analysis without concentrating exclusively on any field of applications...he succeeds quite well..." (Zentralblatt Math, 2003) “...rewritten to reflect new developments...” (Quarterly of Applied Mathematics, Vol. LXI, No. 2, June 2003) "Compared with the large number of other good textbooks in the this field, this is one of the best. I highly recommend that all applied statisticians add this volume to their libraries." (Applied Clinical Trials, May 2003)Table of ContentsBasic Concepts and Models. Observation Schemes, Censoring and Likelihood. Some Nonparametric and Graphical Procedures. Inference Procedures for Parametric Models. Inference procedures for Log-Location-Scale Distributions. Parametric Regression Models. Semiparametric Multiplicative Hazards Regression Models. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models. Multiple Modes of Failure. Goodness of Fit Tests. Beyond Univariate Survival Analysis. Appendix A. Glossary of Notation and Abbreviations. Appendix B. Asymptotic Variance Formulas, Gamma Functions and Order Statistics. Appendix C. Large Sample Theory for Likelihood and Estimating Function Methods. Appendix D. Computational Methods and Simulation. Appendix E. Inference in Location-Scale Parameter Models. Appendix F. Martingales and Counting Processes. Appendix G. Data Sets. References.
£144.85
Dover Publications Inc. Information Theory
Book Synopsis
£13.04
Atlantic Books Quantum Leaps
Book SynopsisHugh Barker is a non-fiction author and editor; as the latter he has edited several successful popular maths books, including A Slice of Pi. Hugh is a keen amateur mathematician and was accepted to study maths at Cambridge University aged 16.
£10.44
John Wiley & Sons Inc Matrix Differential Calculus with Applications in
Book SynopsisMatrix Differential Calculus With Applications in Statistics and Econometrics Revised Edition Jan R. Magnus, CentER, Tilburg University, The Netherlands and Heinz Neudecker, Cesaro, Schagen, The Netherlands .deals rigorously with many of the problems that have bedevilled the subject up to the present time. - Stephen Pollock, Econometric Theory I continued to be pleasantly surprised by the variety and usefulness of its contents - Isabella Verdinelli, Journal of the American Statistical Association Continuing the success of their first edition, Magnus and Neudecker present an exhaustive and self-contained revised text on matrix theory and matrix differential calculus. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioural sciences to econometrics. While the structure and successful elements of the first edition remain, this revised and updated edition contains many new examples and exercises. * CoTrade Review"...the best book to learn matrix and related ideas...statisticians, econometricians, computer scientists, engineers, and psychometricians will find this extremely useful." (Journal of Statistical Computation and Simulation, March 2006) "a most welcome revision" (Computational Statistics & Data Analysis, 28 August 2001)Table of ContentsPreface xv Preface to the first revised printing xvii Preface to the second revised printing xviii Part One- Matrices Part Two- Differentials: the theory Part Three- Differentials: the practice Part Four- Inequalities Part Five- The linear model Part Six- Applications to maximum likelihood estimation Bibliography 379 Index of Symbols 387 Subject Index 390
£89.06
Elsevier Science Differential Equations Dynamical Systems and an
Book SynopsisSuitable for students in the fields of mathematics, science, and engineering, this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study.Table of Contents1. First-Order Equations 2. Planar Linear Systems 3. Phase Portraits 4. Classification of Planar Systems 5. Higher Dimension Linear Algebra 6. Higher Dimension Linear Systems 7. Nonlinear Systems 8. Equilibria in Nonlinear Systems 9. Global Nonlinear Techniques 10. Closed Orbits and Limit Sets 11. Applications in Biology 12. Applications in Circuit Theory 13. Applications in Mechanics 14. The Lorenz System 15. Discrete Dynamical Systems 16. Homoclinic Phenomena 17. Existence and Uniqueness Revisited
£75.04
Cambridge University Press Solitons An Introduction 2 Cambridge Texts in
Book SynopsisThis textbook is an introduction to the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. The authors explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Transform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites (i.e., partial differential equations, calculus of variations, Fourier integrals, linear waves and SturmâLiouville theory), and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas, and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to the solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated Trade Review"...should find an enthusiastic following, and the author is to be congratulated on a job well done." American Scientist"...a fine book, certainly the one that I would choose as the text for an introductory course on solitons." SIAM Review"All things considered, I cannot think of a clearer introduction to the subject from a mathematical point of view." Physics Today"...an excellent book, achieving its goals both concisely and comprehensively." John G. Harris, Applied Mechanics ReviewTable of ContentsPreface; 1. The Kortewag–de Vries equation; 2. Elementary solutions of the Korteweg–de Vries equation; 3. The scattering and inverse scattering problems; 4. The initial-value problem for the Korteweg–de Vries equation; 5. Further properties of the Korteweg–de Vries equation; 6. More general inverse methods; 7. The Painlevé property, perturbations and numerical methods; 8. Epilogue; Answers and hints; Bibliography and author index; Motion picture index; Subject index.
£44.99
CRC Press Analytical Groundwater Modeling
Book SynopsisThis book provides a detailed description of how Python can be used to give insight into the flow of groundwater based on analytic solutions. Starting with simple problems to illustrate the basic principles, complexity is added step by step to show how one-dimensional and two-dimensional models of one or two aquifers can be implemented. Steady and transient flow problems are discussed in confined, semi-confined, and unconfined aquifers that may include wells, rivers, and areal recharge. Special consideration is given to coastal aquifers, including the effect of tides and the simulation of interface flow.Application of Python allows for compact and readable code, and quick visualization of the solutions. Python scripts are provided to reproduce all results. The scripts are also available online so that they can be altered to meet site-specific conditions. This book is intended both as training material for the next generation of university students and as a useful resource forTrade Review 'This is a fantastic addition to the analytical solutions and analytic element modeling canon with a modern approach to programming with Python. I hope readers will use it to learn and explore groundwater theory, and to up their game on making simple reality checks of complex systems to improve all groundwater modeling.''The authors do an excellent job of describing practically important calculations, like determining the critical flowrate at which a pumped well starts to induce flow from a nearby river.'- Michael Fienen, Groundwater - NGWA, Book Review, 7 September 2022'This is a fantastic addition to the analytical solutions and analytic element modeling canon with a modern approach to programming with Python. I hope readers will use it to learn and explore groundwater theory, and to up their game on making simple reality checks of complex systems to improve all groundwater modeling.''The authors do an excellent job of describing practically important calculations, like determining the critical flowrate at which a pumped well starts to induce flow from a nearby river.'- Michael Fienen, Groundwater - NGWA, Book Review, 7 September 2022Table of Contents0. Basics of Groundwater Flow. 1. Steady One-dimensional Flow with Constant Transmissivity. 2. Steady One-dimensional Semi-confined Flow. 3. Steady One-dimensional Unconfined Flow with Variable Saturated Thickness. 4. Steady One-dimensional Flow in Coastal Aquifers. 5. Transient One-dimensional Flow. 6. Steady Two-dimensional Flow to Wells. 7. Steady Two-dimensional Flow to Wells in Uniform Background Flow. 8. Analytic Element Modeling of Steady Two-dimensional Flow. 9. Transient Two-dimensional Flow. 10. Steady Two-dimensional Flow in the Vertical Plane. 11. Appendix - Python Primer
£36.09
John Wiley & Sons Inc Fundamentals of Supply Chain Theory
