Herleitung der Integration für Funktionen von R² nach R bezogen auf das Riemannintegral

Name: Herleitung der Integration für Funktionen von R² nach R bezogen auf das Riemannintegral
Brand: Atlantic Books
SKU: 9783640490646
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ISBN13: 9783640490646
Binding: Paperback
Subject: N/A
Publisher: Grin Verlag
Publisher Imprint: Grin Verlag
Publication Date: January 1, 2010
Pages: 76
Original Price: USD 60.5
Language: German
Edition: 3. Auflage
Item Weight: 109 grams
BISAC Subject(s): Vector Analysis

About The Book

Examensarbeit aus dem Jahr 2009 im Fachbereich Mathematik - Analysis, Note: 1, Universität Koblenz-Landau, Sprache: Deutsch, Abstract: Historisch liegen die Wurzeln der Integralrechnung in der Ermittlung von Flächeninhalten, da man es sich zur Aufgabe machte, den Flächeninhalt auch solcher ebenen Gebilde zu ermitteln, die nicht durch Polygone begrenzt werden. Methodische Ansätze finden sich zwar bereits bei Archimedes, Cavalieri und Barrow, die systematische Entwicklung aber beginnt erst mit der Entdeckung des Zusammenhangs von Differentiation und Integration durch Leibniz und Newton um 1670. Durch sie wurde die Integralrechung im eigentlichen Sinne als "calculus summatorius" und später als "calculus integralis" begründet. Leibniz war es dann auch, der am 29. Oktober 1675 das Integralzeichen ∫festlegte. Es stellt ein stilisiertes S dar, welches dem Wort Summe entnommen wurde. Der Zusammenhang zwischen Summation und Integration ist schon mit der Herleitung gegeben, wie später deutlich wird. Eine Präzisierung des Integralbegriffs für stetige Funktionen nahm erstmals Cauchy (1823) in Angriff. Riemann (1854) erweiterte diesen auf etwas allgemeinere Funktionen. Einen andersartigen, wesentlich flexibleren und sehr umfassenden Integralbegriff führte Lebesque (1902) ein. (vgl. Wolff, 1967, S.61 und Königsberger, 1999, S.191f) Die vorliegende Examensarbeit beschränkt sich im Wesentlichen auf das Integral stetiger Funktionen in ℝ bezogen auf das Riemannintegral, das in Kapitel I 1 hergeleitet und durch einige Eigenschaften, den Mittelwertsatz der Integralrechnung, den Hauptsatz der Differential- und Integralrechnung und die Definition der Stammfunktion beschrieben wird. In Kapitel I 2 wird die Herleitung auf die Integration stetiger Funktionen in 2ℝ erweitert und somit ein direkter Vergleich zum Integral stetiger Funktionen in ℝ geschaffen. Anschlie end wird in Kapitel I 3 gezeigt, wie man das Doppelintegral durch Zerlegung der doppelten Integration in zwei einfache Integr

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