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A new perspective on teaching the natural exponential to engineering students

Ullah, Mukhtar; Aman, Muhammad Naveed; Wolkenhauer, Olaf; Iqbal, Jamshed

Authors

Mukhtar Ullah

Muhammad Naveed Aman

Olaf Wolkenhauer



Abstract

The natural exponential and logarithm are typically introduced to undergraduate engineering students in a calculus course using the notion of limits. We here present an approach to introduce the natural exponential/logarithm through a novel interpretation of derivatives. This approach does not rely on limits, allowing an early and intuitive introduction of these functions. The question behind our contribution is whether one can introduce derivatives using only polynomials and power series? Motivated by an earlier exposure of engineering students to differential equations, we demonstrate that the natural exponential/logarithm can arise from two common differential equations. Our limit-free approach to derivatives provides an intuitive interpretation of (Formula presented.), the Euler number, and an intuitive introduction of time constants in first-order dynamical systems.

Citation

Ullah, M., Aman, M. N., Wolkenhauer, O., & Iqbal, J. (2021). A new perspective on teaching the natural exponential to engineering students. International Journal of Mathematical Education in Science and Technology, https://doi.org/10.1080/0020739X.2021.1896812

Journal Article Type Note
Acceptance Date Dec 1, 2020
Online Publication Date Mar 10, 2021
Publication Date 2021
Deposit Date Sep 14, 2021
Publicly Available Date Mar 28, 2024
Journal International Journal of Mathematical Education in Science and Technology
Print ISSN 0020-739X
Electronic ISSN 1464-5211
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1080/0020739X.2021.1896812
Keywords Exponential function; Logarithmic function; Power series; Ordinary differential equations
Public URL https://hull-repository.worktribe.com/output/3796845

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