Book SynopsisComprehensively teaches the fundamentals of supply chain theory This book presents the methodology and foundations of supply chain management and also demonstrates how recent developments build upon classic models. The authors focus on strategic, tactical, and operational aspects of supply chain management and cover a broad range of topics from forecasting, inventory management, and facility location to transportation, process flexibility, and auctions. Key mathematical models for optimizing the design, operation, and evaluation of supply chains are presented as well as models currently emerging from the research frontier. Fundamentals of Supply Chain Theory, Second Edition contains new chapters on transportation (traveling salesman and vehicle routing problems), integrated supply chain models, and applications of supply chain theory. New sections have also been added throughout, on topics including machine learning models for forecasting, conic optimizaTable of ContentsList of Figures xxi List of Tables xxvii List of Algorithms xxix Preface xxxi 1 Introduction 1 1.1 The Evolution of Supply Chain Theory 1 1.2 Definitions and Scope 2 1.3 Levels of Decision Making in Supply Chain Management 4 2 Forecasting and Demand Modeling 5 2.1 Introduction 5 2.2 Classical Demand Forecasting Methods 6 2.3 Forecast Accuracy 15 2.4 Machine Learning in Demand Forecasting 17 2.5 Demand Modeling Techniques 23 2.6 Bass Diffusion Model 24 2.7 Leading Indicator Approach 30 2.8 Discrete Choice Models 33 Case Study: Semiconductor Demand Forecasting at Intel 38 Problems 39 3 Deterministic Inventory Models 45 3.1 Introduction to Inventory Modeling 45 3.2 Continuous Review: The Economic Order Quantity Problem 51 3.3 Power of Two Policies 57 3.4 The EOQ with Quantity Discounts 60 3.5 The EOQ with Planned Backorders 67 3.6 The Economic Production Quantity Model 70 3.7 Periodic Review: The Wagner–Whitin Model 72 Case Study: Ice Cream Production and Inventory at Scotsburn Dairy Group 76 Problems 77 4 Stochastic Inventory Models: Periodic Review 87 4.1 Inventory Policies 87 4.2 Demand Processes 89 4.3 Periodic Review with Zero Fixed Costs: Base-Stock Policies 89 4.4 Periodic Review with Nonzero Fixed Costs: (s; S) Policies 114 4.5 Policy Optimality 123 4.6 Lost Sales 136 Case Study: Optimization of Warranty Inventory at Hitachi 138 Problems 140 5 Stochastic Inventory Models: Continuous Review 155 5.1 (r; Q) Policies 155 5.2 Exact (r; Q) Problem with Continuous Demand Distribution 156 5.3 Approximations for (r; Q) Problem with Continuous Distribution 161 5.4 Exact (r; Q) Problem with Continuous Distribution: Properties of Optimal r and Q 170 5.5 Exact (r; Q) Problem with Discrete Distribution 177 Case Study: (r; Q) Inventory Optimization at Dell 180 Problems 182 6 Multiechelon Inventory Models 187 6.1 Introduction 187 6.2 Stochastic-Service Models 191 6.3 Guaranteed-Service Models 203 6.4 Closing Thoughts 217 Case Study: Multiechelon Inventory Optimization at Procter & Gamble 222 Problems 223 7 Pooling and Flexibility 229 7.1 Introduction 229 7.2 The Risk-Pooling Effect 230 7.3 Postponement 236 7.4 Transshipments 237 7.5 Process Flexibility 243 7.6 A Process Flexibility Optimization Model 253 Case Study: Risk Pooling and Inventory Management at Yedioth Group 257 Problems 259 8 Facility Location Models 267 8.1 Introduction 267 8.2 The Uncapacitated Fixed-Charge Location Problem 269 8.3 Other Minisum Models 295 8.4 Covering Models 305 8.5 Other Facility Location Problems 314 8.6 Stochastic and Robust Location Models 317 8.7 Supply Chain Network Design 321 Case Study: Locating Fire Stations in Istanbul 332 Problems 335 9 Supply Uncertainty 355 9.1 Introduction to Supply Uncertainty 355 9.2 Inventory Models with Disruptions 356 9.3 Inventory Models with Yield Uncertainty 365 9.4 A Multisupplier Model 372 9.5 The Risk-Diversification Effect 384 9.6 A Facility Location Model with Disruptions 387 Case Study: Disruption Management at Ford 395 Problems 396 10 The Traveling Salesman Problem 403 10.1 Supply Chain Transportation 403 10.2 Introduction to the TSP 404 10.3 Exact Algorithms for the TSP 408 10.4 Construction Heuristics for the TSP 416 10.5 Improvement Heuristics for the TSP 436 10.6 Bounds and Approximations for the TSP 442 10.7 World Records 452 Case Study: Routing Meals on Wheels Deliveries 453 Problems 455 11 The Vehicle Routing Problem 463 11.1 Introduction to the VRP 463 11.2 Exact Algorithms for the VRP 468 11.3 Heuristics for the VRP 475 11.4 Bounds and Approximations for the VRP 495 11.5 Extensions of the VRP 498 Case Study: ORION: Optimizing Delivery Routes at UPS 501 Problems 502 12 Integrated Supply Chain Models 511 12.1 Introduction 511 12.2 A Location–Inventory Model 512 12.3 A Location–Routing Model 529 12.4 An Inventory–Routing Model 531 Case Study: Inventory–Routing at Frito-Lay 534 Problems 535 13 The Bullwhip Effect 539 13.1 Introduction 539 13.2 Proving the Existence of the Bullwhip Effect 541 13.3 Reducing the Bullwhip Effect 552 13.4 Centralizing Demand Information 555 Case Study: Reducing the Bullwhip Effect at Philips Electronics 556 Problems 559 14 Supply Chain Contracts 563 14.1 Introduction 563 14.2 Introduction to Game Theory 564 14.3 Notation 565 14.4 Preliminary Analysis 566 14.5 The Wholesale Price Contract 568 14.6 The Buyback Contract 574 14.7 The Revenue Sharing Contract 578 14.8 The Quantity Flexibility Contract 581 Case Study: Designing a Shared-Savings Contract at McGriff Treading Company 584 Problems 586 15 Auctions 591 15.1 Introduction 591 15.2 The English Auction 593 15.3 Combinatorial Auctions 595 15.4 The Vickrey–Clarke–Groves Auction 599 Case Study: Procurement Auctions for Mars 608 Problems 610 16 Applications of Supply Chain Theory 615 16.1 Introduction 615 16.2 Electricity Systems 615 16.3 Health Care 625 16.4 Public Sector Operations 632 Case Study: Optimization of the Natural Gas Supply Chain in China 639 Problems 641 Appendix A: Multiple-Chapter Problems 643 Problems 643 Appendix B: How to Write Proofs: A Short Guide 651 B.1 How to Prove Anything 651 B.2 Types of Things You May Be Asked to Prove 653 B.3 Proof Techniques 655 B.4 Other Advice 657 Appendix C: Helpful Formulas 661 C.1 Positive and Negative Parts 661 C.2 Standard Normal Random Variables 662 C.3 Loss Functions 662 C.4 Differentiation of Integrals 665 C.5 Geometric Series 666 C.6 Normal Distributions in Excel and MATLAB 666 C.7 Partial Expectations 667 Appendix D: Integer Optimization Techniques 669 D.1 Lagrangian Relaxation 669 D.2 Column Generation 675 References 681 Subject Index 712 Author Index 725
£98.96
Cengage Learning, Inc A First Course in Mathematical Modeling
Book SynopsisOffering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.Table of Contents1. Modeling Change. 2. The Modeling Process, Proportionality, and Geometric Similarity. 3. Model Fitting. 4. Experimental Modeling. 5. Simulation Modeling. 6. Discrete Probabilistic Modeling. 7. Optimization of Discrete Models. 8. Modeling with Graph Theory. 9. Modeling with Decision Theory. 10. Game Theory. 11. Modeling with a Differential Equation. 12. Modeling with Systems of Differential Equations. 13. Optimization of Continuous Modeling. 14. Dimensional Analysis and Similitude. 15. Graphs of Functions as Models. Appendix A: Problems from the Mathematics Contest in Modeling, 1985-2007. Appendix B: An Elevator Simulation Model. Appendix C: The Revised Simplex Method. Appendix D. Brief Review of Integration Techniques.
£83.59
CRC Press Secret History
Book SynopsisThe first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading.Secret History: The Story of Cryptology, Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here.The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told, that is, how the United States was able to come up with systems that were never broken.The text is in t
£54.14
IOP Publishing INVERSE MODELING AN INTRODUCTION THEOPB
Book Synopsis
£23.75
Princeton University Press How Round Is Your Circle
