## Similar

New York Times Bestseller

“Not so different in spirit from the way public intellectuals like John Kenneth Galbraith once shaped discussions of economic policy and public figures like Walter Cronkite helped sway opinion on the Vietnam War…could turn out to be one of the more momentous books of the decade.”

—New York Times Book Review

"Nate Silver's The Signal and the Noise is The Soul of a New Machine for the 21st century."

—Rachel Maddow, author of Drift

"A serious treatise about the craft of prediction—without academic mathematics—cheerily aimed at lay readers. Silver's coverage is polymathic, ranging from poker and earthquakes to climate change and terrorism."

—New York Review of Books

Nate Silver built an innovative system for predicting baseball performance, predicted the 2008 election within a hair’s breadth, and became a national sensation as a blogger—all by the time he was thirty. He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com.

Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the “prediction paradox”: The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.

In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good—or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary—and dangerous—science.

Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

With everything from the health of the global economy to our ability to fight terrorism dependent on the quality of our predictions, Nate Silver’s insights are an essential read.

From the Trade Paperback edition.

These may not sound like typical questions for an economist to ask. But Steven D. Levitt is not a typical economist. He is a much-heralded scholar who studies the riddles of everyday life—from cheating and crime to sports and child-rearing—and whose conclusions turn conventional wisdom on its head.

Freakonomics is a groundbreaking collaboration between Levitt and Stephen J. Dubner, an award-winning author and journalist. They usually begin with a mountain of data and a simple question. Some of these questions concern life-and-death issues; others have an admittedly freakish quality. Thus the new field of study contained in this book: Freakonomics.

Through forceful storytelling and wry insight, Levitt and Dubner show that economics is, at root, the study of incentives—how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they explore the hidden side of . . . well, everything. The inner workings of a crack gang. The truth about real-estate agents. The myths of campaign finance. The telltale marks of a cheating schoolteacher. The secrets of the Ku Klux Klan.

What unites all these stories is a belief that the modern world, despite a great deal of complexity and downright deceit, is not impenetrable, is not unknowable, and—if the right questions are asked—is even more intriguing than we think. All it takes is a new way of looking.

Freakonomics establishes this unconventional premise: If morality represents how we would like the world to work, then economics represents how it actually does work. It is true that readers of this book will be armed with enough riddles and stories to last a thousand cocktail parties. But Freakonomics can provide more than that. It will literally redefine the way we view the modern world.

Bonus material added to the revised and expanded 2006 edition

The original New York Times Magazine article about Steven D. Levitt by Stephen J. Dubner, which led to the creation of this book.Seven “Freakonomics” columns written for the New York Times Magazine, published between August 2005 and April 2006.Selected entries from the Freakonomics blog, posted between April 2005 and May 2006 at http://www.freakonomics.com/blog/.The Essentials For Dummies Series

Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Slay the calculus monster with this user-friendly guide

Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be.

Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win.

Includes foundations in algebra, trigonometry, and pre-calculus concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can't get away withStop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.

A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.

In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.

Fortunately for you, there's Schaum's.

More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

1,370 fully solved problems Complete review of all course fundamentals Clear, concise explanations of all Advanced Calculus conceptsFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!

Topics include: Numbers; Sequences; Functions, Limits, and Continuity; Derivatives; Integrals; Partial Derivatives; Vectors; Applications of Partial Derivatives; Multiple Integrals; Line Integrals, Surface Integrals, and Integral Theorems; Infinite Series; Improper Integrals; Fourier Series; Fourier Integrals; Gamma and Beta Functions; and Functions of a Complex Variable

Schaum's Outlines--Problem Solved.

A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. Supplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book.

1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go.

Gives you a chance to practice and reinforce the skills you learn in your calculus course Helps you refine your understanding of calculus Practice problems with answer explanations that detail every step of every problemThe practice problems in 1001 Calculus Practice Problems For Dummies range in areas of difficulty and style, providing you with the practice help you need to score high at exam time.

An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and theSecond Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB® An appendix that contains proofs of various theorems and other material

The book is divided into three parts and begins with the basics: models, probability, Bayes’ rule, and the R programming language. The discussion then moves to the fundamentals applied to inferring a binomial probability, before concluding with chapters on the generalized linear model. Topics include metric-predicted variable on one or two groups; metric-predicted variable with one metric predictor; metric-predicted variable with multiple metric predictors; metric-predicted variable with one nominal predictor; and metric-predicted variable with multiple nominal predictors. The exercises found in the text have explicit purposes and guidelines for accomplishment.

This book is intended for first-year graduate students or advanced undergraduates in statistics, data analysis, psychology, cognitive science, social sciences, clinical sciences, and consumer sciences in business.

Accessible, including the basics of essential concepts of probability and random samplingExamples with R programming language and JAGS softwareComprehensive coverage of all scenarios addressed by non-Bayesian textbooks: t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis)Coverage of experiment planningR and JAGS computer programming code on websiteExercises have explicit purposes and guidelines for accomplishmentProvides step-by-step instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs

"This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."

—Mathematical Reviews of the American Mathematical Society

An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems.

This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications.

