Sinossi
The manuscript gives a coherent and detailed account of the theory of series in the eighteenth and early nineteenth centuries. It provides in one place an account of many results that are generally to be found - if at all - scattered throughout the historical and textbook literature. It presents the subject from the viewpoint of the mathematicians of the period, and is careful to distinguish earlier conceptions from ones that prevail today.
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Dalla quarta di copertina
The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Most of the results derived from this time were derived using methods which would be found unacceptable today, and as a result, when one looks back to the theory of series prior to Cauchy without reconstructing internal motivations and the conceptual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a magician or diviner rather than the penetrating and complex work of great mathematicians.
This monograph not only describes the entire complex of 17th and 18th century procedures and results concerning series, but it also reconstructs the implicit and explicit principles upon which they are based, draws attention to the underlying philosophy, highlights competing approaches, and investigates the mathematical context where the theory originated. The aim here is to improve the understanding of the framework of 17th and 18th century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some sense, to a unified theory that has come down to us today.
Giovanni Ferraro is Professor of Mathematics and History of Mathematics at University of Molise.
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The Rise and Development of the Theory of Series up to the Early 1820s (Sources and Studies in the History of Mathematics and Physical Sciences)
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The Rise and Development of the Theory of Series up to the Early 1820s
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Indeed, mathematicians of the time derived num- ous results that range from the binomial theorem to the Taylor formula, from the power series expansions of elementary functions to trigonometric series, from Stirling's series to series solution of di erential equations, from theEuler-MaclaurinsummationformulatotheLagrangeinversiontheorem, from Laplace's theory of generating functions to the calculus of operations, etc. Most of these results were, however, derived using methods that would be found unacceptable today, thus, if we look back to the theory of series priortoCauchywithoutreconstructinginternalmotivationsandtheconc- tual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a - gician or diviner rather than the penetrating and complex work of great mathematicians. For this reason, in this monograph, not only do I describe the entire complex of 17th- and 18th-century procedures and results concerning series, but also I reconstruct the implicit and explicit principles upon which they are based, draw attention to the underlying philosophy, highlight competing approaches, and investigate the mathematical context where the series t- ory originated. My aim is to improve the understanding of the framework of 17th- and 18th-century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some unpr- lematic sense, to a uni ed theory that has come down to us today. 408 pp. Englisch. Codice articolo 9781441925206
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The Rise and Development of the Theory of Series up to the Early 1820s
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Carefully researched, accompanied by detailed bibliographyProvides a coherent and detailed account of the theory of series in the 18th and early 19th centuriesIncludes a comprehensive account of many results that were previously scattered t. Codice articolo 4173032
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The Rise and Development of the Theory of Series up to the Early 1820s
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Taschenbuch. Condizione: Neu. The Rise and Development of the Theory of Series up to the Early 1820s | Giovanni Ferraro | Taschenbuch | xvi | Englisch | 2010 | Humana | EAN 9781441925206 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 107219585
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Indeed, mathematicians of the time derived num- ous results that range from the binomial theorem to the Taylor formula, from the power series expansions of elementary functions to trigonometric series, from Stirling¿s series to series solution of di erential equations, from theEuler¿MaclaurinsummationformulatotheLagrangeinversiontheorem, from Laplace¿s theory of generating functions to the calculus of operations, etc. Most of these results were, however, derived using methods that would be found unacceptable today, thus, if we look back to the theory of series priortoCauchywithoutreconstructinginternalmotivationsandtheconc- tual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a - gician or diviner rather than the penetrating and complex work of great mathematicians. For this reason, in this monograph, not only do I describe the entire complex of 17th- and 18th-century procedures and results concerning series, but also I reconstruct the implicit and explicit principles upon which they are based, draw attention to the underlying philosophy, highlight competing approaches, and investigate the mathematical context where the series t- ory originated. My aim is to improve the understanding of the framework of 17th- and 18th-century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some unpr- lematic sense, to a uni ed theory that has come down to us today.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 408 pp. Englisch. Codice articolo 9781441925206
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The Rise and Development of the Theory of Series up to the Early 1820s
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Springer New York, Springer US, 2010
ISBN 10: 1441925201
ISBN 13: 9781441925206
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Indeed, mathematicians of the time derived num- ous results that range from the binomial theorem to the Taylor formula, from the power series expansions of elementary functions to trigonometric series, from Stirling's series to series solution of di erential equations, from theEuler-MaclaurinsummationformulatotheLagrangeinversiontheorem, from Laplace's theory of generating functions to the calculus of operations, etc. Most of these results were, however, derived using methods that would be found unacceptable today, thus, if we look back to the theory of series priortoCauchywithoutreconstructinginternalmotivationsandtheconc- tual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a - gician or diviner rather than the penetrating and complex work of great mathematicians. For this reason, in this monograph, not only do I describe the entire complex of 17th- and 18th-century procedures and results concerning series, but also I reconstruct the implicit and explicit principles upon which they are based, draw attention to the underlying philosophy, highlight competing approaches, and investigate the mathematical context where the series t- ory originated. My aim is to improve the understanding of the framework of 17th- and 18th-century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some unpr- lematic sense, to a uni ed theory that has come down to us today. Codice articolo 9781441925206
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