The Tangled Origins Of The Leibnizian Calculus PDF Download
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Author | : Richard C. Brown |
Publisher | : World Scientific |
Total Pages | : 333 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9814390801 |
Download The Tangled Origins of the Leibnizian Calculus Book in PDF, ePub and Kindle
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."
Author | : Richard C Brown |
Publisher | : World Scientific |
Total Pages | : 333 |
Release | : 2012-03-23 |
Genre | : Mathematics |
ISBN | : 9814401617 |
Download Tangled Origins Of The Leibnizian Calculus, The: A Case Study Of A Mathematical Revolution Book in PDF, ePub and Kindle
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.
Author | : Richard C. Brown |
Publisher | : World Scientific |
Total Pages | : 333 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9814390798 |
Download The Tangled Origins of the Leibnizian Calculus Book in PDF, ePub and Kindle
1. Evolution or revolution in mathematics -- 2. Issues in seventeenth century mathematics -- 3. Isaac Barrow: a foil to Leibniz -- 4. A young central European polymath -- 5. First steps in mathematics -- 6. The creation of calculus -- 7. Logic -- 8. The universal characteristic -- 9. The baroque cultural context -- 10. Epilogue -- 11. Some concluding remarks on mathematical change -- Appendices.
Author | : Viktor Blasjo |
Publisher | : Academic Press |
Total Pages | : 282 |
Release | : 2017-04-22 |
Genre | : Mathematics |
ISBN | : 0128132981 |
Download Transcendental Curves in the Leibnizian Calculus Book in PDF, ePub and Kindle
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
Author | : Carl B. Boyer |
Publisher | : Courier Corporation |
Total Pages | : 431 |
Release | : 2012-10-09 |
Genre | : Mathematics |
ISBN | : 0486175383 |
Download The History of the Calculus and Its Conceptual Development Book in PDF, ePub and Kindle
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.
Author | : C.H.Jr. Edwards |
Publisher | : Springer Science & Business Media |
Total Pages | : 363 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461262305 |
Download The Historical Development of the Calculus Book in PDF, ePub and Kindle
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.
Author | : Margaret E. Baron |
Publisher | : |
Total Pages | : 324 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : |
Download The Origins of the Infinitesimal Calculus Book in PDF, ePub and Kindle
Few among the numerous studies of calculus offer the detailed and fully documented historical perspective of this text, particularly in regard to the geometric techniques and methods developed prior to the work of Newton and Leibniz. Because the contributions of these and other mathematicians arose from a centuries-long struggle to investigate area, volume, tangent, and arc by purely geometric methods, the author begins by establishing background mathematical concepts. Dr. Baron provides an enlightening view of the Greek, Hindu, and Arabic sources that constituted the framework for the development of infinitesimal methods in the seventeenth century. Subsequent chapters offer an illuminating discussion of the arithmetization of integration methods, the role of investigation of special curves, concepts of tangent and arc, the composition of motions, and the developing link between differential and integral processes. Significant changes in proof structure and presentation are considered in relation to the formulation of rules for the construction of tangents and quadrature of curves. An Epilogue concludes the text with a brief chronological survey of the early work of Newton and Leibniz, based on material drawn from original manuscripts. Book jacket.
Author | : Norma B. Goethe |
Publisher | : Springer |
Total Pages | : 215 |
Release | : 2015-04-20 |
Genre | : Science |
ISBN | : 9401796645 |
Download G.W. Leibniz, Interrelations between Mathematics and Philosophy Book in PDF, ePub and Kindle
Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.
Author | : Jason Socrates Bardi |
Publisher | : Basic Books |
Total Pages | : 304 |
Release | : 2009-04-29 |
Genre | : Science |
ISBN | : 0786733640 |
Download The Calculus Wars Book in PDF, ePub and Kindle
This vibrant and gripping history ultimately exposes how these twin mathematical giants (Newton, Leibniz) were proud, brilliant, at times mad, and in the end completely human.
Author | : Carl Benjamin Boyer |
Publisher | : Courier Corporation |
Total Pages | : 376 |
Release | : 1949 |
Genre | : Calculo - Historia |
ISBN | : 9780486158228 |
Download The History of the Calculus and Its Conceptual Development Book in PDF, ePub and Kindle