Additional features of the Third Edition include:

A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy modelsRevised proofs and a discussion on the relevance and solution of the dual problem

A section on developing an example in Data Envelopment Analysis

An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games

Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.

The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.

In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.

The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several variables: the space of several variables and continuous functions, differentiation, multiple integrals, and line and surface integrals, concluding with a selection of related topics. Complete solutions to the problems appear at the end of the text.

"The main object of this book is to dispel the fear of mathematics," declares author W. W. Sawyer, adding that "Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject." Now retired, Sawyer won international renown for his innovative teaching methods, which he used at colleges in England and Scotland as well as Africa, New Zealand, and North America. His insights into the pleasures and practicalities of mathematics will appeal to readers of all backgrounds.

Want to "know it ALL" when it comes to calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to calculus or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves as your own private tutor--without the expense! His clear, friendly guidance helps you tackle the concepts and problems that confuse you the most and work through them at your own pace.

Train your brain with ease! Calculus Know-It-ALL features:

Checkpoints to help you track your knowledge and skill level Problem/solution pairs and chapter-ending quizzes to reinforce learning Fully explained answers to all practice exercises A multiple-choice exam to prepare you for standardized tests "Extra Credit" and "Challenge" problems to stretch your mindStan's expert guidance gives you the know-how to:

Understand mappings, relations, and functions Calculate limits and determine continuity Differentiate and integrate functions Analyze graphs using first and second derivatives Define and evaluate inverse functions Use specialized integration techniques Determine arc lengths, surface areas, and solid volumes Work with multivariable functions Take college entrance examinations with confidence And much more!But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum theory; the quantum-mechanical substitute for phase space; quantum dynamics and the Schrödinger equation; the canonical "quantization" of a classical system; some elementary examples and original discoveries by Schrödinger and Heisenberg; generalized coordinates; linear systems and the quantization of the electromagnetic field; and quantum-statistical mechanics.

The final section on group theory and quantum mechanics of the atom explores basic notions in the theory of group representations; perturbations and the group theoretical classification of eigenvalues; spherical symmetry and spin; and the n-electron atom and the Pauli exclusion principle.

The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "precalculus" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables.

Numerous problems and answers, and a newly added section of "Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.

The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Review from the first edition:

"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."

—MATHEMATICAL REVIEWS

For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.

And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

Tensor Calculus contains eight chapters. The first four deal with the basic concepts of tensors, Riemannian spaces, Riemannian curvature, and spaces of constant curvature. The next three chapters are concerned with applications to classical dynamics, hydrodynamics, elasticity, electromagnetic radiation, and the theorems of Stokes and Green. In the final chapter, an introduction is given to non-Riemannian spaces including such subjects as affine, Weyl, and projective spaces. There are two appendixes which discuss the reduction of a quadratic form and multiple integration. At the conclusion of each chapter a summary of the most important formulas and a set of exercises are given. More exercises are scattered throughout the text. The special and general theory of relativity is briefly discussed where applicable.

Those familiar with mathematics texts will note the fine illustrations throughout and large number of problems offered at the chapter ends. An answer section is provided. Students weary of plodding mathematical prose will find Professor Flanigan's style as refreshing and stimulating as his approach.

The first part of this book covers simple differential calculus, with constants, variables, functions, increments, derivatives, differentiation, logarithms, curvature of curves, and similar topics. The second part covers fundamental ideas of integration (inspection, substitution, transformation, reduction) areas and volumes, mean value, successive and partial integration, double and triple integration. In all cases the author stresses practical aspects rather than theoretical, and builds upon such situations as might occur.

A 50-page section illustrates the application of calculus to specific problems of civil and nautical engineering, electricity, stress and strain, elasticity, industrial engineering, and similar fields. 756 questions answered. 566 problems to measure your knowledge and improvement; answers. 36 pages of useful constants, formulae for ready reference. Index.

Math textbooks can be as baffling as the subject they're teaching. Not anymore. The best-selling author of The Complete Idiot's Guide® to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams.

--Includes 1,000 problems with comprehensive solutions

--Annotated notes throughout the text clarify what's being asked in each problem and fill in missing steps

--Kelley is a former award-winning calculus teacher

The principal aim of analysis of tensors is to investigate those relations which remain valid when we change from one coordinate system to another. This book on Tensors requires only a knowledge of elementary calculus, differential equations and classical mechanics as pre-requisites. It provides the readers with all the information about the tensors along with the derivation of all the tensorial relations/equations in a simple manner. The book also deals in detail with topics of importance to the study of special and general relativity and the geometry of differentiable manifolds with a crystal clear exposition. The concepts dealt within the book are well supported by a number of solved examples. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book. The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book.

This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are engaged in research in General Theory of Relativity and Differential Geometry.

Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, semi-Markov processes, and queuing processes. Each chapter opens with an illustrative case study, and comprehensive presentations include formulation of models, determination of parameters, analysis, and interpretation of results. Programming language–independent algorithms appear for all simulation and numerical procedures.

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you:

Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applicationsFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved.

- Teaches general principles that can be applied to a wide variety of problems.

- Avoids the mindless and excessive routine computations that characterize conventional textbooks.

