Friday, October 7
−
Lecture 14 :
Newton’s iterative procedure.
(Refers to section 4.1
in your text)
Students who have mastered the content of this lecture know about
:
Newton’s iterative formula for
approximating roots of simple functions.
Students who have practiced the techniques presented in this lecture will be able to
:
Use
Newton’s
iterative formula for approximating roots of simple functions by estimating a root at first and then
construct a sequence of numbers which converges to a root, use a spreadsheet to construct such
sequences.
14.1
Newton’s iterative procedure for finding roots
−
Let
f
:
R
→
R
be a continuous
function.
We sketch the curve of
y
=
f
(
x
).
At first glance we can approximate a zero (root)
x
* of
y
=
f
(
x
) by roughly examining
where the curve of
y
=
f
(
x
) intersects the
x
axis.
Say our first approximation of the zero
x
* is denoted by
x
1
and we attempt to improve
on this approximation.

This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 RobertAndre
 Calculus, Continuous function, horizontal tangent line, x*, iterative procedure

Click to edit the document details