Exactness: A Concept Important for Engineering Applications or a Source of Potential Difficulties?

Abstract

Contribution: This article identifies possible ruptures between the ways fundamental notions of exact differential and exact differential equations (EDEs) are employed in mathematics courses and professional engineering disciplines. Background: Engineering students often experience difficulties with mathematics courses which may even lead to dropout from engineering programs. Students also face problems applying acquired mathematics knowledge in professional courses. Research is needed to understand how fundamental mathematics concepts are used in advanced engineering courses. Research Questions: How are the notions of exact differential and EDEs used in mathematics and engineering courses? What potential learning difficulties originate from different institutional practices and how can they be addressed? Methodology: The anthropological theory of the didactic is employed to analyze how six different STEM disciplines approach fundamental concepts of exact differential and EDEs. Distinctions in praxeologies associated with different institutions reveal possible learning difficulties students face relating new knowledge in engineering disciplines to that acquired in mathematics courses. Findings: Student learning can be facilitated by bridging the way exact differentials are introduced in Calculus and Differential Equations. Student conceptual understanding can be facilitated through the cross-disciplinary collaboration between mathematicians and engineers in the development of new courses and study programs.