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Analysis by Norbert Steinmetz

Analysis

by Norbert Steinmetz
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Book cover type: Paperback
  • ISBN13: 9783662680858
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 406
  • Original Price: EUR 32.701
  • Language: German
  • Edition: 2024
  • Item Weight: 590 grams
  • BISAC Subject(s): Mathematical Analysis

Das Buch wendet sich sowohl an Studierende aller mathematischen Fachrichtungen und mathematisch interessierte Studierende der Physik als auch an Dozentinnen und Dozenten, die den Aufbau ihres ersten Analysiskurses noch vor sich haben oder Anregungen für ihre Vorlesungen suchen. Inhalt und Form sind entstanden und vielfach erprobt in immer wieder kritisch veränderten und angepassten 3-semestrigen Analysiskursen. Etwa 2/3 des Buches decken die Erfordernisse einer 2-semestrigen Grundvorlesung Analysis ab, wohingegen das restliche Drittel Elemente der Fourieranalysis, der Differentialgeometrie, der gewöhnlichen Differentialgleichungen und der Funktionentheorie behandeln, Themen, denen eigenständige Vorlesungen auch weiterhin zu wünschen sind. Zu den Besonderheiten zählen die parallele und miteinander verzahnte Einführung des Riemann- und Lebesgueintegrals, die Einbettung einfacher Elemente der komplexen in die reelle Analysis, ausgedehnte Anwendungen - von der Heisenbergschen Unschärferelation über die Lösung der Wärmeleitungsgleichung bis hin zur Black-Scholes-Formel - sowie die Darstellung der Methode von Ostrogradski und des Dixon-Beweises der allgemeinen Cauchyschen Integralformel. Dass an verschiedenen Stellen die eingefahrenen Pfade verlassen wurden, wird der kundigen Leserschaft nicht verborgen bleiben. Die Frage "abstrakt oder anschaulich-verständlich" wird konsequent zugunsten des letzteren entschieden. Die Übungsaufgaben sind in den laufenden Text eingebaut in der Hoffnung, dass sie so mehr Beachtung finden. Schlie lich vermitteln die historischen Anmerkungen und Kurzbiographien einen Eindruck davon, wie die Analysis sich entwickelt hat und wer wesentlich an dieser Entwicklung beteiligt war.

Norbert Steinmetz ist Professor (em) der Mathematik an der TU Dortmund. Sein Arbeitsgebiet umfasst die Funktionentheorie, insbesondere die Nevanlinnatheorie, das Gebiet der gewönlichen Differentialgleichungen im Komplexen und die Theorie der komplexen dynamischen Systeme.

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