Overview
- Carefully researched, accompanied by detailed bibliography
- Provides a coherent and detailed account of the theory of series in the 18th and early 19th centuries
- Includes a comprehensive account of many results that were previously scattered throughout the historical and textbook literature
Part of the book series: Sources and Studies in the History of Mathematics and Physical Sciences (SHMP)
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Table of contents (33 chapters)
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From the beginnings of the 17th century to about 1720: Convergence and formal manipulation
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From the 1720s to the 1760s: The development of a more formal conception
Keywords
About this book
Reviews
From the reviews:
"Giovanni Ferraro’s book must be regarded as an important contribution to the history of mathematical analysis … . In summary, this book is thoroughly researched; it is written with a high degree of accuracy, and the broad range of fascinating material is, in general, very well organized. Therefore … every college and university library should have a copy. In fact, extracts from the book could be used to inject historical perspectives into courses on analysis, and it will certainly appeal to historians in general." (Peter Ruane, MathDL, April, 2008)
"The work is thoroughly referenced and should prove valuable to mathematical history researchers … . Summing Up: Recommended. Researchers/faculty and professionals." (C. Bauer, CHOICE, Vol. 46 (01), September, 2008)
"The author begins his detailed account with the arrival of the calculus with Newton and Leibniz, and their own treatments of series. … The range of series and functions treated is impressive … . The story stops with a brief notice of the start of the critical phase, especially concerning the convergence (or not) of infinite series, which was put forward by Cauchy and his followers … . The book is a valuable contribution, possibly the single most substantial source on the topic." (I. Grattan-Guinness, Mathematical Reviews, Issue 2008 k)
Authors and Affiliations
Bibliographic Information
Book Title: The Rise and Development of the Theory of Series up to the Early 1820s
Authors: Giovanni Ferraro
Series Title: Sources and Studies in the History of Mathematics and Physical Sciences
DOI: https://doi.org/10.1007/978-0-387-73468-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2008
Hardcover ISBN: 978-0-387-73467-5Published: 18 December 2007
Softcover ISBN: 978-1-4419-2520-6Published: 19 November 2010
eBook ISBN: 978-0-387-73468-2Published: 20 December 2007
Series ISSN: 2196-8810
Series E-ISSN: 2196-8829
Edition Number: 1
Number of Pages: XVI, 392
Number of Illustrations: 21 b/w illustrations
Topics: History of Mathematical Sciences, Sequences, Series, Summability, Real Functions, Analysis