Abstract
Laplace transform (LT) is an essential mathematical tool for solving linear ordinary differential equations (ODE) with boundary values, by transforming differential equation into algebraic equations which are easier to manipulate. In this article, we analyse the errors students make and misconceptions they have in solving linear ODE using LT method. The study participants were 81 students enrolled in an engineering mathematics course at a University of Technology in South Africa. The students’ responses to an item based on LT which formed part of an assessment, were analysed. The analysis identified three stages of working that were necessary to reach a solution (introduction of LT and simplification; resolution of expressions using partial fractions (PF); carrying out the inverse LT and manipulations). Within each stage, we distinguished between three types of errors (conceptual, procedural and technical). The results showed that students experienced most problems when working in the PF layer because of the poor background in manipulation of algebraic expressions. It is recommended that students are given opportunities to develop fluency in pre-requisite concepts, so that their efforts at solving problems using LT or other advanced mathematics techniques can be less stressful.
Highlights
The Laplace transformation (LT) is one of the methods that can be used to solve the nonhomogeneous linear ordinary differential equations (ODE) with the given boundary conditions (Deller, 2009)
The study shown that the engineering mathematics students make numerous errors in solving linear ordinary differential equations with constant coefficients using the method of the LT
In considering the 17 who reached the third stage of applying the inverse LT, 6 (35%) were successful
Summary
The Laplace transformation (LT) is one of the methods that can be used to solve the nonhomogeneous linear ordinary differential equations (ODE) with the given boundary conditions (Deller, 2009). Students make numerous errors in the process of solving equations. They do not commit these errors only because of careless mistakes but through intelligent generalisations based on a misunderstanding of underlying concepts (Naseer, 2015). It is important that instructors are conscious of the correct and incorrect conceptions students have regarding the concept of LT, and potential errors and misconceptions (Almog & Ilany, 2012). This might assist instructors to avoid the creation of such errors and misconceptions, but to remedy those errors and misconceptions (Welder, 2012)
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