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A graphical approach to integration and the fundamental theorem
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Tall, David (1986) A graphical approach to integration and the fundamental theorem. Mathematics Teaching, Vol.11 . pp. 48-51. ISSN 0025-5785.
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Abstract
In ‘Understanding the Calculus’ 3 I suggested how the concepts of the calculus could be approached globally using moving computer graphics. The idea of area under a graph
presents a fundamentally greater problem than that of the notion of gradient. Each numerical gradient is found in a single calculation as a quotient f(x+h)-f(x)h but the calculation of the approximate area under a graph requires many intermediate calculations. Using algebraic methods the summation in all but the simplest examples becomes exceedingly difficult. A calculator initially allows easier numerical calculations but these can become tedious to carry out and obscure to interpret. Graduating to a computer
affords insight in two ways: through powerful number-crunching and dynamic graphical
display.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Social Sciences > Institute of Education ( -2013) | ||||
Library of Congress Subject Headings (LCSH): | Mathematics -- Study and teaching, Mathematics -- Graphic methods, Calculus | ||||
Journal or Publication Title: | Mathematics Teaching | ||||
Publisher: | Association of Teachers of Mathematics | ||||
ISSN: | 0025-5785 | ||||
Official Date: | 1986 | ||||
Dates: |
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Volume: | Vol.11 | ||||
Page Range: | pp. 48-51 | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Related URLs: |
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