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A versatile approach to calculus and numerical methods
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Tall, David (1990) A versatile approach to calculus and numerical methods. Teaching Mathematics and Its Applications, Vol.9 (No.3). pp. 124-131. doi:10.1093/teamat/9.3.124 ISSN 0268-3679.
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Official URL: http://dx.doi.org/10.1093/teamat/9.3.124
Abstract
Traditionally the calculus is the study of the symbolic algorithms for differentiation and
integration, the relationship between them, and their use in solving problems. Only at
the end of the course, when all else fails, are numerical methods introduced, such as the
Newton-Raphson method of solving equations, or Simpson’s rule for calculating areas.
The problem with such an approach is that it often produces students who are very well
versed in the algorithms and can solve the most fiendish of symbolic problems, yet
have no understanding of the meaning of what they are doing. Given the arrival of
computer software which can carry out these algorithms mechanically, the question
arises as to what parts of calculus need to be studied in the curriculum of the future. It
is my contention that such a study can use the computer technology to produce a far
more versatile approach to the subject, in which the numerical and graphical
representations may be used from the outset to produce insights into the fundamental
meanings, in which a wider understanding of the processes of change and growth will
be possible than the narrow band of problems that can be solved by traditional symbolic
methods of the calculus.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Social Sciences > Institute of Education ( -2013) | ||||
| Library of Congress Subject Headings (LCSH): | Calculus, Mathematics -- Study and teaching, Computers -- Study and teaching | ||||
| Journal or Publication Title: | Teaching Mathematics and Its Applications | ||||
| Publisher: | Oxford University Press | ||||
| ISSN: | 0268-3679 | ||||
| Official Date: | 1990 | ||||
| Dates: |
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| Volume: | Vol.9 | ||||
| Number: | No.3 | ||||
| Page Range: | pp. 124-131 | ||||
| DOI: | 10.1093/teamat/9.3.124 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Open Access (Creative Commons) |
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