Laplace Transform in Mathematics and Electrical Engineering: A Praxeological Analysis of Two Textbooks on the Differential Equations and Signal Processing

Abstract

Abstract—Contribution: Although a limited number of studies have compared textbooks used in introductory science courses (ISCs) and technical engineering courses (TECs), such a study has not been conducted regarding the Laplace transform (LT). The LT is one of the important topics that electrical engineering students learn as part of their undergraduate degree. It is instrumental in both ISCs (e.g., differential equations (DEs)) and TECs (e.g., signal processing (SP)). Background: Textbooks stand as one of the main resources for teaching and learning mathematics. Previous research has highlighted differences in how mathematical concepts are discussed in ISCs and TECs. These disparities might hinder students’ opportunities to learn mathematics and identify the importance of mathematics in engineering. Intended Outcomes: The findings have the potential to increase awareness of mathematics and engineering instructors regarding the teaching and learning of the LT in ISCs and TECs. Additionally, it could result in the identification of several suggestions for textbook authors of DEs and SP, ultimately contributing to the improvement of engineering education for (electrical) engineering students. Application Design: This study uses the praxeological analysis rooted in the Anthropological Theory of the Didactic to analyze two textbooks. One is tailored for teaching and learning DEs, while the other addresses teaching and learning SP, a mandatory course for electrical engineering students in many countries. Findings: The findings indicate that there are several differences between the two textbooks, including differences in the purpose/motivation of presenting this topic and the definitions provided for the LT.