Infinitesimalrechnung
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Infinitesimalrechnung: Analysis mit hyperreellen Zahlen

Infinitesimalrechnung: Analysis mit hyperreellen Zahlen


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About the Book

In diesem Buch erfahren Sie, wie die Differential- und Integralrechnung schon nach einem einfachen Einstieg mit Hilfe infinitesimaler und infiniter Zahlen und ohne Grenzwertprozesse erlernt werden kann. Sie folgen dabei den intuitiven Vorstellungen der Urväter der Analysis, allerdings in logisch einwandfreier Weise. Dies ist möglich, seit Abraham Robinson in den 1960er-Jahren gezeigt hat, dass die Menge der reellen Zahlen widerspruchsfrei um zusätzliche Elemente zur Menge der hyperreellen Zahlen erweitert werden kann. Die hyperreellen, insbesondere die infinitesimalen, Zahlen haben mehrere didaktische Vorteile: Sie sind anschaulich, der abstrakte Grenzwertformalismus entfällt, und sie stellen ein produktives Werkzeug dar, denn die Regeln können errechnet werden (und müssen nicht erst erraten und dann bewiesen werden). Für Interessierte werden zusätzlich auch tiefer gehende Zugänge zu den hyperreellen Zahlen aufgezeigt. Die vorliegende zweite Auflage ist vollständig durchgesehen, didaktisch weiter verbessert und um zusätzliche Beispiele des Einsatzes von hyperreellen Zahlen ergänzt.

Table of Contents:
Einleitung.- Hyperreelle Zahlen.- Differentialrechnung.- Integralrechnung.- Transzendente Funktionen.- Unendliche Reihen.- Sachverzeichnis.

About the Author :
Peter Baumann studierte an der Technischen Universität Berlin; er arbeitete an verschiedenen Schulen des Sekundarbereichs und war stellvertretender Schulleiter am Hermann-Ehlers-Gymnasium in Berlin. Dr. Thomas Kirski studierte an der Freien Universität Berlin und wurde dort 1991 promoviert. Er war als Gymnasiallehrer tätig, seit 2005 als Fachbereichsleiter Naturwissenschaften am Hans-Carossa-Gymnasium, Berlin. Er starb kurz vor Erscheinen dieses Buches.


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Product Details
  • ISBN-13: 9783662645703
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Springer Spektrum
  • Edition: Revised edition
  • Language: German
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 366264570X
  • Publisher Date: 10 Jun 2022
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 295
  • Sub Title: Analysis mit hyperreellen Zahlen


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