Microworld: Calculus
in Action: Chapter 1, Section 2: Newton's Method
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above to visit the Microworld.
Author:James
E. White
When
you put Mathematics to use to solve even fairly simple problems, you often
encounter difficulties like the one described in the Ballistics microworld.
To find the angle 
that gives the greatest range for a projectile launched from an altitude of
10 meters with speed V, we have to solve for 
in the equation:
In
fact, our best models usually give equations that we cannot solve directly.
This lecture will show you the steps that you might take in real life to draw
some conclusions in such a case. So we now discuss one of the nice uses of
the Calculus for solving problems like this one. It is called "Newton's
Method." We will explore how you may use it to approximate the solutions
of equations of the form:
|
|
where 
is some differentiable function of a single variable 
.
Newton
asked the question: How do I solve the equation 
for 
?
It is an innocent question, and unfortunately, it has no general answer. His
Method makes use of a certain recursive sequence to get an approximation to
a solution.
The
following is the Table of Contents for this 5 page Microworld
- Section 2: Sequences and Iteration
- Section 2: Recursive Sequences
- Section 2: Newton's Recursive Method
- Symbolic Calculator
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| - James E. White, Ph.D. , Library Director, | ||
| author of this website, Mathwright 2000, MindScapes, | ||
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