Applied mathematics Books

Book SynopsisNow considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 < p < 2 Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of HÃlder continuous functions and the space of functions of bounded mean oscillation

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Book SynopsisThis book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math and physics taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The exposition follows an arc through the subject building towards a detailed derivation of the NavierâStokes and energy equations followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations thus allowing a clearer view of the physics. The motivation behind many fundamental concepts such as Bernoulli's equation and the stream function are included. Many exercises are designed with a view toward using MATLAB or equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the bTable of Contents1. Introduction; 2. Eulerian and Lagrangian viewpoints, paths and streamlines; 3. Stream function; 4. Helmholtz decomposition; 5. Sources, sinks and vortices; 6. Doublets and their applications; 7. Complex potential; 8. Accelerating reference frames; 9. Fluids at rest; 10. Incompressibility and mass conservation; 11. Stress tensor - existence and symmetry; 12. Stress tensor in Newtonian fluids; 13. Navier–Stokes equation; 14. Thermodynamic considerations; 15. Energy equation; 16. Complete equations of motion; 17. Applications of Bernoulli's equation and control volumes; 18. Vorticity; 19. Applications to viscous flow; 20. Laminar boundary layers; 21. Some applications to convective heat and mass transfer.

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Book SynopsisThe book has been tested and refined through years of classroom teaching experience. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. This textbook provides complete coverage of continuous-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives.Key features: In-depth coverage of continuous-time theory and methodology Numerous, fully worked out examples and exercises in every chapter Mathematically rigorous and consistent, yet bridging various basic and more advanced concepts Judicious balance of financial theory and mathematiTable of ContentsPart I: Stochastic Calculus with Brownian Motion. 1. One-Dimensional Brownian Motion and Related Processes. 2. Introduction to Continuous-Time Stochastic Calculus. Part II Continuous-Time Modelling. 3. Risk-Neutral Pricing in the (B; S) Economy: One Underlying Stock. 4. Risk-Neutral Pricing in a Multi-Asset Economy. 5. American Options. 6. Interest-Rate Modelling and Derivative Pricing. 7. Alternative Models of Asset Price Dynamics. A. Essentials of General Probability Theory. B. Some Useful Integral (Expectation) Identities and Symmetry Properties of Normal Random Variables. C. Answers and Hints to Exercises. D. Glossary of Symbols and Abbreviations. Greek Alphabet. References. Index.

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Book SynopsisThe second edition of the Handbook of Induction Heating reflects the number of substantial advances that have taken place over the last decade in theory, computer modeling, semi-conductor power supplies, and process technology of induction heating and induction heat treating. This edition continues to be a synthesis of information, discoveries, and technical insights that have been accumulated at Inductoheat Inc. With an emphasis on design and implementation, the newest edition of this seminal guide provides numerous case studies, ready-to-use tables, diagrams, rules-of-thumb, simplified formulas, and graphs for working professionals and students.Trade Review"The 2nd Edition of the Handbook for Induction Heating is equivalent to having 3 world class experts on staff without paying high priced consulting fees. For your seasoned, and probably more importantly, your new and emerging manufacturing and process engineers, this comprehensive guide provides the details your company needs to compete around the world. Significant technical achievements have occurred since 2002 with the last edition. Rudnev, Loveless, and Cook have compiled an indispensable, world class text replete with the basics and advanced concepts of induction heating. The case studies also illustrate and inspire the design and deployment of innovative concepts which transform theory into application. If you are not reading and using this tour de force, it is safe to say that your competitors have read and marked up their copies."—Jon D. Tirpak, PE, FASM; Executive Director, Forging Defense Manufacturing Consortium, and Past President, ASM International (2015 – 2016)"As an automotive plant we are performing several heat treatment processes, among them induction hardening. Rear axle shafts, ring gears, couplers, etc. … all require induction hardening in order to obtain the required material properties like case depth, surface hardness, … . Although we have decades of experience, it is of crucial importance to have -theoretical and practical- technical support from specialists. The Handbook of Induction Heating is an exceptional help and reference work for everyone that is involved in IH. Not only when everything goes fine, but also when you face problems like undesirable or unexplainable results after IH, machine issues, etc. This book has given us the answer to many questions over the years and it will continue to do that. The 2nd edition is even more enhanced, and contains again a wide spectrum of many different issues that belong to the world of the practitioners of IH. One more thing to add: in the seldom event that one of the problems you face is not mentioned in the book, you can easily turn to the authors and ask them your question. This is what we experienced and appreciate enormously."—Mike Bogaerts, Supervisor Materials and Chemical Lab, CNH Industrial, Antwerp, Belgium"Induction heating is used in many applications which include heat treatment, forging, extrusion, rolling, bonding, brazing, sealing, shrink fitting, drying, and bending. A thorough knowledge of the process enables one to optimize its use in ever-increasing number of applications. This handbook assimilates the broad experience of the authors to accomplish this need." — Tirupathi R. Chandrupatla, Rowan University, New Jersey, USA"A very comprehensive, must-have textbook that heat treatment engineers should definitely read. You can learn every aspect of induction hardening and become an expert starting from scratch."—Tusaş Motor Sanayii, Ali Fırat Dinler, Turkey"The 2nd Edition of the Handbook for Induction Heating is equivalent to having 3 world class experts on staff without paying high priced consulting fees. For your seasoned, and probably more importantly, your new and emerging manufacturing and process engineers, this comprehensive guide provides the details your company needs to compete around the world. Significant technical achievements have occurred since 2002 with the last edition. Rudnev, Loveless, and Cook have compiled an indispensable, world class text replete with the basics and advanced concepts of induction heating. The case studies also illustrate and inspire the design and deployment of innovative concepts which transform theory into application. If you are not reading and using this tour de force, it is safe to say that your competitors have read and marked up their copies."—Jon D. Tirpak, PE, FASM; Executive Director, Forging Defense Manufacturing Consortium, and Past President, ASM International (2015 – 2016)"As an automotive plant we are performing several heat treatment processes, among them induction hardening. Rear axle shafts, ring gears, couplers, etc. … all require induction hardening in order to obtain the required material properties like case depth, surface hardness, … . Although we have decades of experience, it is of crucial importance to have -theoretical and practical- technical support from specialists. The Handbook of Induction Heating is an exceptional help and reference work for everyone that is involved in IH. Not only when everything goes fine, but also when you face problems like undesirable or unexplainable results after IH, machine issues, etc. This book has given us the answer to many questions over the years and it will continue to do that. The 2nd edition is even more enhanced, and contains again a wide spectrum of many different issues that belong to the world of the practitioners of IH. One more thing to add: in the seldom event that one of the problems you face is not mentioned in the book, you can easily turn to the authors and ask them your question. This is what we experienced and appreciate enormously."—Mike Bogaerts, Supervisor Materials and Chemical Lab, CNH Industrial, Antwerp, Belgium"Induction heating is used in many applications which include heat treatment, forging, extrusion, rolling, bonding, brazing, sealing, shrink fitting, drying, and bending. A thorough knowledge of the process enables one to optimize its use in ever-increasing number of applications. This handbook assimilates the broad experience of the authors to accomplish this need." — Tirupathi R. Chandrupatla, Rowan University, New Jersey, USA"A very comprehensive, must-have textbook that heat treatment engineers should definitely read. You can learn every aspect of induction hardening and become an expert starting from scratch."—Tusaş Motor Sanayii, Ali Fırat Dinler, TurkeyTable of ContentsIntroduction. Industrial Applications of Induction Heating. Theoretical Background. Heat Treatment by Induction. Joining Applications. Induction Mass Heating. Power Supplies for Modern Induction Heating. Epilogue. Appendix A. References. Index.

