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Author : Donald W. Hight
Publisher : Courier Corporation
Page : 164 pages
File Size : 40,8 Mb
Release : 2012-07-17
Category : Mathematics
ISBN : 9780486153124
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.
Author : Richard A. Silverman
Publisher : M.E. Sharpe
Page : 144 pages
File Size : 51,7 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:49015000675471
Author : Alan F. Beardon
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206972
Intended as an undergraduate text on real analysis, this book includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a novel approach to the subject matter, which has not previously appeared in book form. The author defines the term limit once only, and all of the subsequent limiting processes are seen to be special cases of this one definition. Accordingly, the subject matter attains a unity and coherence that is not to be found in the traditional approach. Students will be able to fully appreciate and understand the common source of the topics they are studying while also realising that they are "variations on a theme", rather than essentially different topics, and therefore, will gain a better understanding of the subject.
Author : Noson S. Yanofsky
Publisher : MIT Press
Page : 419 pages
File Size : 50,9 Mb
Release : 2016-11-04
Category : Science
ISBN : 9780262529846
This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Author : D. H. Meadows
Publisher : Unknown
Page : 205 pages
File Size : 45,6 Mb
Release : 1974
Category : Electronic
ISBN : 0330241699
Author : Gregory Hartman
Publisher : Unknown
Page : 0 pages
File Size : 47,5 Mb
Release : 2015
Category : Calculus
ISBN : 1514225158
APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).
Author : David M. Bressoud
Publisher : Princeton University Press
Page : 242 pages
File Size : 44,5 Mb
Release : 2021-05-04
Category : Mathematics
ISBN : 9780691218786
Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
Author : Matthew Boelkins
Publisher : Createspace Independent Publishing Platform
Page : 560 pages
File Size : 48,8 Mb
Release : 2018-08-13
Category : Electronic
ISBN : 1724458329
Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.
Author : Shyam Wuppuluri,Giancarlo Ghirardi
Publisher : Springer
Page : 530 pages
File Size : 47,7 Mb
Release : 2016-12-01
Category : Science
ISBN : 9783319444185
In this compendium of essays, some of the world’s leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader. Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, yet holistic, independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of space and time, computer scientists theoretically and practically try to optimize the space-time complexities in storing and retrieving data/information. The list is never-ending. Linguists, logicians, artists, evolutionary biologists, geographers etc., all are trying to weave a web of understanding around the same duo. However, our endeavour into a world of such endless imagination is restrained by intellectual dilemmas such as: Can humans comprehend everything? Are there any limits? Can finite thought fathom infinity? We have sought far and wide among the best minds to furnish articles that provide an overview of the above topics. We hope that, through this journey, a symphony of patterns and tapestry of intuitions will emerge, providing the reader with insights into the questions: What is Space? What is Time? Chapter [15] of this book is available open access under a CC BY 4.0 license.
Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 41,5 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author : Liane Carlson
Publisher : Columbia University Press
Page : 232 pages
File Size : 49,8 Mb
Release : 2019-07-30
Category : Religion
ISBN : 9780231548977
Central to the historicizing work of recent decades has been the concept of contingency, the realm of chance, change, and the unnecessary. Following Nietzsche and Foucault, genealogists have deployed contingency to show that all institutions and ideas could have been otherwise as a critique of the status quo. Yet scholars have spent very little time considering the genealogy of contingency itself—or what its history means for its role in politics. In Contingency and the Limits of History, Liane Carlson historicizes contingency by tying it to its theological and etymological roots in “touch,” contending that much of its critical, disruptive power is specific to our current historical moment. She returns to an older definition of contingency found in Christian theology that understands it as the lot of mortal creatures, who suffer, feel, bleed, and change, in contrast to a necessary, unchanging, impassible God. Far from dying out, Carlson reveals, this theological past persists in continental philosophy, where thinkers such as Novalis, Schelling, Merleau-Ponty, and Serres have imagined contingency as a type of radical destabilization brought about by the body’s collision with a changing world. Through studies of sickness, loneliness, violation, and love, she shows that different experiences of contingency can lead to dramatically dissimilar ethical and political projects. A strikingly original reconsideration of one of continental philosophy and critical theory’s most cherished concepts, this book reveals the limits of historicist accounts.
Author : Michelle Aicken,Stephen J. Page,Chris Ryan
Publisher : Routledge
Page : 386 pages
File Size : 52,7 Mb
Release : 2006-08-11
Category : Business & Economics
ISBN : 9781136360275
The concept of margins and limits is often referred to within the tourism academic literature and includes subjects as diverse as carrying capacities, peripheral economies, technological advancement, adventure tourism, dark tourism and socially marginalized communities. After identifying a number of ways in which ‘limits’ might be defined Taking Tourism to the Limits explores concepts and challenges facing contemporary tourism in five main sections, namely in tourism planning and management, nature based tourism, dark tourism, adventure and sport tourism and the accommodation industry. Drawing upon case studies, current research and conceptualizations these different facets of the ‘limits’ are each introduced by the editors with commentaries that seek to identify themes and current practice and thinking in the respective domains. The picture that emerges is of an industry that reinvents itself in response to changing market parameters even while core issues of stakeholder equities and political processes remain problematic. International in scale, the book links with its companion piece Indigenous Tourism – the commodification and management of culture (also published by Elsevier) as an outcome of the very highly successful conference, Taking Tourism to the Limits hosted by the University of Waikato’ Department of Tourism Management in 2003.
Author : Eugenia Cheng
Publisher : Profile Books
Page : 204 pages
File Size : 50,6 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9781782830818
SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Author : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
Page : 610 pages
File Size : 55,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847916
"Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.
Author : William Leiss
Publisher : McGill-Queen's Press - MQUP
Page : 188 pages
File Size : 45,8 Mb
Release : 1988
Category : Business & Economics
ISBN : 0773506888
At a time when the supply of resources is a problem, William Leiss analyses demand and consumption. Why do we need so much? Does the ability to choose from such a wide range of commodities give us more satisfaction? Why do we accept being pushed into buying products about which we know little because they promise to give us a particular characteristic - freshness, happiness, sex appeal?