Book SynopsisInvites readers to explore many of the same fundamental questions that working engineers deal with every day. This title illustrates how physical models are created from abstract mathematical ones.Trade Review"There are many books that include ideas or instructions for making mathematical models. What is special about this one is the emphasis on the relation of model- or tool-building with the physical world. The authors have devoted themselves to making wood or metal models of most of the constructions presented; 33 color plates nicely show off their success in this area."--Stan Wagon, American Scientist "The question posed by this book turns out to be a real toughie, but nevertheless the authors urge you to answer it. This gem of a book tackles several such questions, revealing why they are crucial to engineering and to our understanding of our everyday world. With a nice emphasis on practical experiments, the authors do a refreshing job of bringing out the mathematics you learned in school but sadly never knew why. And they show just how intuitive it can be."--Matthew Killeya, New Scientist "Mathematics teachers and Sudoku addicts will simply be unable to put the book down... Part magic show, part history lesson, and all about geometry, How Round Is Your Circle? is an eloquent testimonial to the authors' passion for numbers. Perhaps it will spark a similar interest in some young numerophile-to-be."--Civil Engineering "This is a great book for engineers and mathematicians, as well as the interested lay person. Although some of the theoretical mathematics may not be familiar, you can skip it without losing the point. For school teachers and lecturers seeking to inspire, this is a fantastic resource."--Owen Smith, Plus Magazine "This book is very clearly written and beautifully illustrated, with line drawings and a collection of photographs of practical models. I can strongly recommend it to anyone with a bit of math knowledge and an interest in engineering problems--a terrific book."--Norman Billingham, Journal of the Society of Model and Experimental Engineers "This book has many gems and rainbows... The book will appeal to all recreational mathematicians ... not just because of the way it is written, but also because of the way puzzles, plane dissections and packing and the odd paper folding or origami task are used to bring a point home... More than one copy of this book should be in every school library... It should help to inspire a new generation into mathematics or engineering as well as be accessible to the general reader to show how much mathematics has made the modern world."--John Sharp, LMS Newsletter "This book can be dense, but it is great for dipping into, a rich resource of interesting thinking and project ideas. Bryant and Sangwin, the engineer and the mathematician, must have had a great time putting this book together. Their enthusiasm and humor shine through."--Tim Erickson, Mathematics Teacher "The book is very nicely printed and contains many nice figures and photographs of physical models, as well as an extensive bibliography. It can be recommended as a formal or recreational lecture both for mathematicians and engineers."--EMS NewsletterTable of ContentsPreface xiii Acknowledgements xix Chapter 1: Hard Lines 1 1.1 Cutting Lines 5 1.2 The Pythagorean Theorem 6 1.3 Broad Lines 10 1.4 Cutting Lines 12 1.5 Trial by Trials 15 Chapter 2: How to Draw a Straight Line 17 2.1 Approximate-Straight-Line Linkages 22 2.2 Exact-Straight-Line Linkages 33 2.3 Hart's Exact-Straight-Line Mechanism 38 2.4 Guide Linkages 39 2.5 Other Ways to Draw a Straight Line 41 Chapter 3: Four-Bar Variations 46 3.1 Making Linkages 49 3.2 The Pantograph 51 3.3 The Crossed Parallelogram 54 3.4 Four-Bar Linkages 56 3.5 The Triple Generation Theorem 59 3.6 How to Draw a Big Circle 60 3.7 Chebyshev's Paradoxical Mechanism 62 Chapter 4: Building the World's First Ruler 65 4.1 Standards of Length 66 4.2 Dividing the Unit by Geometry 69 4.3 Building the World's First Ruler 73 4.4 Ruler Markings 75 4.5 Reading Scales Accurately 81 4.6 Similar Triangles and the Sector 84 Chapter 5: Dividing the Circle 89 5.1 Units of Angular Measurement 92 5.2 Constructing Base Angles via Polygons 95 5.3 Constructing a Regular Pentagon 98 5.4 Building the World's First Protractor 100 5.5 Approximately Trisecting an Angle 102 5.6 Trisecting an Angle by Other Means 105 5.7 Trisection of an Arbitrary Angle 106 5.8 Origami 110 Chapter 6: Falling Apart 112 6.1 Adding Up Sequences of Integers 112 6.2 Duijvestijn's Dissection 114 6.3 Packing 117 6.4 Plane Dissections 118 6.5 Ripping Paper 120 6.6 A Homely Dissection 123 6.7 Something More Solid 125 Chapter 7: Follow My Leader 127 Chapter 8: In Pursuit of Coat-Hangers 138 8.1 What Is Area? 141 8.2 Practical Measurement of Areas 149 8.3 Areas Swept Out by a Line 151 8.4 The Linear Planimeter 153 8.5 The Polar Planimeter of Amsler 158 8.6 The Hatchet Planimeter of Prytz 161 8.7 The Return of the Bent Coat-Hanger 165 8.8 Other Mathematical Integrators 170 Chapter 9: All Approximations Are Rational 172 9.1 Laying Pipes under a Tiled Floor 173 9.2 Cogs and Millwrights 178 9.3 Cutting a Metric Screw 180 9.4 The Binary Calendar 182 9.5 The Harmonograph 184 9.6 A Little Nonsense! 187 Chapter 10: How Round Is Your Circle? 188 10.1 Families of Shapes of Constant Width 191 10.2 Other Shapes of Constant Width 193 10.3 Three-Dimensional Shapes of Constant Width 196 10.4 Applications 197 10.5 Making Shapes of Constant Width 202 10.6 Roundness 204 10.7 The British Standard Summit Tests of BS3730 206 10.8 Three-Point Tests 210 10.9 Shapes via an Envelope of Lines 213 10.10 Rotors of Triangles with Rational Angles 218 10.11 Examples of Rotors of Triangles 220 10.12 Modern and Accurate Roundness Methods 224 Chapter 11: Plenty of Slide Rule 227 11.1 The Logarithmic Slide Rule 229 11.2 The Invention of Slide Rules 233 11.3 Other Calculations and Scales 237 11.4 Circular and Cylindrical Slide Rules 240 11.5 Slide Rules for Special Purposes 241 11.6 The Magnameta Oil Tonnage Calculator 245 11.7 Non-Logarithmic Slide Rules 247 11.8 Nomograms 249 11.9 Oughtred and Delamain's Views on Education 251 Chapter 12: All a Matter of Balance 255 12.1 Stacking Up 255 12.2 The Divergence of the Harmonic Series 259 12.3 Building the Stack of Dominos 261 12.4 The Leaning Pencil and Reaching the Stars 265 12.5 Spiralling Out of Control 267 12.6 Escaping from Danger 269 12.7 Leaning Both Ways! 270 12.8 Self-Righting Stacks 271 12.9 Two-Tip Polyhedra 273 12.10 Uni-Stable Polyhedra 274 Chapter 13: Finding Some Equilibrium 277 13.1 Rolling Uphill 277 13.2 Perpendicular Rolling Discs 279 13.3 Ellipses 287 13.4 Slotted Ellipses 291 13.5 The Super-Egg 292 Epilogue 296 References 297 Index 303
£23.80
Princeton University Press Mathematical Modeling of Earths Dynamical Systems
Book SynopsisGives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. This book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables.Trade Review"The authors do a good job of deriving the mathematical models from physical considerations, and then showing how the equations can be solved by finite difference methods."--Choice "Where was this book when I was in university? ... I enjoyed this book very much and recommend it to students and researchers with an interest in this field."--Ray Wood, Leading EdgeTable of ContentsPreface xi Chapter 1: Modeling and Mathematical Concepts 1 Pros and Cons of Dynamical Models 2 An Important Modeling Assumption 4 Some Examples 4 Example I: Simulation of Chicxulub Impact and Its Consequences 5 Example II: Storm Surge of Hurricane Ivan in Escambia Bay 7 Steps in Model Building 8 Basic Definitions and Concepts 11 Nondimensionalization 13 A Brief Mathematical Review 14 Summary 22 Chapter 2: Basics of Numerical Solutions by Finite Difference 23 First Some Matrix Algebra 23 Solution of Linear Systems of Algebraic Equations 25 General Finite Difference Approach 26 Discretization 27 Obtaining Difference Operators by Taylor Series 28 Explicit Schemes 29 Implicit Schemes 30 How Good Is My Finite Difference Scheme? 33 Stability Is Not Accuracy 35 Summary 37 Modeling Exercises 38 Chapter 3: Box Modeling: Unsteady, Uniform Conservation of Mass 39 Translations 40 Example I: Radiocarbon Content of the Biosphere as a One-Box Model 40 Example II: The Carbon Cycle as a Multibox Model 48 Example III: One-Dimensional Energy Balance Climate Model 53 Finite Difference Solutions of Box Models 57 The Forward Euler Method 57 Predictor-Corrector Methods 59 Stiff Systems 60 Example IV: Rothman Ocean 61 Backward Euler Method 65 Model Enhancements 69 Summary 71 Modeling Exercises 71 Chapter 4: One-Dimensional Diffusion Problems 74 Translations 75 Example I: Dissolved Species in a Homogeneous Aquifer 75 Example II: Evolution of a Sandy Coastline 80 Example III: Diffusion of Momentum 83 Finite Difference Solutions to 1-D Diffusion Problems 86 Summary 86 Modeling Exercises 87 Chapter 5: Multidimensional Diffusion Problems 89 Translations 90 Example I: Landscape Evolution as a 2-D Diffusion Problem 90 Example II: Pollutant Transport in a Confined Aquifer 96 Example III: Thermal Considerations in Radioactive Waste Disposal 99 Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems 101 An Explicit Scheme 102 Implicit Schemes 103 Case of Variable Coefficients 107 Summary 108 Modeling Exercises 109 Chapter 6: Advection-Dominated Problems 111 Translations 112 Example I: A Dissolved Species in a River 112 Example II: Lahars Flowing along Simple Channels 116 Finite Difference Solution Schemes to the Linear Advection Equation 122 Summary 126 Modeling Exercises 128 Chapter 7: Advection and Diffusion (Transport) Problems 130 Translations 131 Example I: A Generic 1-D Case 131 Example II: Transport of Suspended Sediment in a Stream 134 Example III: Sedimentary Diagenes Influence of Burrows 138 Finite Difference Solutions to the Transport Equation 143 QUICK Scheme 144 QUICKEST Scheme 146 Summary 147 Modeling Exercises 147 Chapter 8: Transport Problems with a Twist: The Transport of Momentum 151 Translations 152 Example I: One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers' Equation) 152 An Analytic Solution to Burgers' Equation 157 Finite Difference Scheme for Burgers' Equation 158 Solution Scheme Accuracy 160 Diffusive Momentum Transport in Turbulent Flows 163 Adding Sources and Sinks of Momentum: The General Law of Motion 165 Summary 166 Modeling Exercises 167 Chapter 9: Systems of One-Dimensional Nonlinear Partial Differential Equations 169 Translations 169 Example I: Gradually Varied Flow in an Open Channel 169 Finite Difference Solution Schemes for Equation Sets 175 Explicit FTCS Scheme on a Staggered Mesh 175 Four-Point Implicit Scheme 177 The Dam-Break Problem: An Example 180 Summary 183 Modeling Exercises 185 Chapter 10: Two-Dimensional Nonlinear Hyperbolic Systems 187 Translations 188 Example I: The Circulation of Lakes, Estuaries, and the Coastal Ocean 188 An Explicit Solution Scheme for 2-D Vertically Integrated Geophysical Flows 197 Lake Ontario Wind-Driven Circulation: An Example 202 Summary 203 Modeling Exercises 206 Closing Remarks 209 References 211 Index 217
