AN EPISTEMOLOGICAL ANALYSIS OF THE CONCEPT OF IMPROPER INTEGRAL
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Abstract
An improper integral is the generalization of a definite integral on an unlimited domain or the integrand that approaches infinity at one or more points in the range of integration. Improper integrals cannot be computed using a normal Riemann integral. This paper presents an epistemological analysis of the history of developing and forming the concept of improper integral, which helps determine the epistemological characteristics of an improper integral and some challenges students may face when learning the improper integral.
Keywords
epistemological analysis, epistemological characteristics, improper integral, limit, challenges for students
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References
Boyer, C. B. (1968). A History of Mathematics, NewYork.
Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes en mathématiques. Recherches en Didactique des Mathématiques, 4(2), 141-163.
Jahnke, H. N. (2016). A History of Analysis. History Of Mathematics, 24, American Mathematical Society and London Mathematical Society, 60-61.
Katz, V. J. (2009). A History of Mathematics – An Introduction. 3rd Edition, Pearson Education, Inc.
Le, V. T. (2003). A new perspective on the process of teaching the concept of mathematics [Cách nhìn mới về tiến trình dạy học khái niệm toán học]. Journal of Education, 64, Hanoi.
Mancosu, P. (1996). Philosophy of Mathematics & Mathematical Practice in the Seventeenth Century. New York and Oxford: Oxford University Press.
Nguyen Dinh Phu, Nguyen Cong Tam, Dinh Ngoc Thanh, & Dặng Duc Trong (2012). Syllabus of Analysis of functions of a single variable [Giao trinh Giai tich Ham mot bien]. Viet Nam National University Ho Chi Minh City Press.
Paradís, J., Pla, J., &Viader, P. (2004). Fermat and the Quadrature of the Folium of Descartes. The American Mathematical Monthly, 111(3), 216-229.
Pham Hoang Quan, Dinh Ngoc Thanh, & Dang Duc Trong (2011). Analysis of functions of a single variable, Part 2 – Integral – Number Series – function sequences – function series [Giai tich ham mot bien Phan 2 – Tich phan – Chuoi so – Day ham – Chuoi ham]. Viet Nam National University Ho Chi Minh City Press.
Stewart, J. (2016). Calculus. Eighth Ed. Boston: Cengage Learning, 568-571.
Tran Luong Cong Khanh (2006). La notion d’intégrale dans l’enseignement des mathématiques au lycée: une étude comparative entre la France et le Vietnam. Thèse, Université Joseph Fourier, Grenoble, France.