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Book SynopsisMaple is a powerful symbolic computation system that is widely used in universities around the world. This short introduction gives readers an insight into the rules that control how the system works, and how to understand, fix, and avoid common problems. Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. Each chapter contains numerous illustrative examples, using mathematics that does not extend beyond first-year undergraduate material. Maple worksheets containing these examples are available for download from the author''s personal website. The book is suitable for new users, but where advanced topics are central to understanding Maple they are tackled head-on. Many concepts which are absent from introductory books and manuals are described in detail. With this book, students, teachers and researchers will gain a solid understanding of Maple and how to use it to solve complex mathematical problems in a simple and efficient way.Trade Review'Thompson (Univ. of Liverpool, UK) clearly knows the 'gotchas' that most often plague beginners (and others!) and provides pointed guidance; extracting the same vital information buried in longer and more systematic treatises and manuals can certainly prove a challenge. Summing Up: Recommended. Lower-division undergraduates and above; faculty and professionals.' D. V. Feldman, CHOICETable of Contents1. Introduction; 2. Getting started; 3. Algebra and calculus; 4. Solving equations; 5. Linear algebra; 6. Graphics; 7. Programming; 8. Procedures; 9. Example programs; Appendix A. Other ways to run Maple; Appendix B. Terminating characters; Index of Maple notation.

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Book SynopsisYou've Never Seen What You've Always Needed to Know Until Now Invisible forces are at work. They push and shove on everything you buy or sell. They affect every concept you want to take to market, all the suppliers you'll deal with, and every customer you'll ever see. To be successful, you need to understand them. See them in detail in ways not possible with other methods. Hypernomics: Using Hidden Dimensions to Solve Unseen Problems discovers that markets behave according to previously unknown laws set by the buyers and sellers within them. It reveals those rules and how to detect, describe, and deploy them to your advantage. It doesn't change economics so much as reveal it. It's like a microscope looking at pond water, a telescope tilted to the sky, sonar scanning the bottom of the ocean. Hypernomics lets you see into markets in ways you can't with the unaided eye. Sailors never navigate without a map. You shouldn't either, since your ship coulTable of ContentsIntroduction 1 CHAPTER 1 A Brief History of Position and Direction 9 Ancient Maps 9 Geography Begins 13 Math and Position Problems 13 Summary 26 Vignette: Restaurant Math 27 CHAPTER 2 Four-Dimensional Systems 29 Dot Plots Begin 29 "X" Marks the Spot 30 Most Markets Don't Address Commodities 31 Cartesian Systems and Negativity 33 Geography Is Never Negative 38 Plotting in Four Dimensions 52 Summary 56 CHAPTER 3 Five-Dimensional Systems 57 Physical Changes over Time 57 Economic Changes over Time 62 Summary 69 CHAPTER 4 Value 71 Human Traits 71 What Does Value Mean in Hypernomics? 75 Determining Value 77 The Market as Laboratory 79 Summary 91 Vignette: The Value of Expanding One's Limits 92 CHAPTER 5 Demand 95 Demand Frontiers 95 Aggregate Demand 102 Average Demand 104 Minimum Demand 105 Proxy Demand 106 Submarket, Sub-Submarket, and Mission Market Demand Curves 107 Product Demand Curves 109 Summary 110 A Hypernomics Vignette: The Value of and Demand for Money 111 CHAPTER 6 Price and Quantity Determination 121 The General Problem Calls for Specifics 121 The Neoclassical View: The Law of Supply and Demand 122 Ferrous Blunder: Universal Claim of Upward-Sloping Supply Curves 125 The Hypernomics View: The Law of Value and Demand 128 Summary 133 A Hypernomics Vignette: The Law of Value and Demand 134 CHAPTER 7 Market Mapping and Financial Cat Scans 137 Got Eggs? 137 Market Map Boundaries 141 Feature and Price Gap Maps 143 Financial Cat Scans 146 Summary 155 CHAPTER 8 Aiming and Missing 157 Neoclassical Aiming 157 Immediate Aiming 158 Immediate Aiming in Hypernomics 163 Ultimate Aiming 165 Ultimate Aiming in Hypernomics 167 Summary 170 CHAPTER 9 N-Dimensional Systems 173 Common Object 1—Pie 174 Common Object 2—Logarithmic Scaling 176 Common Object 3—Rolodex 178 Common Object 4—Concentric Circle 180 Common Object 5—Parallelograms (as in Extendable Mirrors) 181 Starting from (0,0,0,0. . .0) 182 Summary 200 CHAPTER 10 An Amazon Mining Expedition 201 Summary 210 CHAPTER 11 More 211 Vignette: What Do Markets Look Like to Viruses? 213 CHAPTER 12 Appendix: Using Hypernomics on Your Own 217 Stating the Problem 220 Data Collection 221 Data Entry 223 Data Manipulation 225 Data Interpretation 229 Summary 235 Vignette: The Importance of Going Deep into the Data 237 CHAPTER 13 Neoclassical Economics and Hypernomics Differences 241 Glossary 243 References 247 Index 279

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Book SynopsisWith a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus.  Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse''s lemma and the Poincaré lemma.  The ideas behind most topics can be understood with just two or three variables.  The book incorporates modern computational tools to give visualization real power.  Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps.  The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books.  This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics.  Prerequisites are an introduction to linear algebra and multivariable calculus.  There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry.  The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.Trade ReviewFrom the reviews:“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)Table of Contents1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises

