$$ {V}_B-{V}_A={\int}_A^Bf(x) dx $$. The Use of Integrals in Engineering Programmes: a Praxeological Analysis of Textbooks and Teaching Practices in Strength of Materials and Electricity and Magnetism Courses

Calculus is a required course in most engineering programmes and is intended to provide students with tools they will use throughout the rest of their training. However, research seems to indicate that calculus is not very prevalent in the engineering workplace or in university engineering courses. To shed some light on how calculus is actually used in engineering programmes, we analysed two courses (Strength of Materials and Electricity and Magnetism) to examine their use of integrals. We first conducted a praxeological analysis examining the introduction of two topics (bending moments and electric potential) in the courses’ textbooks before interviewing the teachers of each course to compare their praxeologies with those of the books. Our results show that integrals are used to introduce engineering notions in both courses, with praxeologies that combine elements from mathematics and engineering but that do not call upon calculus techniques to any great extent. Moreover, integrals do not factor highly in students’ assessments in either course, which implies that students may pass these courses without any knowledge of integrals as taught in their calculus courses.