Grundlagen Der Funktionentheorie: Lehrbuch Für Mathematiker, Physiker Und Elektrotechniker Im 4. Semester

Name: Grundlagen Der Funktionentheorie: Lehrbuch Für Mathematiker, Physiker Und Elektrotechniker Im 4. Semester
Brand: Vieweg+teubner Verlag
SKU: 9783322979339
Price: 3776.0 INR
Availability: InStock

by Wolfgang Tutschke

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ISBN13: 9783322979339
Binding: Paperback
Subject: N/A
Publisher: Vieweg+teubner Verlag
Publisher Imprint: Vieweg+teubner Verlag
Publication Date: January 1, 1969
Pages: 189
Original Price: EUR 51.39
Language: German
Edition: 1967
Item Weight: 313 grams
BISAC Subject(s): General

About The Book

Dieses Buch stellt eine Einführung in die (komplexe) Funktionentheorie dar. Die Funktionentheorie ist eine nach den verschiedensten Richtungen sehr weit entwickelte mathematische Theorie, deren Grundlage die Theorie der komplexen Differentiation ist. Einer der wichtigsten Sätze der Funktionentheorie ist der Cauchysche Integralsatz. Er besagt, da das komplexe Kurvenintegral einer komplexwertigen Funktion 1 (z) über eine geschlossene Kurve gleich Null ist, wenn I(z) in jedem Punkt ihres Definitionsgebietes im komplexen Sinne differen- zierbar ist. Allerdings gilt diese Aussage nur, wenn über die Struktur des Defini- tionsgebietes bestimmte Voraussetzungen gemacht werden. Hierin zeigt sich die enge Verbindung von Funktionentheorie und Topologie der Ebene. Diesen Zusammenhang kann man verwenden, um die Funktionentheorie gleich von Anfang an durch Heranziehung topologischer Aussagen aufzubauen. Ein sol- cher Satz, der an die Spitze der Funktionentheorie gestellt werden kann, ist der Jordansche Kurvensatz. Seine Verwendung ist für die Funktionentheorie äu erst bequem, da in den Begriff des einfach zus mmenhängenden Gebietes, zu dessen Definition man die Aussage de'> Jordanschen Kurvensatzes benötigt, sozusagen alle topologischen Schwierigkeiten hineingesteckt werden. Ein Nach- teil dieser Ansätze ist, da manche Analogien zur reellen Analysis, die erhalten bleiben könnten, verlorengehen. SARS und ZYGMUND waren meines Wissens die ersten, die auf diesen Umstand hingewiesen und in ihrem Buch [56] die Funktionentheorie ohne Verwendung des Jordanschen Kurvensatz3s aufgebaut haben. Diese Idee wurde von L. AHLFoRs [1] erneut aufgegriffen. R. NEVAN- LINNA und V. PAATERO gaben in [48] einen Aufbau der Funktionentheorie mit Hilfe von Elementardeformationen, wodurch unnötige topologische Schwierig- keiten umgangen werden.

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