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Book SynopsisThis book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problemsinspired from the Almgren-Chriss approachand then demonstrates the use of that framework across a wide range of areas.The book introduces the classical tools of optimal execution and market making, along with their practical use. It also demonstrates how the tools used in the optimal execution literature can be used to solve classical and new issues where accounting for liquidity is important. In particular, it presents cutting-edge research on the pricing of block trades, the pricing and hedging of options when liquidity matters, and the management of complex share buy-back contracts.What sets this book apart from others is that it focuses onTrade Review"This excellent monograph covers the mathematical theory of market microstructure with particular emphasis in models of optimal execution and market making. Gueant’s book is a superb introduction to these topics for graduate students in mathematical finance or quants who want to work in execution algorithms or market-making strategies."—Jose A. Scheinkman, Charles and Lynn Zhang Professor of Economics, Columbia University, and Theodore Wells '29 Professor of Economics Emeritus, Princeton University"This is a very timely book that cuts across various fields (applied mathematics, operations research, and quantitative finance). Execution costs due to market illiquidity can significantly reduce returns on investment strategies and, for this reason, affect asset prices. It is therefore important to design trading strategies minimizing these costs and to account for their effect on prices. In the last decade, ‘quants’ and researchers in quantitative finance have made considerable progress on these issues, integrating in their models changes in the way financial markets work (e.g., the development of continuous limit order books, market fragmentation, dark pools, the automation of trading, etc.). "Olivier Guéant’s book takes stock of this effort by providing a rigorous and expert presentation of mathematical tools, models, and numerical methods developed in this area. I strongly recommend it for researchers and graduate students interested in how illiquidity costs affect trading strategies and should be accounted for in asset valuation problems."—Thierry Foucault, HEC Foundation Chair Professor of Finance, HEC, Paris"This book is a must-have for quantitative analysts working at algorithmic trading desks. Olivier Guéant could have written a sophisticated book dedicated to cutting-edge research. He rather decided to put his talent at the service of a far more difficult task: deliver a clear view of modern algorithmic trading to strats or quants having decent scientific training. Scientists will find here all the needed keys to control the intraday risk of their trading models, improving their overall efficiency. Covering brokerage algorithms, market making, hedging, and share buyback techniques, this book is the definitive reference for algorithm builders.Moreover, Olivier links algorithmic trading with market microstructure during the first chapter of the book, including interesting thoughts on corporate bonds trading. On the other hand, he provides a nice introduction to mathematical economics in the Appendix. This book is resolutely more than a bunch of equations thrown on blank pages. I consider it an important step forward in the building of the mathematics of market microstructure."—Charles-Albert Lehalle, Senior Research Advisor, Capital Fund ManagementTable of ContentsIntroduction. Optimal Liquidation. Liquidity in Pricing Models. Market Making.

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Book SynopsisIn knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns (generators). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems.The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa's algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps rTrade Review"Diagram Genus, Generators and Applications contains a systematical study of combinatorial properties of knot diagrams. It focuses on diagrams that represent the canonical genus of a knot, i.e., the minimal genus of all Seifert surfaces for a given knot that are obtained by applying Seifert’s algorithm to diagrams of the knot. The book contains the complete classification of knots up to canonical genus 4. This classification has lots of applications … The book … will certainly become a reference in this area. It is very clearly written and contains enough background material so that it can be used by graduate-level students to learn the subject and do work in this area on their own."—Thomas Fiedler, Institut de Mathématiques, Université Paul Sabatier, Toulouse"This book provides an essential resource for anyone currently doing research or interested in doing research on surfaces in knot complements and their applications. Enough background is included so non-experts can follow the exposition and appreciate the myriad results that ensue."—Professor Colin Adams, Williams College"This monograph is a systematic account of combinatorial knot theory, with a particular focus on spanning surfaces arising from Seifert’s construction. It includes a brief and nicely written introduction to knot theory, concentrating on the background needed for a diagrammatic treatment of knots, including the range of classical and modern knot polynomials.A strong feature of this book, and indeed much of the author’s work elsewhere, is the identification of diagrammatic examples with awkward or unexpected properties, and an analysis of the techniques that can be used effectively on them. This can provide examples that can’t possibly be tackled by certain procedures, and thus directs attention to places where the current repertoire of techniques is lacking.The main topic developed is the notion of diagram genus, or canonical genus, based on Seifert’s algorithm. The related graph theory leads to the selection of a class of alternating knot diagrams, termed generators, and a substantial account of these up to genus 4 is given.This is followed by the discussion of a number of combinatorial results and conjectures. In particular, some nice results for alternating or positive knots are given and their possible extension to the case when k of the knot crossings are switched is explored for small values of k. The earlier calculations are used to extend the knowledge of these results to cover knots with fewer restrictions on their genus or crossing number.There is a good account of the combinatorics for recognizing when a knot diagram actually represents the trivial knot. It is surprisingly easy to draw diagrams of the trivial knot with relatively few crossings that do not have an immediately obvious simplification, and some examples are included in the illustrations.A further section covers the question of finding the braid index for an alternating knot, and the conditions under which the Morton-Franks-Williams bound turn out to be sharp. The concluding section is intended as an appetizer for others and includes a variety of annotated questions and conjectures.The carefully written text is aimed at a graduate-level readership. It gives a comprehensive view of combinatorial questions, both in the monograph itself and in the well-annotated bibliography, and would serve both well as a reference and a source of new ideas.Features A comprehensive account of diagram-centered results in knot theory Focus on Seifert’s construction of oriented-spanning surfaces Analysis of diagrams representing the unknot and their reduction by Reidemeister moves Careful and persuasive writing An excellent reference text and source of ideas" —H.R. Morton, Department of Mathematical Sciences, University of LiverpoolTable of ContentsIntroduction. Preliminaries. The Maximal Number of Generator Crossings and ~-Equivalance Classes. Generators of Genus 4. Unknot Diagrams, Non-Trivial Polynomials, and Achiral Knots. The Signature. Braid Index of Alternating Knots. Minimal String Bennequin Surfaces. The Alexander Polynomial of Alternating Knots. Outlook.

