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Grundkurs Funktionentheorie: Eine Einführung in Die Komplexe Analysis Und Ihre Anwendungen

Grundkurs Funktionentheorie: Eine Einführung in Die Komplexe Analysis Und Ihre Anwendungen

          
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About the Book

Die Analysis findet ihre Vollendung in der komplexen Funktionentheorie, die durch ihre Kraft, Eleganz und Geschlossenheit besticht. Manche Rätsel aus dem Reellen können damit aufgelöst werden, manch schwierige Integrationsaufgabe wird dank neuer, mächtiger Hilfsmittel zum Kinderspiel.

Der "Grundkurs Funktionentheorie" präsentiert in seinen ersten drei Kapiteln (Holomorphe Funktionen, Integration im Komplexen und isolierte Singularitäten) ohne Umwege die wichtigsten Elemente der komplexen Analysis von einer Veränderlichen, vom Rechnen mit komplexen Zahlen über die Grundzüge der verblüffend wirkungsvollen Cauchy-Theorie bis hin zum Residuensatz.

Ausgerüstet mit diesen Werkzeugen erfährt der Leser im vierten Kapitel, wie analytische Funktionen mit vorgegebenen Nullstellen und Polstellen konstruiert werden, als Beispiele dafür werden die Gamma-Funktion und die elliptischen Funktionen behandelt. Konforme Abbildungen werden schon sehr früh eingeführt und dann mit den immer perfekter werdenden Methoden weiter vertieft. Das abschließende fünfte Kapitel über geometrische Funktionentheorie stellt Zusammenhänge zwischen konformen Abbildungen und der Topologie ebener Gebiete her und zeigt, wie analytische Funktionen mit Hilfe des Spiegelungsprinzips auf immer größere Gebiete fortgesetzt werden können.

Wie im Grundkurs Analysis wird viel Wert auf die didaktische Ausarbeitung gelegt, vor allem aber begleiten den Text von Anfang an Ausflüge in die Welt der Anwendungen. Zahlreiche Übungsaufgaben und Illustrationen runden das Bild ab.

Das Buch wendet sich an Diplom-, Bachelor- und Masterstudierende in Mathematik, Naturwissenschaften und Informationstechnologie. Es ist geeignet zum Selbststudium, als Begleitlektüre und zur Prüfungsvorbereitung.


About the Author: Prof. Dr. Klaus Fritzsche forscht und lehrt Mathematik an der Universität Wuppertal mit dem Schwerpunkt "Komplexe Analysis von mehreren Veränderlichen". Von Anfang an wirkte er beim Bologna-Prozess mit, also bei der Realisierung von Bachelor- und Master-Studiengängen.


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Product Details
  • ISBN-13: 9783827419491
  • Publisher: Spektrum Akademischer Verlag
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 13 mm
  • Width: 168 mm
  • ISBN-10: 3827419492
  • Publisher Date: 09 Dec 2008
  • Height: 239 mm
  • No of Pages: 334
  • Series Title: 0
  • Weight: 557 gr


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