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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Allg. & Lexika The Rise and Development of the Theory of Series up to the Early 1820s
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The Rise and Development of the Theory of Series up to the Early 1820s
Giovanni Ferraro (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
19.11.2010
Sprache
Englisch
EAN
9781441925206
Herausgeber
Springer US
Serien- oder Bandtitel
Sources and Studies in the History of Mathematics and Physical Sciences
Sonderedition
Nein
Autor
Giovanni Ferraro
Seitenanzahl
392
Einbandart
Broschiert
Schlagwörter
Fourier series, Taylor series, calculus, differential equation, number theory
Thema-Inhalt
PBX - Geschichte der Mathematik
PBK - Mathematische Analysis, allgemein
PBKB - Reelle Analysis, Real-Variablen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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