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Book SynopsisThe Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the preeminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible.Organized in ascending order of complexity, the material is divided into two parts. The first part is a coherent survey of the most important definitions, formulas, equations, methods, and theorems. It covers arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, special functions, calculus of variations, and probability theory. Numerous specific examples clarify the methods for solving problems and equations. The second part provides many in-depth mathematical tables, including those of exact solutions of various types of equations. This concise, comprehensive compendium of mathematical definitions, formulas, and theorems provides the foundation for exploring scientific and technological phenomena.Trade Review“The book is split into two parts: methods (about 1100 pages), and tables (about 400 pages). Both parts are well structured and well written. … the coverage of the topics included is excellent … this is a fine reference text, offered at a very reasonable price …” —SIAM Review, Vol. 49, No. 3, September 2007Table of ContentsArithmetic and Elementary Algebra. Elementary Functions. Elementary Geometry. Analytic Geometry. Algebra. Limits and Derivatives. Integrals. Series. Differential Geometry. Functions of Complex Variable. Integral Transforms. Ordinary Differential Equations. First-Order Partial Differential Equations. Linear Partial Differential Equations. Nonlinear Partial Differential Equations. Integral Equations. Difference Equations and Other Functional Equations. Special Functions and Their Properties. Calculus of Variations and Optimization. Probability Theory. Mathematical Statistics. Finite Sums and Infinite Series. Integrals. Integral Transforms. Ordinary Differential Equations. Systems of Ordinary Differential Equations. First-Order Partial Differential Equations. Linear Equations and Problems of Mathematical Physics. Nonlinear Mathematical Physics Equations. Systems of Partial Differential Equations. Integral Equations. Functional Equations.

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Book SynopsisThis book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, optimisation and dynamics.The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis. The book’s careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study. This new fourth edition includes two chapters on probability theory, providing the essential mathematical background for upper-level courses on economic theory, econometrics and finance.Trade Review'In spite of the wide scope of this textbook, its presentation is clear and crisp. The materials are very carefully organised. The transition from mathematical principles to economic propositions is remarkably lucid throughout the book. If a first-year undergraduate student in economics comes to ask me which one, among many books on mathematics for economists, to buy for years to come, then I would definitely tell them that this is the one.'Chiaki Hara, Institute of Economic Research, Kyoto University‘This is a great text to learn from – the authors do an excellent job providing intuitive explanations, making connections between results and illustrating the use of mathematics in solving economics problems, and there is a host of solved exercises which perform two roles: providing essential practice material and introducing further applications in economics.’Andrew Chesher, Director of The Centre for Microdata Methods and Practice, IFS and UCL -- .Table of Contents1. Linear equations2. Linear inequalities3. Sets and functions4. Quadratics, indices and logarithms5. Sequences, series and limits6. Introduction to differentiation7. Methods of differentiation8. Maxima and minima9. Exponential and logarithmic functions10. Approximations11. Matrix algebra12. Systems of linear equations13. Determinants and quadratic forms14. Functions of several variables15. Implicit relations16. Optimisation with several variables17. Principles of constrained optimisation18. Further topics in constrained optimisation19. Integration20. Aspects of integral calculus21. Probability22. Expectation23. Introduction to dynamics24. The circular functions25. Complex numbers26. Further dynamics27. Eigenvalues and eigenvectors28. Dynamic systems29. Dynamic optimisation in discrete time30. Dynamic optimisation in continuous time31. Introduction to analysis32. Metric spaces and existence theoremsNotes on further readingIndex

