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Transcendental Curves In The Leibnizian Calculus

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Transcendental Curves in the Leibnizian Calculus

Transcendental Curves in the Leibnizian Calculus Book
Author : Viktor Blasjo
Publisher : Academic Press
Release : 2017-04-22
ISBN : 0128132981
Language : En, Es, Fr & De

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Book Description :

Transcendental Curves in the Leibnizian Calculus analyzes the mathematical and philosophical conflict between Euclidean and Cartesian mathematics. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it. Brings to light this underlying and often implicit complex of concerns that permeate early calculus Evaluates the technical conception and mathematical construction of the geometrical method Reveals a previously unrecognized Liebnizian programmatic cohesion in early calculus Provides a beautifully written work of outstanding original scholarship

The Tangled Origins of the Leibnizian Calculus

The Tangled Origins of the Leibnizian Calculus Book
Author : Richard C. Brown
Publisher : World Scientific
Release : 2012
ISBN : 9814390801
Language : En, Es, Fr & De

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Book Description :

This book is a detailed study of Gottfried Wilhelm Leibniz''s creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known OC calculiOCO Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz. This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz''s mathematical achievement or general issues in the field."

The Tangled Origins of the Leibnizian Calculus

The Tangled Origins of the Leibnizian Calculus Book
Author : Richard C Brown
Publisher : World Scientific
Release : 2012-03-23
ISBN : 9814401617
Language : En, Es, Fr & De

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Book Description :

This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known “calculi” Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz. This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz's mathematical achievement or general issues in the field. Contents:Evolution or Revolution in MathematicsIssues in Seventeenth Century MathematicsIsaac Barrow: A Foil to LeibnizA Young Central European PolymathFirst Steps in MathematicsThe Creation of CalculusLogicThe Universal CharacteristicThe Baroque Cultural ContextEpilogueSome Concluding Remarks on Mathematical ChangeAppendices:A: A Transmutation Theorem of LeibnizB: Leibniz's Series Quadrature of a ConicC: Syllogistic LogicD: The Vis Viva DisputeE: Some Applications of Curves and Neusis in Greek GeometryF: InfinitesimalsA Note on the Author Readership: Advanced undergraduate students, graduate students and researchers in mathematics, history of mathematics or history of science. Keywords:Leibniz;Calculus;Geometry;17th Century MathematicsKey Features:The thoroughness and comprehensiveness of the treatment of this book are based on recent researchTechnical details of the mathematics are carefully dealt with instead of just being summarized for the general readerNo other work on the development of calculus includes a description and analysis of the Baroque/Renaissance atmosphere of fascination with symbols, emblems, Real Characters and philosophical languages which motivated both Leibniz's mathematics and his search for the Universal Characteristic

Leibniz and the Structure of Sciences

Leibniz and the Structure of Sciences Book
Author : Vincenzo De Risi
Publisher : Springer Nature
Release : 2020-01-01
ISBN : 3030255727
Language : En, Es, Fr & De

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Book Description :

The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

Infinitesimal Differences

Infinitesimal Differences Book
Author : Ursula Goldenbaum,Douglas Jesseph
Publisher : Walter de Gruyter
Release : 2008-11-03
ISBN : 3110211866
Language : En, Es, Fr & De

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Book Description :

The development of the calculus during the 17th century was successful in mathematical practice, but raised questions about the nature of infinitesimals: were they real or rather fictitious? This collection of essays, by scholars from Canada, the US, Germany, Japan and Switzerland, gives a comprehensive study of the controversies over the nature and status of the infinitesimal. Aside from Leibniz, the scholars considered are Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. The collection also contains newly discovered marginalia of Leibniz to the writings of Hobbes.

The Britannica Guide to Analysis and Calculus

The Britannica Guide to Analysis and Calculus Book
Author : Erik Gregersen Associate Editor, Astronomy and Space Exploration
Publisher : The Rosen Publishing Group, Inc
Release : 2010-08-15
ISBN : 1615301232
Language : En, Es, Fr & De

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Book Description :

Examines the history of analysis and calculus, including the geniuses of invention and theory, the practical applications of the math, and explanations of the major topics.

