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Direct linkCunningham, Daniel W. – International Journal of Mathematical Education in Science and Technology, 2018
Modern calculus textbooks carefully illustrate how to perform integration by trigonometric substitution. Unfortunately, most of these books do not adequately justify this powerful technique of integration. In this article, we present an accessible proof that establishes the validity of integration by trigonometric substitution. The proof offers…
Descriptors: Mathematics Education, Trigonometry, Calculus, Mathematical Concepts
Adams, Margaret Smolinka – ProQuest LLC, 2013
This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using…
Descriptors: Case Studies, Knowledge Level, Mathematical Concepts, Calculus
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
Pavao, H. Germano; Capelas de Oliveira, E. – International Journal of Mathematical Education in Science and Technology, 2008
We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)
Descriptors: Trigonometry, Calculus, Mathematics Instruction, Computation
Herman, S.; Maceli, J.; Rogala, M.; Yurekli, O. – International Journal of Mathematical Education in Science and Technology, 2008
In the present note, two Parseval-type relations involving the Laplace transform are given. The application of the relations is demonstrated in evaluating improper integrals and Laplace transforms of trigonometric functions.
Descriptors: Trigonometry, Calculus, Equations (Mathematics), Mathematical Concepts
Hogben, Lancelot – Educ Sci Int J, 1969
Descriptors: Calculus, Educational Change, Mathematical Logic, Mathematical Vocabulary
Siadat, M. Vali – AMATYC Review, 2006
In terms of modern pedagogy, having visual interpretation of trigonometric functions is useful and quite helpful. This paper presents, pictorially, an easy approach to prove all single angle trigonometric identities on the axes. It also discusses the application of axial representation in calculus--finding the derivative of trigonometric functions.
Descriptors: Trigonometry, Calculus, Mathematics Instruction, Mathematical Concepts
Download full textArizona State Dept. of Education, Phoenix. – 1992
This document ties the essential skills needed in mathematics to the National Council of Teachers of Mathematics' (NCTM) Curriculum and Evaluation Standards to help facilitate future curriculum development. The overall goal for the 21st century is to make mathematical power a reality for all students. The rationale for this document can be found…
Descriptors: Algebra, Calculus, Curriculum Development, Educational Assessment