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Book SynopsisThis self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.Trade ReviewFrom the reviews: It explains its chosen topics clearly and simply, not including extraneous material, and is written at a level that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb in its clarity and elegance... Just as useful as the writing style are the appendices and hints. Not only does Britton give elementary presentations of some basic mathematical techniques (difference equations, ODEs and PDEs) he also gives extensive hints for the exercises, bordering on complete solutions in some cases. This is a resource that will surely prove extremely useful for all teachers of such a course...there is no denying that Essential Mathematical Biology is superbly designed for the purpose it serves, and will, I am sure, become a popular text book across the world. UK Nonlinear News Britton explains how difference and differential equations have been used to formulate theory and description in biology, but at a level accessible to undergraduate mathematics, physics or engineering majors. His very readable style achieves clear and largely jargon-free explanations with no sacrifice of mathematical rigour.....Clearly intended to be read and used as a course textbook, another attractive feature of this volume is the inclusion of interesting and relevant exercises after each subchapter section, together with an appendix of hints to help students work and understand them. Other appendixes efficiently review the mathematical techniques and concepts that are basic to the applications presented in the chapters....I believe that Essential Mathematical Biology will enrich the personal library of any scholar interested in applied differential equations. The Quarterly Review of Biology, Volume 79, No. 2 "This excellent monograph provides a very readable introduction to the most important aspects of mathematical biology. … The book contains numerous exercises, with hints for the solutions, a guide for further studies, and interesting historical comments. An index helps in finding the many concepts and equations introduced in the monograph. This is a most welcome addition to the literature." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 12 (1), 2005) "This book as a textbook covers a diversity of topics from mathematical biology. Its content is best summarized by the title of its eight substantial Chapters. … It poses questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. … includes many exercises as well as detailed solutions for them. … a good introduction for those beginners that are interested in the fast growing field of mathematical biology." (Lan-Sun Chen, Mathematical Reviews, 2003m) "Each chapter of this textbook provides a brief introduction into an important area of mathematical biology. … In addition, there are four appendices, comprising about one fourth of the whole text, which summarize important techniques … . The book is aimed at the undergraduate level … . Many exercises, together with hints for their solution, complement this text which will be useful as a first introduction." (R. Bürger, Monatshefte für Mathematik, Vol. 143 (4), 2004) "In brevity and simplicity lies the great strength of this book. It explains its chosen topics clearly and simply … that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb … . Just as useful as the writing style are the appendices and the hints. … will surely prove extremely useful for all teachers of such a course. … will, I am sure, become a popular text book across the world." (James Sneyd, UK Nonlinear News, June, 2004) "Britton writes a book that provides for an introductory account of mathematical biology. … Many examples are given … . The figures are clear and precise. All mathematical formulae, equations and models are complete, clear and readable. … The material in the book is clear and concise. The book provides the reader with a wealth of information and is well suited as a textbook for a course in mathematical biology. I highly recommend this book … . It makes a worthwhile addition." (Paul Johnson, New Zealand Mathematical Society Newsletter, Issue 90, April, 2004) "It was a great pleasure reading Essential Mathematical Biology. … the book is very well written without large jumps in the mathematical reasoning, it is also quite concise and covers a large amount of material. … The writing and style are very clear. The mathematical steps are laid out neatly with clear definitions and notation … . The book is a great contribution to students interested in mathematical biology … and a source of important insights for biological scientists." (D. Kault, The Australian Mathematical Society, Vol. 31 (1), 2004) "This book is a self-contained introduction to the fast-growing field of mathematical biology. … it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered … ." (L’Enseignement Mathematique, Vol. 49 (3-4), 2003) "Those of us in mathematical biology like to imagine our field on the verge of achieving critical opalescence … . it is a pleasure and challenge to share the wide spectrum of problems and approaches with eager undergraduates from various backgrounds … . Several textbooks are available, now including Essential Mathematical Biology by Nicholas Britton. The author … exemplifies interdisciplinary approaches … . Essential Mathematical Biology would serve well as a template for an advanced undergraduate or beginning graduate course … ." (Fred Adler, Physics Today, March, 2004) "Each of the eight chapters starts with a brief list of clearly expressed goals, questions or explanations, well motivating the reader to enter the chapter by introducing him into the essential biological problems and their importance. … I can fully recommend to use this ‘undergraduate mathematics textbook’ in any theoretical or practical computer course introducing into Mathematical Biology, but also for other teaching or education purposes within this interdisciplinary filed of growing importance between Mathematics, Scientific Computing, Bioinformatics, Systems Biology, Ecology, Physiology and Biomedicine." (Wolfgang Alt, Mathematical Biosciences, Vol. 208, 2007)Table of Contents1. Single Species Population Dynamics.- 2. Population Dynamics of Interacting Species.- 3. Infectious Diseases.- 4. Population Genetics and Evolution.- 5. Biological Motion.- 6. Molecular and Cellular Biology.- 7. Pattern Formation.- 8. Tumour Modelling.- Further Reading.- A. Some Techniques for Difference Equations.- A.1 First-order Equations.- A.1.1 Graphical Analysis.- A.1.2 Linearisation.- A.2 Bifurcations and Chaos for First-order Equations.- A.2.1 Saddle-node Bifurcations.- A.2.2 Transcritical Bifurcations.- A.2.3 Pitchfork Bifurcations.- A.2.4 Period-doubling or Flip Bifurcations.- A.3 Systems of Linear Equations: Jury Conditions.- A.4 Systems of Nonlinear Difference Equations.- A.4.1 Linearisation of Systems.- A.4.2 Bifurcation for Systems.- B. Some Techniques for Ordinary Differential Equations.- B.1 First-order Ordinary Differential Equations.- B.1.1 Geometric Analysis.- B.1.2 Integration.- B.1.3 Linearisation.- B.2 Second-order Ordinary Differential Equations.- B.2.1 Geometric Analysis (Phase Plane).- B.2.2 Linearisation.- B.2.3 Poincaré-Bendixson Theory.- B.3 Some Results and Techniques for rath Order Systems.- B.3.1 Linearisation.- B.3.2 Lyapunov Functions.- B.3.3 Some Miscellaneous Facts.- B.4 Bifurcation Theory for Ordinary Differential Equations.- B.4.1 Bifurcations with Eigenvalue Zero.- B.4.2 Hopf Bifurcations.- C. Some Techniques for Partial Differential Equations.- C.1 First-order Partial Differential Equations and Characteristics.- C.2 Some Results and Techniques for the Diffusion Equation.- C.2.1 The Fundamental Solution.- C.2.2 Connection with Probabilities.- C.2.3 Other Coordinate Systems.- C.3 Some Spectral Theory for Laplace’s Equation.- C.4 Separation of Variables in Partial Differential Equations.- C.5 Systems of Diffusion Equations with Linear Kinetics.- C.6 Separating the Spatial Variables from Each Other.- D. Non-negative Matrices.- D.1 Perron-Frobenius Theory.- E. Hints for Exercises.

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Book SynopsisThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university. Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures. Table of ContentsTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.

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Book SynopsisThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university. Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures. Table of ContentsTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.

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Book SynopsisThis monograph provides a concise overview of nonlinear internal wave theory. It serves as a self-contained reference for both students of mathematics as well as scientific professionals by presenting the material in two parts, isolating the narrative analysis from the mathematical detail. This unique format allows the text to remain accessible to oceanographers and researchers outside of mathematics by presenting a range of relevant theories on their own terms. Conversely, it enables applied mathematicians to understand how the conversation between mathematics and sciences proceeds in a field that has developed through a combination of the two. In addition, the text is supplemented by hands-on Matlab software, as the book incorporates a collection of working codes that enable readers to reproduce all theoretical figures in the text, with modification potential to fit a range of applications including a number of mini-projects outlined throughout the text.Table of ContentsPreface.- Background and Equation Summaries.- Derivations: Linear, Weakly Nonlinear and Conjugate Flow Theory.- Using Linear and Weakly Nonlinear Theory.- Exact Internal Solitary Waves.- Exact Internal Hydraulics.- Mode-2 Waves.- Concluding Thoughts.

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Book SynopsisThis book explores recent topics in quantitative finance with an emphasis on applications and calibration to time-series. This last aspect is often neglected in the existing mathematical finance literature while it is crucial for risk management. The first part of this book focuses on switching regime processes that allow to model economic cycles in financial markets. After a presentation of their mathematical features and applications to stocks and interest rates, the estimation with the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) is detailed. A second part focuses on self-excited processes for modeling the clustering of shocks in financial markets. These processes recently receive a lot of attention from researchers and we focus here on its econometric estimation and its simulation. A chapter is dedicated to estimation of stochastic volatility models. Two chapters are dedicated to the fractional Brownian motion and Gaussian fields. After a summary of their features, we present applications for stock and interest rate modeling. Two chapters focuses on sub-diffusions that allows to replicate illiquidity in financial markets. This book targets undergraduate students who have followed a first course of stochastic finance and practitioners as quantitative analyst or actuaries working in risk management.Trade Review“Hainaut has written a book which in such panorama has a position of its own and which should be considered with great interest. … the book should definitely be considered an excellent and warmly recommended read. It is likely that it will be soon become a reference for those interested in modern topics and for young researchers in particular.” (Gianluca Cassese, zbMATH 1512.91001, 2023)Table of ContentsPreface.- Acknowledgements.- Notations.- 1. Switching Models: Properties and Estimation.- 2. Estimation of Continuous Time Processes by Markov Chain Monte Carlo.- 3. Particle Filtering and Estimation.- 4. Modeling of Spillover Effects in Stock Markets.- 5. Non-Markov Models for Contagion and Spillover.- 6. Fractional Brownian Motion.- 7. Gaussian Fields for Asset Prices.- 8. Lévy Interest Rate Models With a Long Memory.- 9. Affine Volterra Processes and Rough Models.- 10. Sub-Diffusion for Illiquid Markets.- 11. A Fractional Dupire Equation for Jump-Diffusions.- References.