£46.75
Princeton University Press Modeling Infectious Diseases in Humans and
Book SynopsisOffers an introduction to the modeling of infectious diseases in humans and animals. This book moves from modeling with simple differential equations to more complex models, where spatial structure, seasonal 'forcing', or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory.Trade Review"Matt Keeling and Pejman Rohani...have made important and original contributions to epidemiology...and are well qualified to deliver an authoritative, comprehensive and up-to-date review. [The authors] advocate...the use of mathematical models to help design disease-control programs. They recognize that modeling is a partnership between modelers and empiricists. For that reason, I hope that [readership] will extend beyond existing and new devotees of this challenging and exciting discipline."--Mark Woolhouse, Nature "This book represents a valuable step toward educating readers to have greater appreciation and understanding of the development of mathematical models in infectious diseases."--Carol Y. Lin, Biometrics Book Reviews "[T]he authors have created a well written and essential reference for epidemiologists, mathematicians and other scientists interested in the mathematical modeling of infectious diseases."--Michael Hohle, Biometrical JournalTable of ContentsAcknowledgments xiii Chapter 1: Introduction 1 1.1 Types of Disease 1 1.2 Characterization of Diseases 3 1.3 Control of Infectious Diseases 5 1.4 What Are Mathematical Models? 7 1.5 What Models Can Do 8 1.6 What Models Cannot Do 10 1.7 What Is a Good Model? 10 1.8 Layout of This Book 11 1.9 What Else Should You Know? 13 Chapter 2: Introduction to Simple Epidemic Models 15 2.1 Formulating the Deterministic SIR Model 16 2.1.1 The SIR Model Without Demography 19 2.1.1.1 The Threshold Phenomenon 19 2.1.1.2 Epidemic Burnout 21 2.1.1.3 Worked Example: Influenza in a Boarding School 26 2.1.2 The SIR Model With Demography 26 2.1.2.1 The Equilibrium State 28 2.1.2.2 Stability Properties 29 2.1.2.3 Oscillatory Dynamics 30 2.1.2.4 Mean Age at Infection 31 2.2 Infection-Induced Mortality and SI Models 34 2.2.1 Mortality Throughout Infection 34 2.2.1.1 Density-Dependent Transmission 35 2.2.1.2 Frequency Dependent Transmission 36 2.2.2 Mortality Late in Infection 37 2.2.3 Fatal Infections 38 2.3 Without Immunity: The SIS Model 39 2.4 Waning Immunity: The SIRS Model 40 2.5 Adding a Latent Period: The SEIR Model 41 2.6 Infections with a Carrier State 44 2.7 Discrete-Time Models 46 2.8 Parameterization 48 2.8.1 Estimating R0 from Reported Cases 50 2.8.2 Estimating R0 from Seroprevalence Data 51 2.8.3 Estimating Parameters in General 52 2.9 Summary 52 Chapter 3: Host Heterogeneities 54 3.1 Risk-Structure: Sexually Transmitted Infections 55 3.1.1 Modeling Risk Structure 57 3.1.1.1 High-Risk and Low-Risk Groups 57 3.1.1.2 Initial Dynamics 59 3.1.1.3 Equilibrium Prevalence 62 3.1.1.4 Targeted Control 63 3.1.1.5 Generalizing the Model 64 3.1.1.6 Parameterization 64 3.1.2 Two Applications of Risk Structure 69 3.1.2.1 Early Dynamics of HIV 71 3.1.2.2 Chlamydia Infections in Koalas 74 3.1.3 Other Types of Risk Structure 76 3.2 Age-Structure: Childhood Infections 77 3.2.1 Basic Methodology 78 3.2.1.1 Initial Dynamics 80 3.2.1.2 Equilibrium Prevalence 80 3.2.1.3 Control by Vaccination 81 3.2.1.3 Parameterization 82 3.2.2 Applications of Age Structure 84 3.2.2.1 Dynamics of Measles 84 3.2.2.2 Spread and Control of BSE 89 3.3 Dependence on Time Since Infection 93 3.3.1 SEIR and Multi-Compartment Models 94 3.3.2 Models with Memory 98 3.3.3 Application: SARS 100 3.4 Future Directions 102 3.5 Summary 103 Chapter 4: Multi-Pathogen/Multi-Host Models 105 4.1 Multiple Pathogens 106 4.1.1 Complete Cross-Immunity 107 4.1.1.1 Evolutionary Implications 109 4.1.2 No Cross-Immunity 112 4.1.2.1 Application: The Interaction of Measles and Whooping Cough 112 4.1.2.2 Application: Multiple Malaria Strains 115 4.1.3 Enhanced Susceptibility 116 4.1.4 Partial Cross-Immunity 118 4.1.4.1 Evolutionary Implications 120 4.1.4.2 Oscillations Driven by Cross-Immunity 122 4.1.5 A General Framework 125 4.2 Multiple Hosts 128 4.2.1 Shared Hosts 130 4.2.1.1 Application: Transmission of Foot-and-Mouth Disease 131 4.2.1.2 Application: Parapoxvirus and the Decline of the Red Squirrel 133 4.2.2 Vectored Transmission 135 4.2.2.1 Mosquito Vectors 136 4.2.2.2 Sessile Vectors 141 4.2.3 Zoonoses 143 4.2.3.1 Directly Transmitted Zoonoses 144 4.2.3.2 Vector-Borne Zoonoses: West Nile Virus 148 4.3 Future Directions 151 4.4 Summary 153 Chapter 5: Temporally Forced Models 155 5.1 Historical Background 155 5.1.1 Seasonality in Other Systems 158 5.2 Modeling Forcing in Childhood Infectious Diseases: Measles 159 5.2.1 Dynamical Consequences of Seasonality: Harmonic and Subharmonic Resonance 160 5.2.2 Mechanisms of Multi-Annual Cycles 163 5.2.3 Bifurcation Diagrams 164 5.2.4 Multiple Attractors and Their Basins 167 5.2.5 Which Forcing Function? 171 5.2.6 Dynamical Trasitions in Seasonally Forced Systems 178 5.3 Seasonality in Other Diseases 181 5.3.1 Other Childhood Infections 181 5.3.2 Seasonality in Wildlife Populations 183 5.3.2.1 Seasonal Births 183 5.3.2.2 Application: Rabbit Hemorrhagic Disease 185 5.4 Summary 187 Chapter 6: Stochastic Dynamics 190 6.1 Observational Noise 193 6.2 Process Noise 193 6.2.1 Constant Noise 195 6.2.2 Scaled Noise 197 6.2.3 Random Parameters 198 6.2.4 Summary 199 6.2.4.1 Contrasting Types of Noise 199 6.2.4.2 Advantages and Disadvantages 200 6.3 Event-Driven Approaches 200 6.3.1 Basic Methodology 201 6.3.1.1 The SIS Model 202 6.3.2 The General Approach 203 6.3.2.1 Simulation Time 203 6.3.3 Stochastic Extinctions and The Critical Community Size 205 6.3.3.1 The Importance of Imports 209 6.3.3.2 Measures of Persistence 212 6.3.3.3 Vaccination in a Stochastic Environment 213 6.3.4 Application: Porcine Reproductive and Respiratory Syndrome 214 6.3.5 Individual-Based Models 217 6.4 Parameterization of Stochastic Models 219 6.5 Interaction of Noise with Heterogeneities 219 6.5.1 Temporal Forcing 219 6.5.2 Risk Structure 220 6.5.3 Spatial Structure 221 6.6 Analytical Methods 222 6.6.1 Fokker-Plank Equations 222 6.6.2 Master Equations 223 6.6.3 Moment Equations 227 6.7 Future Directions 230 6.8 Summary 230 Chapter 7: Spatial Models 232 7.1 Concepts 233 7.1.1 Heterogeneity 233 7.1.2 Interaction 235 7.1.3 Isolation 236 7.1.4 Localized Extinction 236 7.1.5 Scale 236 7.2 Metapopulations 237 7.2.1 Types of Interaction 240 7.2.1.1 Plants 240 7.2.1.2 Animals 241 7.2.1.3 Humans 242 7.2.1.4 Commuter Approximations 243 7.2.2 Coupling and Synchrony 245 7.2.3 Extinction and Rescue Effects 246 7.2.4 Levins-Type Metapopulations 250 7.2.5 Application to the Spread of Wildlife Infections 251 7.2.5.1 Phocine Distemper Virus 252 7.2.5.2 Rabies in Raccoons 252 7.3 Lattice-Based Models 255 7.3.1 Coupled Lattice Models 255 7.3.2 Cellular Automata 257 7.3.2.1 The Contact Process 258 7.3.2.2 The Forest-Fire Model 259 7.3.2.3 Application: Power laws in Childhood Epidemic Data 260 7.4 Continuous-Space Continuous-Population Models 262 7.4.1 Reaction-Diffusion Equations 262 7.4.2 Integro-Differential Equations 265 7.5 Individual-Based Models 268 7.5.1 Application: Spatial Spread of Citrus Tristeza Virus 269 7.5.2 Applilcation: Spread of Foot-and-mouth Disease in the United Kingdom 274 7.6 Networks 276 7.6.1 Network Types 277 7.6.1.1 Random Networks 277 7.6.1.2 Lattices 277 7.6.1.3 Small World Networks 279 7.6.1.4 Spatial Networks 279 7.6.1.5 Scale-Free Networks 279 7.6.2 Simulation of Epidemics on Networks 280 7.7 Which Model to Use? 282 7.8 Approximations 283 7.8.1 Pair-Wise Models for Networks 283 7.8.2 Pair-Wise Models for Spatial Processes 286 7.9 Future Directions 287 7.10 Summary 288 Chapter 8: Controlling Infectious Diseases 291 8.1 Vaccination 292 8.1.1 Pediatric Vaccination 292 8.1.2 Wildlife Vaccination 296 8.1.3 Random Mass Vaccination 297 8.1.4 Imperfect Vaccines and Boosting 298 8.1.5 Pulse Vaccination 301 8.1.6 Age-Structured Vaccination 303 8.1.6.1 Application: Rubella Vaccination 304 8.1.7 Targeted Vaccination 306 8.2 Contact Tracing and Isolation 308 8.2.1 Simple Isolation 309 8.2.2 Contact Tracing to Find Infection 312 8.3 Case Study: Smallpox, Contact Tracing, and Isolation 313 8.4 Case Study: Foot-and-Mouth Disease, Spatial Spread, and Local Control 321 8.5 Case Study: Swine Fever Virus, Seasonal Dynamics, and Pulsed Control 327 8.5.1 Equilibrium Properties 329 8.5.2 Dynamical Properties 331 8.6 Future Directions 333 8.7 Summary 334 References 337 Index 361 Parameter Glossary 367
