A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

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…

Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

In this paper we focus on Norwegian first-year engineering students' interpretations of differentials and definite integrals. Through interviews with 15 engineering students, we investigated how the students interpreted the different symbols involved in the Fundamental Theorem of Calculus (FTC), as displayed in the textbook used in their calculus…

Mechanical engineering, mechanical engineering technology, and related educational programs are not addressing in a sufficient way the principles associated with applying analytical investigations in solving actual engineering problems. Because of this, graduates do not have the adequate skills required to use the methods of applied dynamics in…

In this longitudinal study, we track student answers to a question from the Calculus Concept Inventory (CCI) pre- and post-instruction in Calculus I as well as an analogous question in the next semester framed in the context of Aerospace Engineering or Chemical Engineering. Nearly 88% of the students who answered the post-CCI question correctly…

The literature describes different stances concerning the focus on how mathematics should be taught, with some preferring a conceptual knowledge approach and others a procedural knowledge approach. The current study investigated the relationship between students' conceptual and procedural knowledge in a calculus context. To better understand the…

This article shows results on the simulation of partial differential equations such as the heat equation, the Laplace equation and the wave equation in a course called mathematical methods at a university in Bogotá Colombia. In this course, the concept of partial differential equations and different solution methods were explained to them, both in…

Methods of teaching differential equations (DE) have long focused on rote analytic solution methods that align poorly with more industry-relevant numerical and computational methods. Engineering and mathematics educators agree that there is a need to shape DE curricula to reflect the mathematical practices of the disciplines whose students take…

This research paper explores the integration of ChatGPT as a tool for interactive learning of numerical methods in a differential equations (DEs) course. DE course is crucial for engineering students to model real-world phenomena. However, many DE courses focus only on analytical solutions and neglect important numerical solutions. To overcome…

Retrieving information from memory increases the likelihood the information will be remembered later. The strategic use of retrieval to enhance memory is known as retrieval practice. Teachers can exert considerable control over students' retrieval practice, dictating when and how much students practice. Laboratory research has shown that retention…

This paper presents a study of correlation between subjects of Diploma in Electrical Engineering (Electronics/Power) at Universiti Teknologi MARA(UiTM) Cawangan Terengganu using Artificial Neural Network (ANN). The analysis was done to see the effect of mathematical subjects (Pre-calculus and Calculus 1) and core subject (Electric Circuit 1) on…

In this paper, we present a "route of activities" mainly addressed to first and second year engineering students attending the basic mathematics courses. These activities are intended to be a tool both for students and teachers. On the one hand, they should help the students to acquire a deeper understanding of the mathematical ideas and…

The purposes of calculus courses are often the acquisition of knowledge itself, the development of skills and the understanding of important concepts, such as functions, derivatives, the chain rule, integrals and the fundamental theorem of calculus. However, full conceptual understanding is frequently not achieved. In this article, we examine the…