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Book SynopsisThis book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately.Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use. Table of ContentsIntroduction.- Topological foundations, hypercomplexes and homology.- Weighted complexes, cohomology and Laplace operators.- The Laplace operator and the geometry of graphs.- Metric spaces and manifolds.- Linear methods: Kernels, variations, and averaging.- Nonlinear schemes: Clustering, feature extraction and dimension reduction.- Manifold learning, the scheme of Laplacian eigenmaps.- Metrics and curvature.

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Book SynopsisThe aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods.Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.Table of ContentsPreface.- Cell-based, continuum and hybrid models of tissue dynamics.- The Diffusion Limit of Transport Equations in Biology.- Mathematical Models of the Interaction of Cells and Cell Aggregates with the Extracellular Matrix.- Mathematical modeling of morphogenesis in living materials.- Multiscale computational modelling and analysis of cancer invasion.

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Book SynopsisThis introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.Trade Review"(The book is) a lean and largely self-contained introduction to the modern theory of probability, aimed at advanced undergraduate or beginning graduate students. The 28 short chapters belie the book's genesis as polished lecture notes; the exposition is sleek and rigorous and each chapter ends with a supporting collection of mainly routine exercises. ... The authors make it clear what luggage is required for this exhilarating trek,... a good knowledge of advanced calculus, some linear algebra, and some "mathematical sophistication". With this understood, the itinerary is immaculately paced and planned with just the right balances of technical ascents and pauses to admire the scenery. Within the constraints of a slim volume, it is hard to imagine how the authors could have done a more effective or more attractive job." The Mathematical Gazette, Vol. 84, No 500, 2000 "The authors provide the shortest path through the twenty-eight chapter headings. The topics are treated in a mathematically and pedagogically digestible way. The writing is concise and crisp: the average chapter length is about eight pages. ... Numerous exercises add to the value of the text as a teaching tool. In conclusion, this is an excellent text for the intended audience."Short Book Reviews, Vol. 21, No. 2, 2001Table of Contents1. Introduction 2. Axioms of Probability 3. Conditional Probability and Independence 4. Probabilities on a Countable Space 5. Random Variables on a Countable Space 6. Construction of a Probability Measure 7. Construction of a Probability Measure on R 8. Random Variables 9. Integration with Respect to a Probability Measure 10. Independent Random Variables 11. Probability Distributions on R 12. Probability Distributions on Rn 13. Characteristic Functions 14. Properties of Characteristic Functions 15. Sums of Independent Random Variables 16. Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) 17. Convergence of Random Variables 18. Weak Convergence 19. Weak Convergence and Characteristic Functions 20. The Laws of Large Numbers 21. The Central Limit Theorem 22. L2 and Hilbert Spaces 23. Conditional Expectation 24. Martingales 25. Supermartingales and Submartingales 26. Martingale Inequalities 27. Martingales Convergence Theorems 28. The Radon-Nikodym Theorem

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

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

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

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

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Book SynopsisWhat is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly 'rational' human behavior in search of appropriate 'winning strategies'. This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle.This book takes a novel approach to the subject. Its focus is on mathematical models that apply to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably.This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples invite the reader to participate 'actively' when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.

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Book SynopsisThis book explores recent developments in theoretical research and mathematical modelling of real-world complex systems, organized in four parts. The first part of the book is devoted to the mathematical tools for the design and analysis in engineering and social science study cases. We discuss the periodic evolutions in nonlinear chemical processes, vibro-compact systems and their behaviour, different types of metal–semiconductor self-assembled samples, made of silver nanowires and zinc oxide nanorods. The second part of the book is devoted to mathematical description and modelling of the critical events, climate change and robust emergency scales. In three chapters, we consider a climate-economy model with endogenous carbon intensity and the behaviour of Tehran Stock Exchange market under international sanctions. The third part of the book is devoted to fractional dynamic and fractional control problems. We discuss the novel operational matrix technique for variable-order fractional optimal control problems, the nonlinear variable-order time fractional convection–diffusion equation with generalized polynomials The fourth part of the book concerns solvability and inverse problems in differential and integro-differential equations. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists and urban planners.Table of ContentsAlbert C.J. Luo, The Chinese Calligraphy in Memory of Professor Valentin Afraimovich (1945-2018) Chapter 01: Mayra Angélica Bárcenas-Castro, Ramón Díaz de León-Zapata, Saúl Almazán-Cuéllar, Efrén Flores-García, Gustavo Vera-Reveles, José Vulfrano González-Fernández, Applications of the fundamentals of Bézier curves Chapter 02: Siyu Guo, Albert C. J. Luo On complex periodic evolutions of a periodically diffused Brussellator Chapter 03: Victor Bazhenov, Olga Pogorelova, Tatiana Postnikova Analysis of Intermittent and Quasi-periodic Transitions to Chaos in Vibro-impact System with Continuous Wavelet Transform Chapter 04: Lev A. Ostrovsky, Yury A. Stepanyants Complex Dynamics of Solitons in Rotating Fluids Chapter 05: Dmitry V. Kovalevsky A Climate-Economy Model with Endogenous Carbon Intensity Chapter 06: Abootaleb Shirvani, Dimitri Volchenkov A Regulated Market Under Sanctions. On Tail Dependence Between Oil, Gold, and Tehran Stock Exchange Index Chapter 07: Dmitry V. Kovalevsky and Mara Manez Costa Dynamics of Water-Constrained Economies Affected by Climate Change: Nonlinear and Stochastic Effects Chapter 08: H. Hassani, J. A. Tenreiro Machado An efficient operational matrix technique for variable-order fractional optimal control problems Chapter 09: H. Hassani, J. A. Tenreiro Machado, Z. Avazzadeh, E. Naraghirad Solving nonlinear variable-order time fractional convection-diffusion equation with generalized polynomials Chapter 10: C. Connell McCluskey ,Vitali Vougalter Inverse problems for some systems of parabolic equations Chapter 11: Vitali Vougalter, Vitaly Volpert Solvability In The Sense Of Sequences For Some Non Fredholm Operators With The Bi-Laplacian

