Partial Fraction Decomposition by Repeated Synthetic Division

Kim, Youngsoo; Lee, Byunghoon

doi:10.4236/ajcm.2016.62016

Cited by 1 publication

(1 citation statement)

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“…Partial fraction decomposition is also a topic that is commonly taught to school and university students with applications in differential calculus, differential equations and other mathematics subject areas (Kim & Lee, 2016). Hypothetically, every rational function has a distinct PF decomposition but decomposing a rational function into PF can be an intensive exercise.…”

Section: Stage IImentioning

confidence: 99%

Analysis of Students’ Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform

Msomi

Bansilal

2022

INT ELECT J MATH ED

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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.

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Section: Stage IImentioning

confidence: 99%