A new perspective on teaching the natural exponential to engineering students

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

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 11, 2022
• 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