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Grundkurs Funktionentheorie

Grundkurs Funktionentheorie


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About the Book

Dieser Grundkurs Funktionentheorie präsentiert in seinen ersten drei Kapiteln ohne Umwege die wichtigsten Elemente der komplexen Analysis einer Veränderlichen, von den komplexen Zahlen über die Grundzüge der Cauchy-Theorie bis hin zum Residuensatz.

Darauf aufbauend werden im vierten Kapitel analytische Funktionen mit vorgegebenen Nullstellen und Polstellen konstruiert, zum Beispiel die Gamma-Funktion und die elliptischen Funktionen. Das abschließende fünfte Kapitel über geometrische Funktionentheorie stellt Zusammenhänge zwischen konformen Abbildungen und der Topologie ebener Gebiete her und zeigt, mit welchen Mitteln analytische Funktionen über ihren Definitionsbereich hinaus fortgesetzt werden können.

Viel Wert wird auf die didaktische Ausarbeitung gelegt, und jedes Kapitel endet zudem mit einer passenden Auswahl von Anwendungen aus der Mathematik, Physik oder den Ingenieurwissenschaften. Zahlreiche Illustrationen und Übungsaufgaben samt Lösungen runden das Bild ab.

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

Für die vorliegende dritte Auflage wurde der Text komplett durchgesehen, an vielen Stellen korrigiert und didaktisch weiter optimiert, um den Runge'schen Approximationssatz und seine Anwendungen ergänzt sowie um eine Einführung in Riemannsche Flächen und den Garbenbegriff.

Der Autor

Klaus Fritzsche ist Autor zahlreicher erfolgreicher Lehrbücher, u.a. des beliebten Brückenkurses "Mathematik für Einsteiger" und der Grundkurse Analysis 1/2.


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Product Details
  • ISBN-13: 9783662700921
  • Publisher: Springer
  • Binding: Paperback
  • No of Pages: 425
  • Sub Title: Eine Einführung in Die Komplexe Analysis Und Ihre Anwendungen
  • ISBN-10: 3662700921
  • Publisher Date: 16 Oct 2024
  • Language: German
  • Returnable: Y


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