CWT Vol. 2 - Newton's Apple - finished at last
wdfla...@aol.com
great.......I think.....available from me (see below) on on EBAY...
>>>>>>>>>INTRODUCTION
In 1680 Isaac Newton watched as an apple fell from a tree, and went on
to discover the Law of Gravity and the Laws of Motion. Applying these
laws to the analysis of a falling apple he wrote a differential
equation that characterized the apple's motion. In Chapter 1 we
retrace Newton's steps to arrive at this differential equation.
The motion of a falling apple, however, is not constant velocity
motion, and the techniques we learned in CWT Vol. 1 will not solve the
differential equation for its trajectory. In CWT Vol 2, we add to
the repertoire of functions we can differentiate and integrate, and
differential equations we can solve, to include the differential
equation for a falling apple.
One of the unique features of the CWT series is that differential
equations are studied from the beginning. Many of the laws of physics
are written as differential equations, starting with F = M*A, the
equation that launched modern science. One of the reasons that
differential equations are delayed for so long, almost indefinitely, in
the standard curriculum, is that even an innocuous looking differential
equation can be very difficult to solve. Many of the differential
equations I encountered as an engineer for twenty years in the
aerospace industry were not only difficult, they were impossible to
solve. That is, to solve exactly, but, they were easy to solve
approximately! In fact, the method of linear approximation will solve
any differential equation; it's based on the equation 'distance =
velocity * time" from constant velocity motion. Best of all, it's
easy; it's covered in Chapter 2 in CWT Vol. 2!
The method of linear approximation can be used to solve any
differential equation, and it also is the basis for demonstrating the
most important differentiation rules and The Fundamental Theorem of
Calculus (in CWT Vol. 3). All from the equation 'distance = velocity *
time'!
Calculus is the mathematics of motion, and we use it to analyze the
following types of motion, a falling object acted on by gravity along,
a falling object acted on by gravity and drag, a spring-mass assembly,
and the moon in its orbit. More generally, calculus is the mathematics
of change, and we also analyze changing current and voltage in an
electrical circuit.
We studied constant velocity motion in Vol. 1, and one of the reasons
it was so easy is that everything there is to know about constant
velocity motion is contained in the formula 'distance = velocity *
time'. In Vol. 2 we study some interesting and less transparent
examples of motion and change that demonstrate more of the power of
calculus.
>>>>>>>>>>>>>
To buy CWT Vol 2 send $14.95 + $3.00 s/h to W.D.Flannery, 529 Bonnie
Dr., El Cerrito, CA, 94530, or send 17.95 via PayPal to
wdfla...@aol.com. Or buy it on EBAY.
Angela Rodriguez
Start your day with Yahoo! - make it your home page
harold marsh
harold marsh
haro...@tds.net
>
517-394-0524
michael archer
your list.
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com
tim halladay
Betty Traciak
From: <wdfla...@aol.com>
To: <CalculusWi...@googlegroups.com>
Sent: Friday, July 22, 2005 11:55 AM
Subject: CWT Vol. 2 - Newton's Apple - finished at last
>
Vinod Patel
-
Akash Goel received a perfect math score of 800 in six hours of Vinod Patel's tutoring
-
Vinod Patel