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 with
Stop 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.
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 you1,370 fully solved problems Complete review of all course fundamentals Clear, concise explanations of all Advanced Calculus concepts
Fully 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.
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 problem
The 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
This P.S. edition features an extra 16 pages of insights into the book, including author interviews, recommended reading, and more.
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.
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 accomplishment
Provides step-by-step instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs
The canopy voyagers are young–just college students when they start their quest–and they share a passion for these trees, persevering in spite of sometimes crushing personal obstacles and failings. They take big risks, they ignore common wisdom (such as the notion that there’s nothing left to discover in North America), and they even make love in hammocks stretched between branches three hundred feet in the air.
The deep redwood canopy is a vertical Eden filled with mosses, lichens, spotted salamanders, hanging gardens of ferns, and thickets of huckleberry bushes, all growing out of massive trunk systems that have fused and formed flying buttresses, sometimes carved into blackened chambers, hollowed out by fire, called “fire caves.” Thick layers of soil sitting on limbs harbor animal and plant life that is unknown to science. Humans move through the deep canopy suspended on ropes, far out of sight of the ground, knowing that the price of a small mistake can be a plunge to one’s death.
Preston’s account of this amazing world, by turns terrifying, moving, and fascinating, is an adventure story told in novelistic detail by a master of nonfiction narrative. The author shares his protagonists’ passion for tall trees, and he mastered the techniques of tall-tree climbing to tell the story in The Wild Trees–the story of the fate of the world’s most splendid forests and of the imperiled biosphere itself.
From the Hardcover edition.
"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 models
Revised 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 world's population is exploding, wild species are vanishing, our environment is degrading, and the costs of resources from oil to water are going nowhere but up. So what kind of world are we leaving for our children and grandchildren? Geoscientist and Guggenheim fellow Laurence Smith draws on the latest global modeling research to construct a sweeping thought experiment on what our world will be like in 2050. The result is both good news and bad: Eight nations of the Arctic Rim (including the United States) will become increasingly prosperous, powerful, and politically stable, while those closer to the equator will face water shortages, aging populations, and crowded megacities sapped by the rising costs of energy and coastal flooding.
The World in 2050 combines the lessons of geography and history with state-of-the-art model projections and analytical data-everything from climate dynamics and resource stocks to age distributions and economic growth projections. But Smith offers more than a compendium of statistics and studies- he spent fifteen months traveling the Arctic Rim, collecting stories and insights that resonate throughout the book. It is an approach much like Jared Diamond took in Guns, Germs, and Steel and Collapse, a work of geoscientific investigation rich in the appreciation of human diversity.
Packed with stunning photographs, original maps, and informative tables, this is the most authoritative, balanced, and compelling account available of the world of challenges and opportunities that we will leave for our children.
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 mind
Stan'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!
Interweaving physics, astronomy, chemistry, geology, and biology, this sweeping account tells Earth’s complete story, from the synthesis of chemical elements in stars, to the formation of the Solar System, to the evolution of a habitable climate on Earth, to the origin of life and humankind. The book also addresses the search for other habitable worlds in the Milky Way and contemplates whether Earth will remain habitable as our influence on global climate grows. It concludes by considering the ways in which humankind can sustain Earth’s habitability and perhaps even participate in further planetary evolution.
Like no other book, How to Build a Habitable Planet provides an understanding of Earth in its broadest context, as well as a greater appreciation of its possibly rare ability to sustain life over geologic time.
Leading schools that have ordered, recommended for reading, or adopted this book for course use:Arizona State University Brooklyn College CUNY Columbia University Cornell University ETH Zurich Georgia Institute of Technology Harvard University Johns Hopkins University Luther College Northwestern University Ohio State University Oxford Brookes University Pan American University Rutgers University State University of New York at Binghamton Texas A&M University Trinity College Dublin University of Bristol University of California-Los Angeles University of Cambridge University Of Chicago University of Colorado at Boulder University of Glasgow University of Leicester University of Maine, Farmington University of Michigan University of North Carolina at Chapel Hill University of North Georgia University of Nottingham University of Oregon University of Oxford University of Portsmouth University of Southampton University of Ulster University of Victoria University of Wyoming Western Kentucky University Yale University
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."
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.
Why do people believe bunk? And what causes them to embrace such pseudoscientific beliefs and practices? Noted skeptic Massimo Pigliucci sets out to separate the fact from the fantasy in this entertaining exploration of the nature of science, the borderlands of fringe science, and—borrowing a famous phrase from philosopher Jeremy Bentham—the nonsense on stilts. Presenting case studies on a number of controversial topics, Pigliucci cuts through the ambiguity surrounding science to look more closely at how science is conducted, how it is disseminated, how it is interpreted, and what it means to our society. The result is in many ways a “taxonomy of bunk” that explores the intersection of science and culture at large.
No one—not the public intellectuals in the culture wars between defenders and detractors of science nor the believers of pseudoscience themselves—is spared Pigliucci’s incisive analysis. In the end, Nonsense on Stilts is a timely reminder of the need to maintain a line between expertise and assumption. Broad in scope and implication, it is also ultimately a captivating guide for the intelligent citizen who wishes to make up her own mind while navigating the perilous debates that will affect the future of our planet.
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.
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.
Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
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.
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.
In this volume, the most important contemporary questions on lightning are addressed and analyzed under many experimental and theoretical aspects. Lightning detection techniques using ground-based and space-borne methods are described, along with network engineering and statistical analysis.
