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 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 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 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 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 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 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:
Download or read book Reflexions on the Metaphysical Principles of the Infinitesimal Analysis Translated by the Rev W R Browell written by Lazare Nicolas Marguerite CARNOT (Count.) and published by . This book was released on 1832 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 A Brief Introduction to the Infinitesimal Calculus written by Irving Fisher and published by . This book was released on 1897 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Nature of Infinitesimals written by Peter F. Erickson and published by Xlibris Corporation. This book was released on 2006-05-05 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Erickson explores and explains the infinite and the infinitesimal with application to absolute space, time and motion, as well as absolute zero temperature in this thoughtful treatise. Mathematicians, scientists and philosophers have explored the realms of the continuous and discrete for centuries. Erickson delves into the history of these concepts and how people learn and understand them. He regards the infinitesimal as the key to understanding much of the scientific basis of the universe, and intertwines mathematical examples and historical context from Aristotle, Kant, Euler, Newton and more with his deductions-resulting in a readable treatment of complex topics. The reader will gain an understanding of potential versus actual infinity, irrational and imaginary numbers, the infinitesimal, and the tangent, among other concepts. At the heart of Ericksons work is the veritable number system, in which positive and negative numbers are incompatible for the basic mathematical operations of addition, subtraction, multiplication, division, roots and ratios. This number system, he demonstrates, can provide a new interpretation of imaginary numbers, as a combination of the real and the veritable. Erickson further explores limits, derivatives and integrals before turning his attention to non-Euclidean geometry. In each topic, he applies his new understanding of the infinitesimal to the ideas of mathematics and draws conclusions. In the case of non-Euclidean geometry, the author determines that its inconsistent with the infinitesimal. Erickson supplies illustrative examples both in words and images-he clearly defines new notation as needed for concepts such as eternity, the infinitesimal, the instant and an unlimited quantity. In the final chapters, the author addresses absolute space, time and motion through the lens of the infinitesimal. While explaining his deductions and thoughts on these complex topics, he raises new questions for his readers to contemplate, such as the origin of memory. A weighty tome for devotees of mathematics and physics that raises interesting questions.
Download or read book An Introduction to the Infinitesimal Calculus written by Horatio Scott Carslaw and published by . This book was released on 1905 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Treatise on Infinitesimal Calculus written by Bartholomew Price and published by . This book was released on 1856 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Treatise on Infinitesimal Calculus The dynamics of material systems 1862 written by Bartholomew Price and published by . This book was released on 1889 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A First Course in Infinitesimal Calculus written by Daniel Alexander Murray and published by . This book was released on 1903 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Treatise on Infinitesimal Calculus written by Bartholomew Price and published by . This book was released on 1854 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