Mathematics and Its History

Mathematics and Its History Book
Author : John Stillwell
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 1489900071
Language : En, Es, Fr & De

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Book Description :

A concise, unified view of mathematics together with its historical development. Aiming at mathematicians who have mastered the basic topics but wish to gain a better grasp of mathematics as a whole, the author gives the reasons for the emergence of the main fields of modern mathematics, and explains the connections between them by tracing the course of a few mathematical themes from ancient times down to the 20th century. The emphasis here is on history as a method for unifying and motivating mathematics, rather than as an end in itself, and there is more mathematical detail than in other general histories. However, no historical expertise is assumed, and classical mathematics is rephrased in modern terms where needed. Nevertheless, there are copious references to original sources for readers wishing to explore the classics for themselves. In summary, readers will be able to add to their mathematical knowledge as well as gaining a new perspective on what they already know.

The Mind of Leibniz

The Mind of Leibniz Book
Author : Kurt von S. Kynell
Publisher :
Release : 2003
ISBN : 9780773468931
Language : En, Es, Fr & De

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Book Description :

This volume attempts to resolve the century old dispute between Newton and Leibniz over the discovery of the calculus, and also explores both the mind and the life long research of Gottfried Wilhelm von Leibniz, documenting his phenomenal mathematical and philosophical research, as well as the apparent nature and possible origins of genius and human intelligence.

e The Story of a Number

e  The Story of a Number Book
Author : Eli Maor
Publisher : Princeton University Press
Release : 2011-10-12
ISBN : 1400832349
Language : En, Es, Fr & De

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Book Description :

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

Advanced Engineering Mathematics

Advanced Engineering Mathematics Book
Author : Dennis G. Zill,Warren S. Wright
Publisher : Jones & Bartlett Publishers
Release : 2009-12-21
ISBN : 0763782416
Language : En, Es, Fr & De

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Book Description :

Now with a full-color design, the new Fourth Edition of Zill's Advanced Engineering Mathematics provides an in-depth overview of the many mathematical topics necessary for students planning a career in engineering or the sciences. A key strength of this text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fourth Edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. Numerous new projects contributed by esteemed mathematicians have been added. New modern applications and engaging projects makes Zill's classic text a must-have text and resource for Engineering Math students!

Advanced Engineering Mathematics

Advanced Engineering Mathematics Book
Author : Dennis G. Zill,Warren S. Wright
Publisher : Jones & Bartlett Publishers
Release : 2009-12-21
ISBN : 1449653898
Language : En, Es, Fr & De

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Book Description :

Now with a full-color design, the new Fourth Edition of Zill's Advanced Engineering Mathematics provides an in-depth overview of the many mathematical topics necessary for students planning a career in engineering or the sciences. A key strength of this text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fourth Edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. Numerous new projects contributed by esteemed mathematicians have been added. New modern applications and engaging projects makes Zill's classic text a must-have text and resource for Engineering Math students!

Advanced Engineering Mathematics

Advanced Engineering Mathematics Book
Author : Dennis Zill,Warren S. Wright,Michael R. Cullen
Publisher : Jones & Bartlett Learning
Release : 2011
ISBN : 9780763779665
Language : En, Es, Fr & De

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Book Description :

Accompanying CD-ROM contains ... "a chapter on engineering statistics and probability / by N. Bali, M. Goyal, and C. Watkins."--CD-ROM label.

Equivalence and Priority

Equivalence and Priority Book
Author : Domenico Bertoloni Meli,Gottfried Wilhelm Freiherr von Leibniz,Research Fellow Domenico Bertoloni Meli
Publisher : Oxford University Press, USA
Release : 1993
ISBN :
Language : En, Es, Fr & De

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Book Description :

Leibniz's dispute with Newton over the physico-mathematical theories expounded in the Principia Mathematica (1687) have long been identified as a crucial episode in the history of science. Bertolini Meli here examines several hitherto unpublished manuscripts in Leibniz's hand illustrating his first reading of and reaction to Newton's Principia. Six of the most important manuscripts are here presented for the first time. Contrary to Leibniz's own claims, this new evidence shows that he had studied Newton's masterpiece before publishing An Essay on the Causes of Celestial Motions. This article, representing his response to Newton, also included in English translation. Meli analyzes the important implications of this episode on a variety of themes ranging from priority claims to the mathematization of nature in the 17th century. Besides providing a careful study of Leibniz's style and strategy, the author examines how our perception of Newton's achievement is affected and the reception of the rival theories by the mathematical community around 1700. This unique work will interest all historians of science and philosophy.

Newton and Leibniz

Newton and Leibniz Book
Author : Margaret E. Baron,H. J. M. Bos
Publisher :
Release : 1974
ISBN :
Language : En, Es, Fr & De

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Book Description :

Bulletin

Bulletin Book
Author : Institute of Mathematics and Its Applications
Publisher :
Release : 1985
ISBN :
Language : En, Es, Fr & De

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Book Description :