£70.40
Princeton University Press The Fascinating World of Graph Theory
Book SynopsisTrade ReviewOne of Choice's Outstanding Academic Titles for 2015 "The Fascinating World of Graph Theory shows its pedagogic value. Traditional courseware develops subject matter from the bottom on up, going from basic definitions to the more complex. [This book] is different, not starting with the simplest structures or algorithms but with interesting problems to be solved, puzzles that use graphs and networks... [It is] readable and 'student-friendly'--more so than the typical math textbook."--New York Journal of Books "[The authors] have set out to make graph theory not only accessible to people with a limited mathematics background, but also to make it interesting. They have--by virtue of very clear writing, combined with a greater-than-usual emphasis on the historical and personal side of the subject--succeeded admirably."--MAA Reviews "The book is written masterfully; the narrative in each chapter flows naturally, engagingly... [I]t's a popular but also comprehensive introduction into graph theory."--Alexander Bogomolny, Cut the Knot blog "A fun and interesting tour of graph theory, leaving each visitor with a feeling of accomplishment and a satisfying understanding of this unusual mathematical world... This is an entertaining book for those who enjoy solving problems, plus readers will learn about some powerful mathematical ideas along the way!"--Choice "Here is a book with an enjoyable mix of mathematics and its applications, spiced with liberal amounts of history and anecdote... The value of books like this is that they make mathematics come alive to a broad range of readers who might not look twice at a textbook or monograph."--Norman Biggs, London Mathematical Society Newsletter "Deftly written and dynamic...The Fascinating World of Graph Theoryis an aptly named book, able to present a wide variety of central topics in graph theory, including the history behind them... in a lively and entertaining manner... A superb example of approachable mathematical writing."--SIAM Review "The authors manage to motivate all topics with interesting applications, historical problems and discussion of concepts from an intuitive point of view."--Radu Trimbitas, Studia Mathematica "I am not going to try to list the topics that are covered, since there is a great variety. This breadth, along with the superb writing, make the book a must-have for anyone with serious interest in graph theory."--James M. Cargal, UMAP JournalTable of ContentsPreface vii Prologue xiii 1 Introducing Graphs 1 2 Classifying Graphs 22 3 Analyzing Distance 45 4 Constructing Trees 67 5 Traversing Graphs 91 6 Encircling Graphs 108 7 Factoring Graphs 125 8 Decomposing Graphs 143 9 Orienting Graphs 164 10 Drawing Graphs 183 11 Coloring Graphs 206 12 Synchronizing Graphs 226 Epilogue Graph Theory: A Look Back-The Road Ahead 251 Exercises 255 Selected References 309 Index of Names 317 Index of Mathematical Terms 319
£16.19
MP-AMM American Mathematical Quantum Fields and Strings
Book SynopsisIdeas from quantum field theory and string theory have had considerable impact on mathematics. In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. These volumes are a written record of the program.Table of ContentsVolume 1, Part 1. Classical Fields and Supersymmetry: Notes on supersymmetry (following Joseph Bernstein) by P. Deligne and J. W. Morgan Notes on spinors by P. Deligne Classical field theory by P. Deligne and D. S. Freed Supersolutions by P. Deligne and D. S. Freed Sign manifesto by P. Deligne and D. S. Freed Volume 1, Part 2. Formal Aspects of QFT: Note on quantization by P. Deligne Introduction to QFT by D. Kazhdan Perturbative quantum field theory by E. Witten Index of Dirac operators by E. Witten Elementary introduction to quantum field theory by L. Faddeev Renormalization groups by D. Gross Note on dimensional regularization by P. Etingof Homework by E. Witten Index Volume 2, Part 3. Conformal Field Theory and Strings: Lectures on conformal field theory by K. Gawedzki Perturbative string theory by E. D'Hoker Super space descriptions of super gravity by P. Deligne Notes on 2d conformal field theory and string theory by D. Gaitsgory Kaluza-Klein compactifications, supersymmetry, and Calabi-Yau spaces by A. Strominger Volume 2, Part 4. Dynamical Aspects of QFT: Dynamics of Quantum Field Theory by E. Witten $N = 1$ supersymmetric field theories in four dimensions by N. Sieberg Index.
£105.45
Oxford University Press 50 Visions of Mathematics
Book SynopsisRelax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain. The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging). The topics covered are deliberately diverse and involve concepts from simple numerology to the very cutting edge of mathematics research. Each article is designed to be read in one sittinTrade ReviewMotorways; Sherlock Holmes; networks; mysterious numbers; sweets; champagne; interviews; mathematical poetry; ravens and even The Simpsons - this book has them all and more! Don't miss it! * Alan Stevens, Mathematics Today *The 50 essays in the book cover both pure and applied topics, and even the most esoteric subjects are addressed in an accessible way. * Physics World *Warmly recommended as recreational and stimulating reading to all mathematics aficionado! * Yuriy V. Rogovchenko, Zentralblatt MATH *Table of Contents1. What's the problem with mathematics? ; 2. The mathematics of messages ; 3. Decathlon: The art of scoring points ; 4. Queen Dido and the mathematics of the extreme ; 5. Can strings tie things together? ; 6. Grooves and knuckleballs ; 7. Pigs didn't fly but swine flu ; 8. Bill Tutte: Unsung Bletchley hero ; 9. What's the use of a quadratic equation? ; 10. Tony Hilton Royle Skyrme ; 11. The mathematics of obesity ; 12. It's a small world really ; 13. How does mathematics help at a murder scene? ; 14. Mathematics: The language of the universe ; 15. The troublesome geometry of CAT scanning ; 16. The mathematics of sports gambling ; Pythagoras's Theorem: a2 ; 17. A conversation with Freeman Dyson ; 18. A glass of bubbly ; 19. The influenza virus: It's all in the packaging ; 20. Mathematicians at the movies: Sherlock Holmes vs Professor Moriarty ; 21. Solving the Bristol bridge problem ; 22. All ravens are black: Puzzles and paradoxes in probability and statistics ; 23. The Tower of Hanoi: Where mathematics meets psychology ; 24. Career: A sample path ; 25. Sweets in the jar ; 26. Mary Cartwright ; 27. The fallibility of mathematics ; 28. Anecdotes of Dr Barrow ; 29. Finding Apollo ; 30. The golden ratio in astronomy and astrophysics ; 31. The high-power hypar ; 32. This is not a carrot: Paraconsistent mathematics ; 33. The mystery of Groombridge Place ; Pythagoras's Theorem: b2 ; 34. Mysterious number 6174 ; 35. Percolating possibilities ; 36. Milestones on a non-Euclidean journey ; 37. Simpson's rule ; 38. Risking your life ; 39. Networks and illusions ; 40. Emmy Noether: Against the odds ; 41. Of catastrophes and creodes: How maths benefits from collaboration with other fields ; 42. Conic section hide and seek ; 43. Sir James Lighthill: A life in waves ; 44. Fail safe or fail dangerous ; 45. Leapfrogging into the future: How child's play is at the heart of weather and climate models ; 46. Motorway mathematics ; 47. The philosophy of applied mathematics ; 48. Mighty Morphogenesis ; 49. Called to the barcode ; 50. Roughly fifty-fifty? ; Pythagoras's Theorem: c2
£37.99
Oxford University Press Linear Algebra
Book SynopsisLinear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader''s confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading pTrade ReviewThis book gives an introduction to linear algebra for students with limited mathematical preparation. ... The steady pace of the book is so gentle that no student need be left behind. * Peter Macgregor, Mathematical Gazette *Table of Contents1. Linear Equations and Matrices ; 2. Euclidean Space ; 3. General Vector Spaces ; 4. Inner Product Spaces ; 5. Linear Transformation ; 6. Determinants ; 7. Eigenvalues and Eigenvectors
£32.49
Dover Publications Inc. Differential Forms with Applications to the
Book SynopsisA graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.
