2.13 Newton's Method
By the end of your studying, you should know:
On-screen applet instructions:
Type a starting value followed by the Enter key. Try different starting values and observe the effect. Can you explain what happens when the starting value is 1?
ExamplesConsider the equation
and say you intend to solve it using Newton's method. If the initial value chosen is not 0, what will happen when you apply Newton's method?
VideosSee short videos of worked problems for this section.
ExercisesSee Exercises for 2.13 Newton's Method (PDF).
Work online to solve the exercises for this section, or for any other section of the textbook.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Although we are studying real-valued functions of a real variable, Newton's Method can be applied to complex numbers as well. The results yield some interesting pictures that show so-called Newton Basins, the set of iterative points leading to the solution.
|2.12 Derivatives of Exponential and Logarithm Functions||Table of Contents||2.14 Linear Approximations|
Software requirements: For best results viewing and interacting with this page, get the free software listed here.
Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel