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Deposit #94
A Streaming Video

Michael
Krebs, CSULA
Jamie
Pommersheim, Reed College 

The Definition of the Limit: A Streaming Video

Stream the video here:
Download the video here:
We
invite you to download
this video to your laptop for use into the classroom. 
Turn on your audio
and be patient. The speed of your internet
connection makes a difference.
Note: If your connection has problems streaming in RealOne
Player, try downloading to the "mp4" format.
Windows Media Player version 8 or greater is recommended. If not
installed on your computer a free
download is available.

A message to faculty:
We
present a short video which may be used in a Calculus, Analysis, or
History of Math. After first discussing the historical
development of the epsilondelta definition, the video then briefly
takes students through the underlying visual logic.
We
wish to reassure faculty that we consider the video as only an initial
introduction to a definition of the limit. We leave it to the classroom
professor to lead students in a precise discussion of rigor in
the theory of limits.

"One magnitude is
said to be the limit
of another magnitude when the second may approach the first within any
given magnitude, however small, though the second magnitude may never
exceed the magnitude it approaches."
D'Alembert
in
his
article on the term limit in
the famous French Encyclopédie.


Errata:
 Spelling error:
"Issac Newton" should be "Isaac Newton."
 The precise quote
from Berkeley is: "And what are these Fluxions . . . may we not call
them the ghosts of departed quantities?"
 Weierstrass
(18151897), the "father of modern
analysis," was working in the mid to late
1800's. His "ε  δ" terminology has become standard
universal notation.


Useful
Links and Book

James Stewart, Calculus, 5th ed,.
Thomson Brooks/Cole, 2003, p. 92. Read "The Precise Definition of
a Limit."

David M. Burton, The
History of Mathematics, 6th ed., McGraw Hill, 2007, pp.
602608. Read "The Age of Rigor: D'Alembert and Cauchy on Limits."

Howard Eves, An Introduction to
the History of Mathematics, 6th ed,. The Saunders College
Publishing, 1990.

Victor J.
Katz, A Brief History
of Mathematics, BRIEF VERSION, Pearson
Addison
Wesley, 2004, p. 356; 432433.

If you enjoyed the streaming video on Definition
of the Limit, we suggest you also view two other important
calculus videos in the NCB.
Geometric Series 
Convergence
Robert Meyer < http://winmedia2.calstatela.edu/GRAY/Geometric.wmv
>
Harmonic Series 
Divergence
Michael Krebs and Jeffrey L. Dergidge < http://curvebank.calstatela.edu/hseries/hseries.htm
> 
Information Technology Services,
Taping and Editing by
Shirley
Gray, Producer
William
Stellmacher, Director
Dennis Kimura,
Graphics
Yarimar
RodasCordova, Video Editor