£11.24
Elsevier Science Computability Complexity and Languages
Book SynopsisCovers the key areas of computer science, including recursive function theory, formal languages, and automata. This book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability. It also covers in a variety of different arrangements automata theory, computational logic, and complexity theory.Trade Review"If there is a single book on the theory of computing that should be in every college library collection, this is it. Although written as a text for an advanced undergraduate course in theoretical computer science, the book may serve as an introductory resource, or the foundation for independent study, in many areas of theoretical computing: grammars, automata theory, computability, complexity theory, and unsolvability. The beauty of this book is that the breadth of coverage is complemented with extraordinary depth." --CHOICE "Theoretical computer science is often viewed as a collection of disparate topics, including computability theory, formal language theory, complexity theory, logic, and so on. This well-written book attempts to unify the subject by introducing each of these topics in turn, then showing how they relate to each other... This is an excellent book that succeeds in tying together a number of areas in theoretical computer science." --COMPUTING REVIEWSTable of ContentsPreliminaries. Computability: Programs and Computable Functions. Primitive Recursive Functions. A Universal Program. Calculations on Strings. Turing Machines. Processes and Grammars. Classifying Unsolvable Problems. Grammars and Automata: Regular Languages. Context-Free Languages. Context-Sensitive Languages. Logic: Propositional Calculus. Quantification Theory. Complexity: Abstract Complexity. PolynomialTime Computability. Semantics: Approximation Orderings. Denotational Semantics of Recursion Equations. Operational Semantics of Recursion Equations. Suggestions for Further Reading. Subject Index.
£47.49
Elsevier Science The Science of Algorithmic Trading and Portfolio Management
Book SynopsisDiscusses algorithmic trading across the various asset classes, provides key insights into ways to develop, test, and build trading algorithms. This title helps readers learn how to evaluate market impact models and assess performance across algorithms, traders, and brokers, and acquire the knowledge to implement electronic trading systems.Trade Review"Kissell... introduces the mathematical models for constructing, calibrating, and testing market impact models that calculate the change in stock price caused by a large trade or order, and presents an advanced portfolio optimization process that incorporates market impact and transaction costs directly into portfolio optimization." --ProtoView.com, March 2014 "This book provides excellent coverage of the challenges faced by portfolio managers and traders in implementing investment ideas and the advanced modeling techniques to address these challenges." --Kumar Venkataraman, Southern Methodist UniversityTable of ContentsI - Introduction 1. Algorithmic Trading 2. Market Microstructure 3. Transaction Cost Analysis (TCA) II – Mathematical Modeling 4.. Market Impact 5. Multi-Asset Class Market Impact 6 Price 7. Algorithmic Trading Risk 8. Algorithmic Decision Making Framework 9. Portfolio Algorithms III – Portfolio Management 10. Portfolio Construction 11. Quant Factors 12. Black Box Models
£43.19
Princeton University Press Complex Adaptive Systems
Book SynopsisProvides an account of complex adaptive social systems, by two of the field's leading authorities. This work focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It also demonstrates how the usual extremes used in modeling can be fruitfully transcended.Trade Review"The use of computational, especially agent-based, models has already shown its value in illuminating the study of economic and other social processes. Miller and Page have written an orientation to this field that is a model of motivation and insight, making clear the underlying thinking and illustrating it by varied and thoughtful examples. It conveys with remarkable clarity the essentials of the complex systems approach to the embarking researcher."—Kenneth J. Arrow, winner of the Nobel Prize in economics"In Complex Adaptive Systems, two masters of this burgeoning field provide a highly readable and novel restatement of the logic of social interactions, linking individually based micro processes to macrosocial outcomes, ranging from Adam Smith's invisible hand to Thomas Schelling's models of standing ovations. The book combines the vision of a new Santa Fe school of computational, social, and behavioral science with essential 'how to' advice for apprentice modelers."—Samuel Bowles, author of Microeconomics: Behavior, Institutions, Evolution"This is a wonderful book that will be read by graduate students, faculty, and policymakers. The authors write in an extraordinarily clear manner about topics that are very technical and difficult for many people. I sat down to begin thumbing through and found myself deeply engaged."—Elinor Ostrom, author of Understanding Institutional DiversityTable of ContentsList of Figures xiii List of Tables xv Preface xvii Part I: Introduction 1 Chapter 1: Introduction 3 Chapter 2: Complexity in Social Worlds 9 2.1 The Standing Ovation Problem 10 2.2 What's the Buzz? 14 2.2.1 Stay Cool 14 2.2.2 Attack of the Killer Bees 15 2.2.3 Averaging Out Average Behavior 16 2.3 A Tale of Two Cities 17 2.3.1 Adding Complexity 20 2.4 New Directions 26 2.5 Complex Social Worlds Redux 27 2.5.1 Questioning Complexity 27 Part II: Preliminaries 33 Chapter 3: Modeling 35 3.1 Models as Maps 36 3.2 A More Formal Approach to Modeling 38 3.3 Modeling Complex Systems 40 3.4 Modeling Modeling 42 Chapter 4: On Emergence 44 4.1 A Theory of Emergence 46 4.2 Beyond Disorganized Complexity 48 4.2.1 Feedback and Organized Complexity 50 Part III: Computational Modeling 55 Chapter 5: Computation as Theory 57 5.1 Theory versus Tools 59 5.1.1 Physics Envy: A Pseudo-Freudian Analysis 62 5.2 Computation and Theory 64 5.2.1 Computation in Theory 64 5.2.2 Computation as Theory 67 5.3 Objections to Computation as Theory 68 5.3.1 Computations Build in Their Results 69 5.3.2 Computations Lack Discipline 70 5.3.3 Computational Models Are Only Approximations to Specific Circumstances 71 5.3.4 Computational Models Are Brittle 72 5.3.5 Computational Models Are Hard to Test 73 5.3.6 Computational Models Are Hard to Understand 76 5.4 New Directions 76 Chapter 6: Why Agent-Based Objects? 78 6.1 Flexibility versus Precision 78 6.2 Process Oriented 80 6.3 Adaptive Agents 81 6.4 Inherently Dynamic 83 6.5 Heterogeneous Agents and Asymmetry 84 6.6 Scalability 85 6.7 Repeatable and Recoverable 86 6.8 Constructive 86 6.9 Low Cost 87 6.10 Economic E. coli (E. coni?) 88 Part IV: Models of Complex Adaptive Social Systems 91 Chapter 7: A Basic Framework 93 7.1 The Eightfold Way 93 7.1.1 Right View 94 7.1.2 Right Intention 95 7.1.3 Right Speech 96 7.1.4 Right Action 96 7.1.5 Right Livelihood 97 7.1.6 Right Effort 98 7.1.7 Right Mindfulness 100 7.1.8 Right Concentration 101 7.2 Smoke and Mirrors: The Forest Fire Model 102 7.2.1 A Simple Model of Forest Fires 102 7.2.2 Fixed, Homogeneous Rules 102 7.2.3 Homogeneous Adaptation 104 7.2.4 Heterogeneous Adaptation 105 7.2.5 Adding More Intelligence: Internal Models 107 7.2.6 Omniscient Closure 108 7.2.7 Banks 109 7.3 Eight Folding into One 110 7.4 Conclusion 113 Chapter 8: Complex Adaptive Social Systems in One Dimension 114 8.1 Cellular Automata 115 8.2 Social Cellular Automata 119 8.2.1 Socially Acceptable Rules 120 8.3 Majority Rules 124 8.3.1 The Zen of Mistakes in Majority Rule 128 8.4 The Edge of Chaos 129 8.4.1 Is There an Edge? 130 8.4.2 Computation at the Edge of Chaos 137 8.4.3 The Edge of Robustness 139 Chapter 9: Social Dynamics 141 9.1 A Roving Agent 141 9.2 Segregation 143 9.3 The Beach Problem 146 9.4 City Formation 151 9.5 Networks 154 9.5.1 Majority Rule and Network Structures 158 9.5.2 Schelling's Segregation Model and Network Structures 163 9.6 Self-Organized Criticality and Power Laws 165 9.6.1 The Sand Pile Model 167 9.6.2 A Minimalist Sand Pile 169 9.6.3 Fat-Tailed Avalanches 171 9.6.4 Purposive Agents 175 9.6.5 The Forest Fire Model Redux 176 9.6.6 Criticality in Social Systems 177 Chapter 10: Evolving Automata 178 10.1 Agent Behavior 178 10.2 Adaptation 180 10.3 A Taxonomy of 2 x 2 Games 185 10.3.1 Methodology 187 10.3.2 Results 189 10.4 Games Theory: One Agent, Many Games 191 10.5 Evolving Communication 192 10.5.1 Results 194 10.5.2 Furthering Communication 197 10.6 The Full Monty 198 Chapter 11: Some Fundamentals of Organizational Decision Making 200 11.1 Organizations and Boolean Functions 201 11.2 Some Results 203 11.3 Do Organizations Just Find Solvable Problems? 206 11.3.1 Imperfection 207 11.4 Future Directions 210 Part V: Conclusions 211 Chapter 12: Social Science in Between 213 12.1 Some Contributions 214 12.2 The Interest in Between 218 12.2.1 In between Simple and Strategic Behavior 219 12.2.2 In between Pairs and Infinities of Agents 221 12.2.3 In between Equilibrium and Chaos 222 12.2.4 In between Richness and Rigor 223 12.2.5 In between Anarchy and Control 225 12.3 Here Be Dragons 225 Epilogue 227 The Interest in Between 227 Social Complexity 228 The Faraway Nearby 230 Appendixes A An Open Agenda For Complex Adaptive Social Systems 231 A.1 Whither Complexity 231 A.2 What Does it Take for a System to Exhibit Complex Behavior? 233 A.3 Is There an Objective Basis for Recognizing Emergence and Complexity? 233 A.4 Is There a Mathematics of Complex Adaptive Social Systems? 234 A.5 What Mechanisms Exist for Tuning the Performance of Complex Systems? 235 A.6 Do Productive Complex Systems Have Unusual Properties? 235 A.7 Do Social Systems Become More Complex over Time 236 A.8 What Makes a System Robust? 236 A.9 Causality in Complex Systems? 237 A.10 When Does Coevolution Work? 237 A.11 When Does Updating Matter? 238 A.12 When Does Heterogeneity Matter? 238 A.13 How Sophisticated Must Agents Be Before They Are Interesting? 239 A.14 What Are the Equivalence Classes of Adaptive Behavior? 240 A.15 When Does Adaptation Lead to Optimization and Equilibrium? 241 A.16 How Important Is Communication to Complex Adaptive Social Systems? 242 A.17 How Do Decentralized Markets Equilibrate? 243 A.18 When Do Organizations Arise? 243 A.19 What Are the Origins of Social Life? 244 B Practices for Computational Modeling 245 B.1 Keep the Model Simple 246 B.2 Focus on the Science, Not the Computer 246 B.3 The Old Computer Test 247 B.4 Avoid Black Boxes 247 B.5 Nest Your Models 248 B.6 Have Tunable Dials 248 B.7 Construct Flexible Frameworks 249 B.8 Create Multiple Implementations 249 B.9 Check the Parameters 250 B.10 Document Code 250 B.11 Know the Source of Random Numbers 251 B.12 Beware of Debugging Bias 251 B.13 Write Good Code 251 B.14 Avoid False Precision 252 B.15 Distribute Your Code 253 B.16 Keep a Lab Notebook 253 B.17 Prove Your Results 253 B.18 Reward the Right Things 254 Bibliography 255 Index 261
