Download or read book Cauchy s Calcul Infinit simal written by Dennis M. Cates and published by Springer. This book was released on 2019-04-03 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a complete English translation of Augustin-Louis Cauchy's historic 1823 text (his first devoted to calculus), Résumé des leçons sur le calcul infinitésimal, "Summary of Lectures on the Infinitesimal Calculus," originally written to benefit his École Polytechnique students in Paris. Within this single text, Cauchy succinctly lays out and rigorously develops all of the topics one encounters in an introductory study of the calculus, from his classic definition of the limit to his detailed analysis of the convergence properties of infinite series. In between, the reader will find a full treatment of differential and integral calculus, including the main theorems of calculus and detailed methods of differentiating and integrating a wide variety of functions. Real, single variable calculus is the main focus of the text, but Cauchy spends ample time exploring the extension of his rigorous development to include functions of multiple variables as well as complex functions. This translation maintains the same notation and terminology of Cauchy's original work in the hope of delivering as honest and true a Cauchy experience as possible so that the modern reader can experience his work as it may have been like 200 years ago. This book can be used with advantage today by anyone interested in the history of the calculus and analysis. In addition, it will serve as a particularly valuable supplement to a traditional calculus text for those readers who desire a way to create more texture in a conventional calculus class through the introduction of original historical sources.
Download or read book The Math Book written by Clifford A. Pickover and published by Sterling Publishing Company, Inc.. This book was released on 2009 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers 250 milestones in mathematical history, beginning millions of years ago with ancient "ant odometers" and moving through time to our modern-day quest for new dimensions.
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 Metaphysical Principles of the Infinitesimal Calculus written by René Guénon and published by Sophia Perennis. This book was released on 2003 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: René Guénon (1886-1951) is undoubtedly one of the luminaries of the twentieth century, whose critique of the modern world has stood fast against the shifting sands of recent philosophies. His oeuvre of 26 volumes is providential for the modern seeker: pointing ceaselessly to the perennial wisdom found in past cultures ranging from the Shamanistic to the Indian and Chinese, the Hellenic and Judaic, the Christian and Islamic, and including also Alchemy, Hermeticism, and other esoteric currents, at the same time it directs the reader to the deepest level of religious praxis, emphasizing the need for affiliation with a revealed tradition even while acknowledging the final identity of all spiritual paths as they approach the summit of spiritual realization. Guénon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet threat throughout his doctrinal studies. In this late text published just five years before his death, Guénon devotes an entire volume to questions regarding the nature of limits and the infinite, both with respect to the calculus as a mathematical discipline, and to the symbolism of the initiatic path. This book therefore extends and complements the geometrical symbolism Guénon employs in several of his other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. A sampling of chapter titles will convey some sense of this remarkable work: 'Infinite and Indefinite', 'Degrees of Infinity', 'Zero is not a Number', 'The Law of Continuity', 'Vanishing Quantities', 'Various Orders of Indefinitude', 'The Arguments of Zeno of Elea', 'The True Conception of Passage to the Limit'. The Collected Works of René Guénon brings together the writings of one of the greatest prophets of our time, whose voice is even more important today than when he was alive. Huston Smith, author of The World's Religions, etc.
Download or read book Cauchy s Calcul Infinit simal written by Augustin Louis Baron Cauchy and published by . This book was released on 2012-05-10 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The History of the Calculus and Its Conceptual Development written by Carl B. Boyer and published by Courier Corporation. This book was released on 2012-10-09 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.
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 144 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 Infinitesimal Calculus written by Jean Dieudonné and published by . This book was released on 1971 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Diff and Integral Calculus written by J. Thomson (L. L. D.) and published by . This book was released on 1839 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles of Infinitesimal Stochastic and Financial Analysis written by Imme van den Berg and published by World Scientific. This book was released on 2000 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been a tremendous growth in the volume of financial transactions based on mathematics, reflecting the confidence in the Nobel-Prize-winning Black-Scholes option theory. Risks emanating from obligatory future payments are covered by a strategy of trading with amounts not determined by guessing, but by solving equations, and with prices not resulting from offer and demand, but from computation. However, the mathematical theory behind that suffers from inaccessibility. This is due to the complexity of the mathematical foundation of the Black-Scholes model, which is the theory of continuous-time stochastic processes: a thorough study of mathematical finance is considered to be possible only at postgraduate level. The setting of this book is the discrete-time version of the Black-Scholes model, namely the Cox-Ross-Rubinstein model. The book gives a complete description of its background, which is now only the theory of finite stochastic processes. The novelty lies in the fact that orders of magnitude -- in the sense of nonstandard analysis -- are imposed on the parameters of the model. This not only makes the model more economically sound (such as rapid fluctuations of the market being represented by infinitesimal trading periods), but also leads to a significant simplification: the fundamental results of Black-Scholes theory are derived in full generality and with mathematical rigour, now at graduate level. The material has been repeatedly taught in a third-year course to econometricians.
Download or read book Lazare and Sadi Carnot written by Charles Coulston Gillispie and published by Springer Science & Business Media. This book was released on 2014-02-03 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lazare Carnot was the unique example in the history of science of someone who inadvertently owed the scientific recognition he eventually achieved to earlier political prominence. He and his son Sadi produced work that derived from their training as engineering and went largely unnoticed by physicists for a generation or more, even though their respective work introduced concepts that proved fundamental when taken up later by other hands. There was, moreover, a filial as well as substantive relation between the work of father and son. Sadi applied to the functioning of heat engines the analysis that his father had developed in his study of the operation of ordinary machines. Specifically, Sadi's idea of a reversible process originated in the use his father made of geometric motions in the analysis of machines in general. This unique book shows how the two Carnots influenced each other in their work in the fields of mechanics and thermodynamics and how future generations of scientists have further benefited from their work.
Download or read book Introduction to the Differential and Integral Calculus written by James Thomson and published by . This book was released on 1848 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finding List for Seminary Libraries written by Princeton University. Library and published by . This book was released on 1907 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to the Differential and Integral Calculus with an appendix illustrative of the Theory of Curves and other subjects Second edition written by James THOMSON (LL.D., Professor of Mathematics in the University of Glasgow.) and published by . This book was released on 1848 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculus Set Free written by C. Bryan Dawson and published by Oxford University Press. This book was released on 2021-11-30 with total page 1280 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 Mathematical Seminary written by Princeton University. Library and published by . This book was released on 1915 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reflexions on the Metaphysical Principles of the Infinitesimal Analysis written by Lazare Carnot and published by . This book was released on 1832 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
