National Science Foundation
National Curve Bank

The Derivative

Deposit #9

Dr. Lou Talman


Caution: The following blank boxes may load slowly with the QuickTime animations.  Unless your computer setup is quite recent, you may need to update your version.  The current QuickTime version is v6.0.  It is free and available from  http://www.apple.com/quicktime/products/qt .  You have the choice of installing directly from the internet or downloading a standalone  installer.
 
 

The Derivative:  This particular graph has been printed in calculus texts for more than 200 years to introduce the concept and definition of the derivative.


slope equations

 
 

Moving Slope Triangle

An ellipse is the collection of all points in the plane the sum of whose distances 
( blue  +  red) from two fixed points, called the foci, is a constant.

Though the blue and red segments vary, their sum is constant.
Deposit # 9 Links and Books
The National Curve Bank thanks  Dr. LOU TALMAN for Deposit # 9.

Talman has generated a large collection of interesting animations.

Darryl K. Nester, Professor of Mathematics, Bluffton College, Bluffton, Ohio suggests the following site:       http://www.2dcurves.com/index.html .

Edwards, C. H., Jr.,  The Historical Development of the Calculus, Springer-Verlag, 1982.

Simmons, George F.,  Calculus GEMS: Brief Lives and Memorable Mathematics, McGraw-Hill,  1992.

Jean d'Alembert (1717 - 1783) published an article entitled  Différentiel in vol. 4 (1754) of the French Academy's Encyclopédie using notation that is very similar to modern usage but avoiding Leibniz's labyrinth of differentials.

dy/dx limit