£31.50
Princeton University Press Why Cats Land on Their Feet
Book SynopsisEver wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? This title offers a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. It also features an appendix that explains all physical concepts used in the book.Trade Review"A collection of physical puzzlers, often with counter intuitive manifestations, which, for all that, admit rigorous explanation supported by physical intuition... [H]ugely entertaining and provide hours of brainy activities."--Alexander Bogomolny, CTK Insights "This book seeks to nurture this physical intuition in readers by analyzing several paradoxes while keeping the math to a minimum. Through examining one puzzle or paradox after another, Levi emphasizes the underlying principles involved and helps foster an intuitive understanding of why things work the way they do. Readers will find themselves coaxed into learning because they want to satisfy their curiosity as they examine each puzzle... [A]n excellent resource for understanding some less-obvious principles of physics."--William Baer, Library Journal "Each chapter can be read in a few minutes time, say while you are drinking a cup of tea or coffee. It will give you a lot of inspiration to challenge or entertain your friends during a reception or another get-together with some different kind of beverages. Of course you will impress them only when they haven't read the book themselves already. Hence make sure that you are the first."--Adhemar Bultheel, European Mathematical Society "Mathematician Levi has assembled a fascinating collection of 77 puzzles, some clever new originals and some twists to old ones that challenge physical intuition... [A] pleasurable challenge."--Choice "Quite how a falling cat manages to land on its feet is a classic conundrum for undergraduate students of physics. Levi presents this and other puzzles, with a few clues to how to go about solving them using only high-school mathematics. He explains all the necessary physics concepts in the appendix too."--Nature Physics "Why Cats Land On Their Feet relies on a novel approach to problem solving that is not based on mathematics, but on models and physical intuition... By looking beyond formulas and equations, Levi's goal is to provide readers who have a familiarity with basic high-school math and physics with critical thinking skills that can be applied to a range of physics problems beyond the book."--Mechanical Engineering-CIME "Levi uses titillating puzzles and a humorous tone to truly infuse fun into the book. A must have for anyone that likes physics, or for that matter hates. Why Cats Land On Their Feet is a book that introduces the reader to the cool side of physics and then engages for hours."--Sarthak Shankar, Organiser "The book is written in an accessible style and presumes little mathematical knowledge: a couple of puzzles refer to some basic calculus, but most require only arithmetic. It is suitable for everyone from sixth form students upwards... Teachers and lecturers will particularly appreciate this text, finding in it numerous quirky thought-experiments, actual experiments and trivia to catch their students' attention."--Paul Taylor, Mathematics Today "This book will cultivate and challenge your physical intuition. Above all, it shows that physics and mathematics can be fun and useful at the same time."--Catherine A. Gorini, Mathematics Teacher "It is written with a lot of humor, and provides helpful insights without going into unnecessarily complicated physical or mathematical techniques. The style is informal and attractive, which makes the reading of the book a real pleasure."--Kiril Bankov, Mathematical GazetteTable of ContentsChapter 1 Fun with Physical Paradoxes, Puzzles, and Problems 1 1.1 Introduction 1 1.2 Background 3 1.3 Sources 3 Chapter 2 Outer Space Paradoxes 5 2.1 A Helium Balloon in a Space Shuttle 5 2.2 Space Navigation without Jets 9 2.3 A Paradox with a Comet 13 2.4 Speeding Up Causes a Slowdown 14 Chapter 3 Paradoxes with Spinning Water 17 3.1 A Puzzle with a Floating Cork 17 3.2 Parabolic Mirrors and Two Kitchen Puzzles 19 3.3 A Cold Parabolic Dish 21 3.4 Boating on a Slope 23 3.5 Navigating with No Engine or Sails 24 3.6 The Icebergs 25 Chapter 4 Floating and Diving Paradoxes 28 4.1 A Bathtub on Wheels 28 4.2 The Tub Problem--In More Depth 30 4.3 How to Lose Weight in a Fraction of a Second 32 4.4 An Underwater Balloon 33 4.5 A Scuba Puzzle 35 4.6 A Weight Puzzle 36 Chapter 5 Flows and Jets 39 5.1 Bernoulli's Law and Water Guns 39 5.2 Sucking on a Straw and the Irreversibility of Time 42 5.3 Bernoulli's Law and Moving Around in a Space Shuttle 44 5.4 A Sprinker Puzzle 45 5.5 Ejecting Water Fast but with Zero Speed? 48 5.6 A Pouring Water Puzzle 49 5.7 A Stirring Paradox 51 5.8 An Inkjet Printer Question 54 5.9 A Vorticity Paradox 55 Chapter 6 Moving Experiences: Bikes, Gymnastics, Rockets 57 6.1 How Do Swings Work? 57 6.2 The Rising Energy Cost 58 6.3 A Gymnast Doing Giants and a Hamster in a Wheel 60 6.4 Controlling a Car on Ice 63 6.5 How Does a Biker Turn? 64 6.6 Speeding Up by Leaning 65 6.7 Can One Gain Speed on a Bike by Body Motion Only? 66 6.8 Gaining Weight on a Motorbike 68 6.9 Feeling the Square in mv2 2 Through the Bike Pedals 69 6.10 A Paradox with Rockets 70 6.11 A Coffee Rocket 72 6.12 Throwing a Ball from a Moving Car 74 Chapter 7 Paradoxes with the Coriolis Force 77 7.1 What Is the Coriolis Force? 77 7.2 Feeling Coriolis in a Boeing 747 79 7.3 Down the Drain with Coriolis 80 7.4 High Pressure and Good Weather 80 7.5 What Causes Trade Winds? 82 Chapter 8 Centrifugal Paradoxes 84 8.1 What's Cheaper: Flying West or East? 84 8.2 A Coriolis Paradox 85 8.3 An Amazing Inverted Pendulum: What Holds It Up? 87 8.4 Antigravity Molasses 91 8.5 The "Proof" That the Sling Cannot Work 92 8.6 A David-Goliath Problem 93 8.7 Water in a Pipe 97 8.8 Which Tension Is Greater? 98 8.9 Slithering Ropes in Weightlessness 100 Chapter 9 Gyroscopic Paradoxes 104 9.1 How Does the Spinning Top Defy Gravity? 104 9.2 Gyroscopes in Bikes 108 9.3 A Rolling Coin 109 9.4 Staying on a Slippery Dome 111 9.5 Finding North with a Gyroscope 113 Chapter 10 Some Hot Stuff and Cool Things 117 10.1 Can Heat Pass from a Colder to a Hotter Object? 117 10.2 A Bike Pump and Molecular Ping-Pong 121 10.3 A Bike Pump as a Heat Pump 122 10.4 Heating a Room in Winter 124 10.5 Freezing Things with a Bike Tire 125 Chapter 11 Two Perpetual Motion Machines 127 11.1 Perpetual Motion by Capillarity 128 11.2 An Elliptical Mirror Perpetuum Mobile 129 Chapter 12 Sailing and Gliding 132 12.1 Shooting Cherry Pits and Sailing 133 12.2 Sailing Straight into the Wind 135 12.3 Biking against the Wind 136 12.4 Soaring without Updrafts 138 12.5 Danger of the Horizontal Shear Wind 141 Chapter 13 The Flipping Cat and the Spinning Earth 142 13.1 How Do Cats Flip to Land on Their Feet? 142 13.2 Can Trade Winds Slow Earth's Rotation? 144 Chapter 14 Miscellaneous 146 14.1 How to Open a Wine Bottle with a Book 146 14.2 :"t's Alive!" 149 14.3 Falling Faster Than g: A Falling Chain "Sucked in" by the Floor 150 14.4 A Man in a Boat with Drag 151 14.5 A "Phantom" Boat: No Wake and No Drag 154 14.6 A Constant-G Roller Coaster 156 14.7 Shooting at a Cart 158 14.8 Computing 2 with a Shoe 159 Appendix 161 A.1 Newton's Laws 161 A.2 Kinetic Energy, Potential Energy, Work 163 A.2.1 Work 163 A.2.2 Kinetic Energy 165 A.2.3 Potential Energy 166 A.2.4 Conservation of Energy 168 A.3 Center of Mass 169 A.4 Linear Momentum 171 A.5 The Torque 174 A.6 Angular Momentum 175 A.7 Angular Velocity, Centripetal Acceleration 178 A.8 Centrifugal and Centripetal Forces 181 A.9 Coriolis, Centrifugal, and Complex Exponentials 181 A.10 The Fundamental Theorem of Calculus 184 Bibliography 187 Index 189
£15.29
Princeton University Press Discrete and Computational Geometry
Book SynopsisAn essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only) Trade Review"Discrete and Computational Geometry meets an urgent need for an undergraduate text bridging the theoretical sides and the applied sides of the field. It is an excellent choice as a textbook for an undergraduate course in discrete and computational geometry! The presented material should be accessible for most mathematics or computer science majors in their second or third year in college. The book also is a valuable resource for graduate students and researchers."--Egon Schulte, Zentralblatt MATH "[W]e recommend this book for an undergraduate course on computational geometry. In fact, we hope to use this book ourselves when we teach such a class."--Brittany Terese Fasy and David L. Millman, SigAct News
