Analysis: Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden

Analysis: Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden
ISBN-10
3642415067
ISBN-13
9783642415067
Series
Analysis
Category
Mathematics
Pages
512
Language
German
Published
2013-12-10
Publisher
Springer Spektrum
Author
Friedrich Sauvigny

Description

Das Buch bietet eine moderne Darstellung der Differential- und Integralrechnung für Funktionen in einer und mehreren reellen Veränderlichen sowie in einer komplexen Variablen. Die elementaren Funktionen werden über komplexe Potenzreihen definiert und die Logarithmusfunktion auf ihrer Riemannschen Fläche betrachtet. Nachdem die eindimensionale Integration mittels reeller und komplexer Stammfunktionen durchgeführt ist, wird über das uneigentliche n-dimensionale Riemannsche Integral die Integration auf Mannigfaltigkeiten mit Hilfe von Differentialformen vorgestellt. Mit dem Lebesgueschen Integral und dessen Maßtheorie werden die Banachräume p-fach integrierbarer Funktionen eingeführt. Es werden für gewöhnliche Differentialgleichungen systematisch Existenz-, Eindeutigkeits- und Stabilitätsfragen behandelt. In einem Kapitel zur Variationsrechnung wird direkt über die Untersuchung von Geodätischen der Riemannsche Raum und sein Krümmungsbegriff vorgestellt.

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