The Origins Of The Infinitesimal Calculus
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The Origins Of Infinitesimal Calculus
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Author : Margaret E. Baron
language : en
Publisher: Elsevier
Release Date : 2014-05-09
The Origins Of Infinitesimal Calculus written by Margaret E. Baron and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.
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.
The Origins Of The Infinitesimal Calculus
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Author :
language : en
Publisher:
Release Date : 1969
The Origins Of The Infinitesimal Calculus written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
The Origins Of The Infinitesimal Calculus
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Author : Margaret E. Baron
language : en
Publisher:
Release Date : 1994
The Origins Of The Infinitesimal Calculus written by Margaret E. Baron and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
The Historical Development Of The Calculus
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Author : C.H.Jr. Edwards
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Historical Development Of The Calculus written by C.H.Jr. Edwards and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.
Foundations Of Infinitesimal Calculus
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Author : H. Jerome Keisler
language : en
Publisher: Prindle Weber & Schmidt
Release Date : 1976-01-01
Foundations Of Infinitesimal Calculus written by H. Jerome Keisler and has been published by Prindle Weber & Schmidt this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-01-01 with Mathematics categories.
Cauchy S Calcul Infinit Simal
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Author : Dennis M. Cates
language : en
Publisher: Springer
Release Date : 2019-04-03
Cauchy S Calcul Infinit Simal written by Dennis M. Cates and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-03 with Mathematics categories.
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.
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics
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Author : John L. Bell
language : en
Publisher: Springer Nature
Release Date : 2019-09-09
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics written by John L. Bell and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
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.
The History Of The Calculus And Its Conceptual Development
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Author : Carl B. Boyer
language : en
Publisher: Courier Corporation
Release Date : 2012-10-09
The History Of The Calculus And Its Conceptual Development written by Carl B. Boyer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-09 with Mathematics categories.
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.
Calculus Reordered
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Author : David M. Bressoud
language : en
Publisher: Princeton University Press
Release Date : 2019-07-16
Calculus Reordered written by David M. Bressoud and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-16 with Mathematics categories.
How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to change Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, 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 represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus’s birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, 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 that the historical order—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.