An introduction to differentials based on hyperreal numbers and infinite microscopes

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we propose to introduce the differential of a function through a non-classical way, lying on hyperreals and infinite microscopes. This approach is based on the developments of nonstandard analysis, wants to be more intuitive than the classical one and tries to emphasize the functional and geometric aspects of the differential. In the second part of the work, we analyze the results of an experiment made with undergraduate students who had been taught calculus by a non standard way for nearly two years.

Original languageEnglish
Pages (from-to)39-49
Number of pages11
JournalPrimus
Volume20
Issue number1
DOIs
Publication statusPublished - 1 Jan 2010

Keywords

  • Differential
  • Hyperreal numbers
  • Infinite microscope
  • Nonstandard analysis

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