Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-11T04:05:27.630Z Has data issue: false hasContentIssue false
  • English
  • Français

Cubics, chaos and Newton's method

Published online by Cambridge University Press:  01 August 2016

Thomas Dence
Thomas Dence*
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30606, USA
Get access Rights & Permissions [Opens in a new window]

Extract

It is common today for students in elementary calculus to possess a powerful graphics calculator, such as the TI-82. These machines have had a dramatic impact on how teachers present the subject. The teacher population is clearly divided when it comes to the emphasis on the use of the calculators. There are instances, though, where it is difficult to argue with the calculator's effectiveness as a teaching tool in calculus. One such case is in using Newton's method to find the roots of an equation, for once the algorithm is presented, it is merely a matter of performing the numerical calculations for the sequence of iterates, and this is an operation that the TI-82 does very well.

Type
Articles
Information
The Mathematical Gazette , Volume 81 , Issue 492 , November 1997 , pp. 403 - 408
Copyright
Copyright © The Mathematical Association 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Dunnett, Ray Newton-Raphson and the cubic, Math. Gaz. 78 (November 1994) pp. 347–348.Google Scholar
2. Edwards, C. H. and Penney, D. Calculus with analytic geometry 4th edition, Prentice-Hall (1994) pp. 189–192.Google Scholar
3. Devaney, Robert Chaos, fractals, and dynamics: computer experiments in mathematics, Addison-Wesley, (1990).Google Scholar
4. Ruelle, D. Elements of differentiable dynamics and bifurcation theory, Academic Press (1989) p. 71.Google Scholar