Polynomial Approximation of Functions: Historical Perspective and New Tools |
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Authors: | Ivy Kidron |
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Institution: | (1) Department of Applied Mathematics, Jerusalem College of Technology, Jerusalem, Israel |
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Abstract: | This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual
interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation,
were taught according to their historical development, and the students tried to follow the thinking process of the creators
of the theory. They used a Computer Algebra System to manipulate algebraic expressions and generate a wide variety of dynamic
graphics; thus21st century technology was applied in order to “walk” with the students from the period of Euler in 1748 to
the period of Runge in 1901. We describe some situations in which the combination of dynamic graphics,algorithms, and historical
perspective enabled the students to improve their understanding of concepts such as limit, convergence, and the quality of
approximation.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | animation approximation CAS (Computer Algebra System) historical perspective interpolation limit |
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