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Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2017

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

Descriptors: Mathematics Instruction, Fractions, Teaching Methods, Problem Solving

Man, Yiu-Kwong; Poon, Kin-Keung – International Journal of Mathematical Education in Science and Technology, 2014

In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/x and tan(x)/x as x approaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the…

Descriptors: College Mathematics, Mathematics Instruction, Undergraduate Students, Calculators

Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2012

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

Descriptors: Computers, Algebra, Mathematics, Mathematical Formulas

Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2012

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…

Descriptors: Undergraduate Students, Number Concepts, Problem Solving, Mathematics Instruction

Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2012

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

Descriptors: Tests, Algebra, Equations (Mathematics), Foreign Countries

Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2009

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

Descriptors: Equations (Mathematics), Computation, Secondary School Mathematics, College Mathematics

Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2007

A simple algorithm for computing the partial fraction expansions of proper rational functions with multiple poles is presented. The main idea is to use the Heaviside's cover-up technique to determine the numerators of the partial fractions and polynomial divisions to reduce the multiplicities of the poles involved successively, without the use of…

Descriptors: Calculus, Mathematics, Computation, Methods

Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2004

In this note, a modified Golomb algorithm for computing unit fraction expansions is presented. This algorithm has the advantage that the maximal denominators involved in the expansions will not exceed those computed by the original algorithm. In fact, the differences between the maximal denominators or the number of terms obtained by these two…

Descriptors: Computers, Mathematics