Read e-book online Analysis in historischer Entwicklung PDF

By Ernst Hairer, Gerhard Wanner, Andreas Lochmann

ISBN-10: 3642137660

ISBN-13: 9783642137662

Diese Einführung in die research orientiert sich in ihrem Aufbau an der zeitlichen Entwicklung der Themen. Die ersten zwei Kapitel schlagen den Bogen von historischen Berechnungsmethoden praktischer Problemen hin zu unendlichen Reihen, Differential- und Integralrechnung und zu Differentialgleichungen. Das Etablieren einer mathematisch stringenten Denkhaltung im 19. Jahrhundert für research ein und mehrerer Variablen wird in den Kapiteln III und IV behandelt. Viele Beispiele, Berechnungen und Bilder ergänzen das Buch und machen es zu einem Lesevergnügen für Studierende, Lehrer und Forscher. Aus den Besprechungen: the purpose of this attention-grabbing new contribution to the sequence Readings in arithmetic is an try and repair the ancient order within the presentation of simple mathematical analysis...such a old strategy delivers a really fruitful and engaging method of mathematical research. Jean Mawhin, Zentralblatt The authors comprise lots of once-traditional topics that have now vanished from the research curriculum. ...The paintings is particularly good illustrated. The e-book is well an research textual content, instead of a background, yet loads of trustworthy historic fabric is integrated. For these looking a substitute for the normal process, it sort of feels to me to be of significant curiosity. Thomas Archibald, Mathematical studies The authors...have assembled a magnificent array of annotated effects, quotations, tables, charts, figures and drawings, many copied from unique documents....they write with nice enthusiasm and with obtrusive affection for either research and heritage. John Troutman, American Mathematical Monthly

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Additional resources for Analysis in historischer Entwicklung

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1 mit Genehmigung der Bibl. Publ. Univ. Gen`eve. 2 Exponentialfunktion und binomischer Lehrsatz 21 was bedeutet, dass wir in der n¨achsten Zeile dieselbe Struktur vorfinden. 7) gegeben sind durch n/1, (n−1)/2, (n−2)/3, . . 1 allgemeing¨ultig ist. ⊓ ⊔ Diese Koeffizienten n(n − 1) . . (n − j + 1) n(n − 1) . . (n − j + 1) (n − j) . . 1 = 1 · 2 ·... ·j 1 · 2 · . . · j · 1 · 2 · . . 10) n! n = = j! (n − j)! j werden Binomialkoeffizienten genannt, und n! = 1 · 2 · . . · n heißt die Fakult¨at von n.

1 N! 2,0 2,5 2,66 2,708 2,7166 2,71805 2,718253 2,7182787 2,71828152 2,718281801 2,7182818261 2,71828182828 2,718281828446 2,7182818284582 2,71828182845899 2,7182818284590422 2,71828182845904507 2,718281828459045226 2,7182818284590452349 2,718281828459045235339 2,7182818284590452353593 2,718281828459045235360247 2,7182818284590452353602857 2,718281828459045235360287404 2,7182818284590452353602874687 2,71828182845904523536028747125 2,718281828459045235360287471349 2,71828182845904523536028747135254 Wir k¨onnen aber auch M = N/x, N = xM f¨ur jene Werte von N einsetzen, f¨ur die M eine ganze Zahl ist.

2. Mehrfache Wurzeln von 10 und ihre Produkte Es bleibt aber ein Problem: Uns w¨urden vielmehr Logarithmen zu Zahlen wie 2, 3, 4, . . interessieren, als solche zu 4, 2170 oder 2, 3714. Briggs Methode. , 54 Mal (siehe die Nachbildung in Abb. 3). 9a) 10c = 1,00000 00000 00000 12781 91493 20032 35 = 1 + a. 9b) 2c = 1,00000 00000 00000 03847 73979 65583 10 = 1 + b. Wir wollen den Wert von x = log10 2 berechnen, dieser erf¨ullt 2 = 10x. 10) log10 (2) = x ≈ b 3847739796558310 = ≈ 0,3010299956638812.

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Analysis in historischer Entwicklung by Ernst Hairer, Gerhard Wanner, Andreas Lochmann


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