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Geometrisch argumentieren in der Analysis

In: Freude an Geometrie – Zum Gedenken an Hans Schupp

Author

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  • Manfred Schmelzer

Abstract

Zusammenfassung Die Ableitungen und Integrale der elementaren Basisfunktionen u. a. der Sinus-, Potenz- und Exponentialfunktionen werden geometrisch hergeleitet. Die Skalierung von Funktionsgraphen überträgt sich auf deren Tangenten und Integralflächen. Dabei treten Grenzwerte, h-Methode sowie Ober- und Untersummen in den Hintergrund. Alle vorgestellten Herleitungen verzichten auf den Hauptsatz der Differential- und Integralrechnung. Getreu dem Motto „Bilder sagen mehr als tausend Worte“ soll die Perspektive in der Analysis von der formal-symbolischen zur konstruktiv-ikonischen Ebene verlagert werden.

Suggested Citation

  • Manfred Schmelzer, 2023. "Geometrisch argumentieren in der Analysis," Springer Books, in: Andreas Filler & Anselm Lambert & Marie-Christine von der Bank (ed.), Freude an Geometrie – Zum Gedenken an Hans Schupp, chapter 0, pages 249-262, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-67394-2_11
    DOI: 10.1007/978-3-662-67394-2_11
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