Contributions detail research on atmospheric electricity, cloud physics, lightning physics, modeling of electrical storms and middle atmospheric events. Special phenomena such as triggered lightning and sprite observations are examined. Lightning-induced nitrogen oxides and their effects on atmospheric chemistry and climate are discussed.
Each topic is presented by international experts in the field. Topics include:
* air chemistry
* convective storms
* infrasound from lightning
* lightning and climate change
* lightning and precipitation
* lightning and radiation
* lightning and supercells
* lightning and thunderstorms
* lightning detection
* lightning from space
* lighting protection
* lightning return strokes
* observations and interpretations
* spatial distribution and frequency
* triggered lightning
* weather extremes
The fifth edition of this successful undergraduate textbook has been extensively modernized and extended in the parts dealing with the Milky Way, extragalactic astronomy and cosmology as well as with extrasolar planets and the solar system (as a consequence of recent results from satellite missions and the new definition by the International Astronomical Union of planets, dwarf planets and small solar-system bodies). Furthermore a new chapter on astrobiology has been added.
Long considered a standard text for physical science majors, Fundamental Astronomy is also an excellent reference and entrée for dedicated amateur astronomers.
*Review of GPR theory and applications by leaders in the field
*Up-to-date information and references
*Effective handbook and primary research reference for both experienced practitioners and newcomers
In the summer of 1997, Charles Moore set sail from Honolulu with the sole intention of returning home after competing in a trans-Pacific race. To get to California, he and his crew took a shortcut through the seldom-traversed North Pacific Subtropical Gyre, a vast "oceanic desert" where winds are slack and sailing ships languish. There, Moore realized his catamaran was surrounded by a "plastic soup." He had stumbled upon the largest garbage dump on the planet-a spiral nebula where plastic outweighed zooplankton, the ocean's food base, by a factor of six to one.
In Plastic Ocean, Moore recounts his ominous findings and unveils the secret life and hidden properties of plastics. From milk jugs to polymer molecules small enough to penetrate human skin or be unknowingly inhaled, plastic is now suspected of contributing to a host of ailments including infertility, autism, thyroid dysfunction, and some cancers. A call to action as urgent as Rachel Carson's seminal Silent Spring, Moore's sobering revelations will be embraced by activists, concerned parents, and seafaring enthusiasts concerned about the deadly impact and implications of this man made blight.
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.
- 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.
1. A Few Basics
5. Linear & Quadratic Equations
6. Inequalities & Absolute Values
7. Coordinates in a Plane
8. Functions & Graphs
9. Straight Lines
12. Types of Functions
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
Much has been written about global warming, but the crucial relationship between people and ice has received little focus—until now. As one of the world’s leading experts on climate change, Henry Pollack provides an accessible, comprehensive survey of ice as a force of nature, and the potential consequences as we face the possibility of a world without ice.
A World Without Ice traces the effect of mountain glaciers on supplies of drinking water and agricultural irrigation, as well as the current results of melting permafrost and shrinking Arctic sea ice—a situation that has degraded the habitat of numerous animals and sparked an international race for seabed oil and minerals. Catastrophic possibilities loom, including rising sea levels and subsequent flooding of lowlying regions worldwide, and the ultimate displacement of millions of coastal residents. A World Without Ice answers our most urgent questions about this pending crisis, laying out the necessary steps for managing the unavoidable and avoiding the unmanageable.
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 applications
Fully 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.
Drawing on her broad travels across the continent, in Antarctica Gabrielle Walker weaves all the significant threads of life on the vast ice sheet into an intricate tapestry, illuminating what it really feels like to be there and why it draws so many different kinds of people. With her we witness cutting-edge science experiments, visit the South Pole, lodge with American, Italian, and French researchers, drive snowdozers, drill ice cores, and listen for the message Antarctica is sending us about our future in an age of global warming.
This is a thrilling trip to the farthest reaches of earth by one of the best science writers working today.
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.
At last, many unanswered questions about the earth’s creation can be resolved with confidence. For example, how long did it take? Where did it take place? What about evolution, fossils, dinosaurs and cave men? Well-supported answers are here.
For those who have been challenged to explain the earth’s creation from an LDS viewpoint, this book will be helpful and enlightening. And for those who enjoy contemplating both the discoveries of science and the revelations of God, this book will be extremely stimulating and thought-provoking.
Readers have commented:
Dan from Canada: “This book has enlightened my mind and given me the wonderful opportunity to see the intermeshing between science and our religion.”
Paul from Texas: “Well-supported viewpoint and thought-provoking reading.... I appreciate Brother Skousen’s heavy usage of scriptural references and quotes from trustworthy Church leaders.”
Kristy from Utah: “Answered a lot of questions I had from my geology classes and gave me a deeper appreciation for this awesome planet we live on and the creator of it.”
Kelly from California: “This book explained so much about issues that had previously confused or bothered me.”
Jerome from Georgia: “Life altering, made me a better person.... If you really want to understand the ‘Big Picture’ then this book is a must read.”
Dave from Washington: “One unexpected blessing received from reading this book was an enhanced Temple worship experience.”
Ed from Iowa: “If you are LDS, this will open your eyes to things that are incredible and you will not look at the world we live in in the same way again.”
Devon: “Scholarly material well presented for the layman.”
This eBook includes the original index, illustrations, footnotes, table of contents and page numbering from the printed format.
-Review of limits, continuity, differentiability.
Mean Value Theorem, Taylor Theorem, Maxima and Minima.
Riemann integrals, Fundamental theorem of Calculus, Improper integrals, application to area,
Convergence of sequences and series, power series.
Partial Derivatives, gradient and directional derivatives, chain rule, maxima and minima,
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.