£56.00
Taylor & Francis Ltd Electrodynamics of Density Ducts in Magnetized
Book SynopsisProviding a systematic and self-contained treatment of excitation, propagation and re- emission of electromagnetic waves guided by density ducts in magnetized plasmas, this book describes in detail the theoretical basis of the electrodynamics of ducts. The classical dielectric-waveguide theory in open guiding systems in magnetoplasma is subjected to rigorous generalization. The authors emphasize the conceptual physical and mathematical aspects of the theory, while demonstrating its applications to problems encountered in actual practice. The opening chapters of the book discuss the underlying physical phenomena, outline some of the results obtained in natural and artificial density ducts, and describe the basic theory crucial to understanding the remainder of the book. The more specialized and complex topics dealt with in subsequent chapters include the theory of guided wave propagation along axially uniform ducts, finding the field excited by the source in the presence of a duct, excitation of guided modes, the asymptotic theory of wave propagation along axially nonuniform ducts, and mode re-emission from a duct. The full wave theory is used throughout most of the book to ensure consistency, and the authors start with simpler cases and gradually increase the complexity of the treatment.Table of Contents1. The Basic Equations 2. Integral Representation of Source-excited Fields on a Duct 3. Modal Representation of Source-excited Fields on a Duct 4. Wave Re-emission from a Density Duct 5. Modes in Axially Uniform Ducts 6. Radiation from Given Sources in a Uniform Unbounded Magnetoplasma 7. Wave Propagation Along Axially Non-uniform Ducts
£166.25
Society for Industrial and Applied Mathematics Ten Lectures on Wavelets 61 CBMSNSF Regional
Book SynopsisThis monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. Wavelets are a mathematical development that many experts think may revolutionize the world of information storage and retrieval. They are a fairly simple mathematical tool now being applied to the compression of data, such as fingerprints, weather satellite photographs, and medical x-rays - that were previously thought to be impossible to condense without losing crucial details. The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose fun
£63.00
Princeton University Press A Course in Complex Analysis
Book SynopsisTrade Review"A no-nonsense, clearly written graduate level textbook . . . . far more approachable than many other books on complex analysis"---Jonathan Shock, Mathemafrica"An excellent textbook. . . . Carefully and precisely written in a lively style."---Ali Abkar, zbMATH Open"Beautifully produced, beautifully written, on an incomparably beautiful area of mathematics, this is an inspirational book that I shall gratefully return to again and again."---Nick Lord, Mathematical Gazette
£54.40
Elsevier Science Transportation Engineering
Book SynopsisTable of Contents1. Introduction 2. Transportation Systems 3. Traffic and Transportation Analysis Techniques 4. Traffic Flow Theory 5. Capacity and Level of Service 6. Traffic Control 7. Public Transportation Systems 8. Transportation Demand Analysis 9. Freight Transportation and Logistics 10. Transport Economics 11. Transportation, Environment, and Society 12. Reliability, Resilience, Robustness, and Vulnerability of Transportation Systems
£124.20
Taylor & Francis Inc The Mathematics Companion
Book SynopsisEverything You Need to Know about Mathematics for Science and EngineeringUpdated and expanded with new topics, The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition presents the essential core of mathematical principles needed by scientists and engineers. Starting from the basic concepts of trigonometry, the book covers calculus, differential equations, and vector calculus. A new chapter on applications discusses how we see objects mathematically with the eye, how quantum mechanics works, and more.A Convenient, Student-Friendly Format Rich with Diagrams and Clear ExplanationsThe book presents essential mathematics ideas from basic to advanced level in a way that is useful to both students and practicing professionals. It offers a unique and educational approach that is the signature style of the author's companion books. The author explains mathematical concepts clearly, concisely, and visually, ilTrade Review"The book summarizes basic notions of mathematical methods for physicists and engineers in a schematic way. It is aimed both at science students and physicists who need a quick handy reference when they have to solve a specific mathematical problem."—Applications of Mathematics, 60, 2015Praise for the First Edition:"This is an interesting and useful little book … .it is very well done, and everything that might be expected to be there is there … . The book might also be invaluable for those undergraduate students in Mathematics, Science, or Engineering, who need to undertake first- and second-year courses in Mathematics, and it will serve those who wish to have quick access to all those formulae that seem to be so readily forgotten."—Australian Physics, March/April 2006Table of ContentsPart 1 Essential Mathematics: Basic mathematics. Differentiation. Integration. Exponentials and logarithms. Hyperbolic functions. Infinite series. Part 2 Advance Mathematics: Ordinary differential equations. Laplace transforms. Vector analysis. Partial derivatives. Multiple integrals. Fourier series. Special functions. Partial differential equations.
£36.09
CRC Press Measure Theory and Fine Properties of Functions
Book SynopsisMeasure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in ân, Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions as well as functions of bounded variation.The text provides complete proofs of many key results omitted from other books, including Besicovitch's covering theorem, Rademacher's theorem (on the differentiability a.e. of Lipschitz functions), area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrov's theorem (on the twice differentiability a.e. oTrade Review"This is a new revised edition of a very successful book dealing with measure theory in Rn and some special properties of functions, usually omitted from books dealing with abstract measure theory, but which a working mathematician analyst must know. … The book is clearly written with complete proofs, including all technicalities. … The new edition benefits from LaTeX retyping, yielding better cross-references, as well as numerous improvements in notation, format, and clarity of exposition. The bibliography has been updated and several new sections were added … this welcome, updated, and revised edition of a very popular book will continue to be of great interest for the community of mathematicians interested in mathematical analysis in Rn."—Studia Universitatis Babes-Bolyai Mathematica, 60, 2015Table of ContentsGeneral Measure Theory. Hausdorff Measures. Area and Coarea Formulas. Sobolev Functions. Functions of Bounded Variation, Sets of Finite Perimeter. Differentiability, Approximation by C1 Functions. Bibliography.
£79.99
Penguin Books Ltd Love Triangle
Book SynopsisA #1 SUNDAY TIMES BESTSELLERExplore the life-changing magic of trigonometry with Matt Parker, stand-up mathematician and No. 1 bestselling author of Humble PiWhy can no two people ever see the same rainbow? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? Why does the wake behind a duck always form an angle of exactly 39 degrees? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle.In Love Triangle, stand-up comedian, ex-maths teacher and Sunday Times number one bestselling author Matt Parker is on a mission to prove why we should all show a lot more love for triangles, along with the useful trigonometry and geometry they enable. To make his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich into three equal parts, and measure tall building
£22.36
Oxford University Press Fluid Mechanics A Very Short Introduction Very
Book SynopsisVery Short Introductions: Brilliant, Sharp, Inspiring Fluid mechanics is an important branch of physics concerned with the way in which fluids, such as liquids and gases, behave when in motion and at rest. A quintessential interdisciplinary field of science, it interacts with many other scientific disciplines, from chemistry and biology to mathematics and engineering.This Very Short Introduction presents the field of fluid mechanics by focusing on the underlying physical ideas and using everyday phenomena to demonstrate them, from dripping taps to swimming ducks. Eric Lauga shows how this set of fundamental physical concepts can be applied to a wide range of flow behaviours and highlights the role of fluid motion in both the natural and industrial worlds. This book also considers future applications of fluid mechanics in science.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Trade ReviewOverall, the book should definitely be an individual's go-to source when seeking an authoritative perspective on the field of fluid mechanics. * Anita T. Layton, Society for Industrial and Applied Mathematics Vol 65.4 *Table of Contents1: Fluids 2: Viscosity 3: Pipes 4: Dimensions 5: Boundary layers 6: Vortices 7: Instabilities 8: Researching fluids and flows Further Reading Index
£9.49
MP-AMM American Mathematical Illustrating Mathematics
Book SynopsisA book for anyone who wishes to illustrate their mathematical ideas. It is organised by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way.Table of Contents Drawings Paper & fiber arts Laser cutting Graphics Video & virtual reality 3D printing Mechanical constructions and other materials Multiple ways to illustrate the same thing Acknowledgments Image credits Index.
£25.60
