Download or read book Elementary Calculus written by H. Jerome Keisler and published by . This book was released on 1976 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinitesimal Calculus written by James M. Henle and published by Courier Corporation. This book was released on 2014-01-15 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.
Download or read book Calculus Set Free written by and published by Oxford University Press. This book was released on 2021-11-30 with total page 1617 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods. The procedures used throughout make many of the calculations simpler and the concepts clearer for undergraduate students, heightening success and easing a significant burden of entry into STEM disciplines. This text features a student-friendly exposition with ample marginal notes, examples, illustrations, and more. The exercises include a wide range of difficulty levels, stretching from very simple rapid response questions to the occasional exercise meant to test knowledge. While some exercises require the use of technology to work through, none are dependent on any specific software. The answers to odd-numbered exercises in the back of the book include both simplified and non-simplified answers, hints, or alternative answers. Throughout the text, notes in the margins include comments meant to supplement understanding, sometimes including line-by-line commentary for worked examples. Without sacrificing academic rigor, Calculus Set Free offers an engaging style that helps students to solidify their understanding on difficult theoretical calculus.
Download or read book A Primer of Infinitesimal Analysis written by John L. Bell and published by Cambridge University Press. This book was released on 2008-04-07 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Download or read book Foundations of Infinitesimal Calculus written by H. Jerome Keisler and published by Prindle Weber & Schmidt. This book was released on 1976-01-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elementary Calculus written by H. Jerome Keisler and published by Orange Groove Books. This book was released on 2009-09-01 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinitesimal written by Amir Alexander and published by Simon and Schuster. This book was released on 2014-07-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.
Download or read book Stochastic Calculus with Infinitesimals written by Frederik S. Herzberg and published by Springer. This book was released on 2012-11-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Download or read book Infinite Powers written by Steven Strogatz and published by Mariner Books. This book was released on 2019 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Aristotle to today's million-dollar reward that awaits whoever cracks Reimann's hypothesis. Filled with idiosyncratic characters from Pythagoras to Euler, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilization, including science, politics, ethics, philosophy, and much besides.
Download or read book Real Analysis Through Modern Infinitesimals written by Nader Vakil and published by Cambridge University Press. This book was released on 2011-02-17 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
Download or read book The Origins of Infinitesimal Calculus written by Margaret E. Baron and published by Elsevier. This book was released on 2014-05-09 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.
Download or read book The Continuous the Discrete and the Infinitesimal in Philosophy and Mathematics written by John L. Bell and published by Springer Nature. This book was released on 2019-09-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Download or read book Infinitesimal Differences written by Ursula Goldenbaum and published by Walter de Gruyter. This book was released on 2008-11-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes over status of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its procedures seemed to lack an adequate metaphysical or methodological justification. The topic is also of philosophical interest, because Leibniz freely employed the language of infinitesimal quantities in the foundations of his dynamics and theory of forces. Thus, philosophical disputes over the Leibnizian science of bodies naturally involve questions about the nature of infinitesimals. The volume also includes newly discovered Leibnizian marginalia in the mathematical writings of Hobbes.
Download or read book Yet Another Calculus Text written by Dan Sloughter and published by Orange Grove Texts Plus. This book was released on 2009-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Elementary Course of Infinitesimal Calculus written by Sir Horace Lamb and published by . This book was released on 1924 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non standard Analysis written by Abraham Robinson and published by Princeton University Press. This book was released on 2016-08-11 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Download or read book The Arithmetic of Infinitesimals written by John Wallis and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Wallis (1616-1703) was the most influential English mathematician prior to Newton. He published his most famous work, Arithmetica Infinitorum, in Latin in 1656. This book studied the quadrature of curves and systematised the analysis of Descartes and Cavelieri. Upon publication, this text immediately became the standard book on the subject and was frequently referred to by subsequent writers. This will be the first English translation of this text ever to be published.