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Book SynopsisThis book introduces machine learning methods in finance. It presents a unified treatment of machine learning and various statistical and computational disciplines in quantitative finance, such as financial econometrics and discrete time stochastic control, with an emphasis on how theory and hypothesis tests inform the choice of algorithm for financial data modeling and decision making. With the trend towards increasing computational resources and larger datasets, machine learning has grown into an important skillset for the finance industry. This book is written for advanced graduate students and academics in financial econometrics, mathematical finance and applied statistics, in addition to quants and data scientists in the field of quantitative finance. Machine Learning in Finance: From Theory to Practice is divided into three parts, each part covering theory and applications. The first presents supervised learning for cross-sectional data from both a Bayesian and frequentist perspective. The more advanced material places a firm emphasis on neural networks, including deep learning, as well as Gaussian processes, with examples in investment management and derivative modeling. The second part presents supervised learning for time series data, arguably the most common data type used in finance with examples in trading, stochastic volatility and fixed income modeling. Finally, the third part presents reinforcement learning and its applications in trading, investment and wealth management. Python code examples are provided to support the readers' understanding of the methodologies and applications. The book also includes more than 80 mathematical and programming exercises, with worked solutions available to instructors. As a bridge to research in this emergent field, the final chapter presents the frontiers of machine learning in finance from a researcher's perspective, highlighting how many well-known concepts in statistical physics are likely to emerge as important methodologies for machine learning in finance.Trade Review“This book is, however, a well-structured and self-contained graduate textbook on ML applications in finance. Exercises and some applications are included at the end of each chapter and the Python code used in this book makes use of the Python Tensor Flow library. This book could also serve as a useful reference book for researchers and practitioners in quantitative finance.” (Gilles Teyssière, Mathematical Reviews, February, 2023)“Each part is introduced with background information, examples of relevant practical applications, and references to the most recent scientific literature. … The book covers all essential areas of machine learning with relevance to quantitative finance. … An additional strong advantage of this book is the clear and consistent structure of its chapters. … Overall, the book covers multiple machine learning approaches with advanced technical exposition and is therefore especially suitable as an academic reference point, especially on Reinforcement Learning.” (Antoniya Shivarova, Financial Markets and Portfolio Management, Issue 35, 2021)“This volume aims to present a broad yet technical treatment of (ML) algorithms used by financial practitioners and scholars alike. … the book fills a large void. … This encourages reproducibility as well as learning by doing, which is highly appreciated.” (Guillaume Coqueret, Quantitative Finance, October 15, 2020)Table of ContentsChapter 1. Introduction.- Chapter 2. Probabilistic Modeling.- Chapter 3. Bayesian Regression & Gaussian Processes.- Chapter 4. Feed Forward Neural Networks.- Chapter 5. Interpretability.- Chapter 6. Sequence Modeling.- Chapter 7. Probabilistic Sequence Modeling.- Chapter 8. Advanced Neural Networks.- Chapter 9. Introduction to Reinforcement learning.- Chapter 10. Applications of Reinforcement Learning.- Chapter 11. Inverse Reinforcement Learning and Imitation Learning.- Chapter 12. Frontiers of Machine Learning and Finance.

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Book SynopsisAlong the way, he tells us what various cultures knew about math and how they came to learn it, providing instructors with a wonderful way to incorporate multicultural mathematics into the middle school, high school, and college classroom.Trade ReviewSwetz has collected word problems, or story problems, used to teach mathematics around the world and throughout history, so mathematics teachers in middle and secondary schools can use them today. University students of mathematics and its history might also find them useful as well as entertaining. Reference and Research Book News Mathematical Expeditions is a wonderful resource for any teacher who would like to use old problems in a course to help students understand the context of mathematical ideas. -- Victor J. Katz Mathematical Reviews The book is well thought-out and is recommended to readers interested in the history of mathematics. -- E. Keith Lloyd London Mathematical Society Newsletter One of my graduate students, who is majoring in mathematics, was excited when I showed her a sample of problems in the book. A month later, she asked whether I had finished my review-she wanted to borrow the book! -- Winifred A. Mallam Mathematics TeacherTable of ContentsPreface1. Word Problems: Footprints from the History of Mathematics2. Problems, Problems: A Resource for Teaching3. Ancient Babylonia (2002–1000 BCE)4. Ancient Egypt5. Ancient Greece6. Ancient China7. India8. Islam9. Medieval Europe10. Renaissance Europe11. Japanese Temple Problems12. The Ladies Diary (1704–1841)13. Nineteenth-Century Victorian Problems14. Eighteenth- and Nineteenth-Century American Problems15. Problems from the Farmer's Almanac16. Nineteenth-Century Calculus Problems17. Some Sample Problem Solution Methods18. Where to from Here? Where Do You Want to Go?AcknowledgmentsAnswers to Numbered ProblemsGlossary of Strange and Exotic Terms: Measurements, Monetary Units, and Culturally Relevant WordsBibliographyIndex

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Book SynopsisProvides an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas.Trade Review[T]his is a wonderful introduction to geometry and topology and their applications to the sciences. The book contains a unique collection of topics that might entice young readers to continue their academic careers by learning more about the world of mathematics." - Claus Ernst, Zentralblatt MATHTable of Contents Universes: An introduction to the shape of the universe Visualizing four dimensions Geometry and topology of different universes Orientability Flat manifolds Connected sums of spaces Products of spaces Geometries of surfaces Knots: Introduction to knot theory Invariants of knots and links Knot polynomials Molecules: Mirror image symmetry from different viewpoints Techniques to prove topological chirality The topology and geometry of DNA The topology of proteins Index

