Product ID: 99716

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# Newton's Method and Fractal Patterns (UMAP)

### Author: Philip D. Straffin, Jr

This module discusses Newton's method as an efficient iterative procedure for approximating zeros of a differentiable function. It claims that Newton's method is intricate even for real polynomials, and in the complex plane it generates beautiful fractal patterns.** Table of Contents:HOW DOES NEWTON'S METHOD BEHAVE IN THE LARGE?NEWTON'S METHODNEWTON'S METHOD IN THE LARGE: AN EXAMPLE ON THE REAL LINENEWTON'S METHOD IN THE COMPLEX PLANEFURTHER DIRECTIONSSOLUTIONS TO THE EXERCISESREFERENCESACKNOWLEDGMENTSABOUT THE AUTHOR**

©1992 by COMAP, Inc.

UMAP Module

22 pages

#### Mathematics Topics:

Calculus

#### Application Areas:

Fractals, Chaotic Dynamics

#### Prerequisites:

Derivatives of polynomials and rational functions; derivative as a linear approximation

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