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RISE AND DEVELOPMENT OF THEORY OF SERIES UP TO EARLY 1820S (SOURCES AND STUDIES IN HISTORY OF MATHEMATICS AND PHYSICAL SCIENCES) - Erstausgabe

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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) - gebunden oder broschiert

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Bibliographische Daten des bestpassenden Buches

Details zum Buch
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)

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.

Detailangaben zum Buch - 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)


EAN (ISBN-13): 9780387734675
ISBN (ISBN-10): 0387734678
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2008
Herausgeber: Springer
392 Seiten
Gewicht: 0,676 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-11-06T01:18:56+01:00 (Berlin)
Detailseite zuletzt geändert am 2023-11-15T13:31:11+01:00 (Berlin)
ISBN/EAN: 9780387734675

ISBN - alternative Schreibweisen:
0-387-73467-8, 978-0-387-73467-5
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: ferraro, giovanni, jay early, taylor
Titel des Buches: series, theory development, the rise early science, mathematics and history, the rise six, physical mathematics, history 2008, the sources, history and theory studies the, history the sciences


Daten vom Verlag:

Autor/in: Giovanni Ferraro
Titel: Sources and Studies in the History of Mathematics and Physical Sciences; The Rise and Development of the Theory of Series up to the Early 1820s
Verlag: Springer; Springer US
392 Seiten
Erscheinungsjahr: 2007-12-18
New York; NY; US
Sprache: Englisch
109,99 € (DE)

BB; Hardcover, Softcover / Mathematik/Allgemeines, Lexika; Geschichte der Mathematik; Verstehen; Fourier series; Taylor series; calculus; differential equation; number theory; History of Mathematical Sciences; Sequences, Series, Summability; Real Functions; Analysis; Mathematische Analysis, allgemein; Reelle Analysis, Real-Variablen; BC

From the beginnings of the 17th century to about 1720: Convergence and formal manipulation.- Series before the rise of the calculus.- Geometrical quantities and series in Leibniz.- The Bernoulli series and Leibniz’s analogy.- Newton’s method of series.- Jacob Bernoulli’s treatise on series.- The Taylor series.- Quantities and their representations.- The formal-quantitative theory of series.- The first appearance of divergent series.- From the 1720s to the 1760s: The development of a more formal conception.- De Moivre’s recurrent series and Bernoulli’s method.- Acceleration of series and Stirling’s series.- Maclaurin’s contribution.- The young Euler between innovation and tradition.- Euler’s derivation of the Euler–Maclaurin summation formula.- On the sum of an asymptotic series.- Infinite products and continued fractions.- Series and number theory.- Analysis after the 1740s.- The formal concept of series.- The theory of series after 1760: Successes and problems of the triumphant formalism.- Lagrange inversion theorem.- Toward the calculus of operations.- Laplace’s calculus of generating functions.- The problem of analytical representation of nonelementary quantities.- Inexplicable functions.- Integration and functions.- Series and differential equations.- Trigonometric series.- Further developments of the formal theory of series.- Attempts to introduce new transcendental functions.- D’Alembert and Lagrange and the inequality technique.- The decline of the formal theory of series.- Fourier and Fourier series.- Gauss and the hypergeometric series.- Cauchy’s rejection of the 18th-century theory of series.

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