Electronic Proceedings of the Eleventh Annual International Conference on Technology in Collegiate Mathematics

New Orleans, Louisiana, November 19-22, 1998

Paper C036

Newton Method and HP-48G

De Ting Wu

Departament of Math.
Morehouse College
830 Westview Dr. S.W.
Atlanta, GA 30314
Phone: (404) 681-2800 x2459

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Newton Method is an often-used procedure to find the approximate values of the solution of an equation. Now, it is covered by most textbooks of Calculus as an application of derivative.

When using Newton Method, usually we follow 3 steps:

It should be emphasized the Step 1 is significant and difficult. Since the sequence of approximations may not converge if the initial guess is selected blindly. And, some -time Step 2 is formidable if f(x) is complicated. Moreover, Step 3 always is a time-consuming job. However, HP-48G can help a lot when using Newton Method.

This approach is as follows:

  1. Use 'Plot Application' of HP-48G to graph the equation so that it is easy to locate the solution and make good initial guess.
  2. Use the program 'ITF' to set up the iterative formula. ITF:<< DUP x d/dx / x SWAP - 'NF' STO>>
  3. Use the program 'APV' to compute the approximate values. APV:<<NF -->NUM DUP 'X' STO>>

Finally, an example is given to illustrate this approach.

Also, this approach make it easy to grade the problem of Newton Method with different initial guess.

Keyword(s): numerical methods, HP48G