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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. 4851. ISSN 00255785

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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 numbercrunching and dynamic graphical
display.
Item Type:  Journal Article  

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:  00255785  
Official Date:  1986  
Dates: 


Volume:  Vol.11  
Page Range:  pp. 4851  
Status:  Not Peer Reviewed  
Access rights to Published version:  Open Access  
Related URLs:  
References:  1. H Neill & H Shuard : Teaching Calculus (Blackie) 1982 

URI:  http://wrap.warwick.ac.uk/id/eprint/498 
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