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Book SynopsisThis book introduces machine learning methods in finance. It presents a unified treatment of machine learning and various statistical and computational disciplines in quantitative finance, such as financial econometrics and discrete time stochastic control, with an emphasis on how theory and hypothesis tests inform the choice of algorithm for financial data modeling and decision making. With the trend towards increasing computational resources and larger datasets, machine learning has grown into an important skillset for the finance industry. This book is written for advanced graduate students and academics in financial econometrics, mathematical finance and applied statistics, in addition to quants and data scientists in the field of quantitative finance. Machine Learning in Finance: From Theory to Practice is divided into three parts, each part covering theory and applications. The first presents supervised learning for cross-sectional data from both a Bayesian and frequentist perspective. The more advanced material places a firm emphasis on neural networks, including deep learning, as well as Gaussian processes, with examples in investment management and derivative modeling. The second part presents supervised learning for time series data, arguably the most common data type used in finance with examples in trading, stochastic volatility and fixed income modeling. Finally, the third part presents reinforcement learning and its applications in trading, investment and wealth management. Python code examples are provided to support the readers' understanding of the methodologies and applications. The book also includes more than 80 mathematical and programming exercises, with worked solutions available to instructors. As a bridge to research in this emergent field, the final chapter presents the frontiers of machine learning in finance from a researcher's perspective, highlighting how many well-known concepts in statistical physics are likely to emerge as important methodologies for machine learning in finance.Trade Review“This book is, however, a well-structured and self-contained graduate textbook on ML applications in finance. Exercises and some applications are included at the end of each chapter and the Python code used in this book makes use of the Python Tensor Flow library. This book could also serve as a useful reference book for researchers and practitioners in quantitative finance.” (Gilles Teyssière, Mathematical Reviews, February, 2023)“Each part is introduced with background information, examples of relevant practical applications, and references to the most recent scientific literature. … The book covers all essential areas of machine learning with relevance to quantitative finance. … An additional strong advantage of this book is the clear and consistent structure of its chapters. … Overall, the book covers multiple machine learning approaches with advanced technical exposition and is therefore especially suitable as an academic reference point, especially on Reinforcement Learning.” (Antoniya Shivarova, Financial Markets and Portfolio Management, Issue 35, 2021)“This volume aims to present a broad yet technical treatment of (ML) algorithms used by financial practitioners and scholars alike. … the book fills a large void. … This encourages reproducibility as well as learning by doing, which is highly appreciated.” (Guillaume Coqueret, Quantitative Finance, October 15, 2020)Table of ContentsChapter 1. Introduction.- Chapter 2. Probabilistic Modeling.- Chapter 3. Bayesian Regression & Gaussian Processes.- Chapter 4. Feed Forward Neural Networks.- Chapter 5. Interpretability.- Chapter 6. Sequence Modeling.- Chapter 7. Probabilistic Sequence Modeling.- Chapter 8. Advanced Neural Networks.- Chapter 9. Introduction to Reinforcement learning.- Chapter 10. Applications of Reinforcement Learning.- Chapter 11. Inverse Reinforcement Learning and Imitation Learning.- Chapter 12. Frontiers of Machine Learning and Finance.

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Book SynopsisThis text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics. Trade Review“The presentation of the material is guided by applications so that physics and engineering students will find the text engaging and see the relevance of multivariable calculus to their work. The text contains over 500 exercises with answers and/or solutions to half provided at the back of the book, enabling students to gauge their understanding of the content as they proceed. A well-written, engaging text. Summing Up: Highly recommended. Upper-division undergraduates and professionals.” (J. T. Zerger, Choice, Vol. 56 (03), November, 2018)“This book belongs to a collection aimed at third- and fourth-year undergraduate mathematics students at North American universities. … There are more than 200 figures to help the reader to understand the explanations and about 500 problems. … I think this book can be recommended since, moreover, it is very pedagogical.” (Richard Becker, Mathematical Reviews, October, 2018)“Lax and Terrell’s sequel to their Calculus With Applications presents a first course in multivariable calculus that fits in just over 400 pages. Even instructors who use standard texts will find much of value in this refreshing first edition. The book is written with a wide range of STEM students in mind, and its exposition remains remarkably fluid without scarificing precision. Every section of each chapter ends with an excellent collection of exercises, which should be graciously welcomed by independent learners and instructors alike.” (Tushar Das, MAA Reviews, September, 2018)“The main achievement of the authors is that they essentially have simplified the teaching of the old topics to make a place for new ones. The proofs are exposited to encourage understanding, not meaningless rigor. … the presented book is a useful tool for all mathematicians (not only for students) and I find it regrettable that this book was not written when I was a student.” (Andrey Zahariev, zbMATH 1396.26002, 2018)Table of Contents1. Vectors and matrices.- 2. Functions.- 3. Differentiation.- 4. More about differentiation.- 5. Applications to motion.- 6. Integration.- 7. Line and surface integrals.- 8. Divergence and Stokes’ Theorems and conservation laws.- 9. Partial differential equations.- Answers to selected problems.- Index.

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Book SynopsisTechnical Analysis of Stock Trends helps investors make smart, profitable trading decisions by providing proven long- and short-term stock trend analysis. It gets right to the heart of effective technical trading concepts, explaining technical theory such as The Dow Theory, reversal patterns, consolidation formations, trends and channels, technical analysis of commodity charts, and advances in investment technology. It also includes a comprehensive guide to trading tactics from long and short goals, stock selection, charting, low and high risk, trend recognition tools, balancing and diversifying the stock portfolio, application of capital, and risk management. This updated new edition includes patterns and modifiable charts that are tighter and more illustrative. Expanded material is also included on Pragmatic Portfolio Theory as a more elegant alternative to Modern Portfolio Theory; and a newer, simpler, and more powerful alternative to Dow Theory is presented.Table of ContentsPart I: Technical theory 1. The technical approach to trading and investing 2. Charts 3. The Dow Theory 4. The Dow Theory’s defects 5. Replacing Dow Theory with John Magee’s Basing points Procedure 6. Important Reversal Patterns 7. Important Reversal Patterns: continued 8. Important Reversal Patterns: the Triangles 9. More important Reversal Patterns 10. Other Reversal phenomena 11. Consolidation Formations 12. Gaps 13. Support and Resistance 14. Trendlines and Channels 15. Major Trendlines 16. Technical analysis of commodity charts 17. A summary and concluding comments Part II: Trading tactics 18. The tactical problem 19. The all-important details 20. The kind of stocks we want: the speculator’s viewpoint 21. Selection of stocks to chart 22. Selection of stocks to chart: continued 23. Choosing and managing high-risk stocks: tulip stocks, Internet sector, and speculative frenzies 24. The probable moves of your stocks 25. Two touchy questions 26. Round lots or odd lots? 27. Stop orders 28. What is a Bottom and what is a Top? 29. Trendlines in action 30. Use of Support and Resistance 31. Not all in one basket 32. Measuring implications in technical chart patterns 33. Tactical review of chart action 34. A quick summation of tactical methods 35. Effect of technical trading on market action 36. Automated trendline: the Moving Average 37. The same old patterns 38. Balanced and diversified 39. Trial and error 40. How much capital to use in trading 41. Application of capital in practice 42. Portfolio risk management 43. Stick to your guns

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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

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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.

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

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Book Synopsis

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

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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

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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

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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

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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

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