- Treats algebra as a logically coherent discipline, not as a disjointed collection of techniques.

- Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.

- Omits digressions, excessive formalities, and repetitive exercises.

- Covers all the algebra needed to take a calculus course.

- Includes solutions to all problems.

Contents

1. A Few Basics

2. Exponents

3. Polynomials

4. Factoring

5. Linear & Quadratic Equations

6. Inequalities & Absolute Values

7. Coordinates in a Plane

8. Functions & Graphs

9. Straight Lines

10. Circles

11. Parabolas

12. Types of Functions

13. Logarithms

14. Dividing Polynomials

15. Systems of Linear Equations

16. Geometric Progressions & Series

17. Arithmetic Progressions

18. Permutation & Combinations

19. The Binomial Theorem

20. Mathematical Induction

21. Solutions

Since many abstractions and generalizations originate with the real line, the author has made it the unifying theme of the text, constructing the real number system from the point of view of a Cauchy sequence (a step which Dr. Sprecher feels is essential to learn what the real number system is).

The material covered in Elements of Real Analysis should be accessible to those who have completed a course in calculus. To help give students a sound footing, Part One of the text reviews the fundamental concepts of sets and functions and the rational numbers. Part Two explores the real line in terms of the real number system, sequences and series of number and the structure of point sets. Part Three examines the functions of a real variable in terms of continuity, differentiability, spaces of continuous functions, measure and integration, and the Fourier series.

An especially valuable feature of the book is the exercises which follow each section. There are over five hundred, ranging from the simple to the highly difficult, each focusing on a concept previously introduced.

The first five chapters consist of a systematic development of many of the important properties of the real number system, plus detailed treatment of such concepts as mappings, sequences, limits, and continuity. The sixth and final chapter discusses metric spaces and generalizes many of the earlier concepts and results involving arbitrary metric spaces.

An index of axioms and key theorems appears at the end of the book, and more than 300 problems amplify and supplement the material within the text. Geared toward students who have taken several semesters of basic calculus, this volume is an ideal prerequisite for mathematics majors preparing for a two-semester course in advanced calculus.

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community."

(European Mathematical Society)

"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."

(Denis Bonheure, Bulletin of the Belgian Society)

This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.

- Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis.

This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.

Though the Japanese abacus may appear mysterious or even primitive, this intriguing tool is capable of amazing speed and accuracy. it is still widely used throughout the shop and markets of Asia and its popularity shows no sign of decline.

This volume is designed for the student desiring a greater understanding of the abacus and its calculative functions. The text provides thorough explanations of the advanced operations involving negative numbers, decimals, different units of measurement, and square roots. Diagrams illustrate bead manipulation, and numerous exercises provide ample practice.

Concise and easy-to-follow, this book will improve your abacus skills and help you perform calculations with greater efficiency and precision.

As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of the essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics.

Fast Fourier Transform - Algorithms and Applications provides a thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.

Fast Fourier Transform - Algorithms and Applications is designed for senior undergraduate and graduate students, faculty, engineers, and scientists in the field, and self-learners to understand FFTs and directly apply them to their fields, efficiently. It is designed to be both a text and a reference. Thus examples, projects and problems all tied with MATLAB, are provided for grasping the concepts concretely. It also includes references to books and review papers and lists of applications, hardware/software, and useful websites. By including many figures, tables, bock diagrams and graphs, this book helps the reader understand the concepts of fast algorithms readily and intuitively. It provides new MATLAB functions and MATLAB source codes. The material in Fast Fourier Transform - Algorithms and Applications is presented without assuming any prior knowledge of FFT. This book is for any professional who wants to have a basic understanding of the latest developments in and applications of FFT. It provides a good reference for any engineer planning to work in this field, either in basic implementation or in research and development.

The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics.

Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.

-Review of limits, continuity, differentiability.

Mean Value Theorem, Taylor Theorem, Maxima and Minima.

Riemann integrals, Fundamental theorem of Calculus, Improper integrals, application to area,

volume.

Convergence of sequences and series, power series.

Partial Derivatives, gradient and directional derivatives, chain rule, maxima and minima,

Lagrange multipliers.

Double and triple integration, Jacobians and change of variables formula.

Parametrization of curves and surfaces, vector _elds, line and surface integrals. Divergence and

curl, theorems of Green, Gauss, Stokes.

Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.

"In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology...the book also contains many good illustrations of fractals (including 16 color plates)."

Mathematics Teaching

"The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples."

Christoph Bandt, Mathematical Reviews

"...not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. Especially, for the last students the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out."

H.Haase, Zentralblatt

About the second edition: Changes throughout the text, taking into account developments in the subject matter since 1990; Major changes in chapter 6. Since 1990 it has become clear that there are two notions of dimension that play complementary roles, so the emphasis on Hausdorff dimension will be replaced by the two: Hausdorff dimension and packing dimension. 6.1 will remain, but a new section on packing dimension will follow it, then the old sections 6.2--6.4 will be re-written to show both types of dimension; Substantial change in chapter 7: new examples along with recent developments; Sections rewritten to be made clearer and more focused.

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The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions.

Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.”

This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.