✍️ 🧑‍🦱 💚 Autor:innen verdienen bei uns doppelt. Dank euch haben sie so schon 253.133 € mehr verdient. → Mehr erfahren 💪 📚 🙏

The Rise and Development of the Theory of Series up to the Early 1820s

von Giovanni Ferraro
Hardcover - 9780387734675
106,99 €
  • Versandkostenfrei
Auf meine Merkliste
  • Hinweis: Print on Demand. Lieferbar in 7 Tagen.
  • Lieferzeit nach Versand: ca. 1-2 Tage
  • inkl. MwSt. & Versandkosten (innerhalb Deutschlands)

Weitere Formate

Softcover - 9781441925206
117,69 €

Autorenfreundlich Bücher kaufen?!

Weitere Formate

Softcover - 9781441925206
117,69 €

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.

Details

Verlag Springer US
Ersterscheinung 18. Dezember 2007
Maße 23.5 cm x 15.5 cm
Gewicht 776 Gramm
Format Hardcover
ISBN-13 9780387734675
Seiten 392

Herstellerinformationen +