
Product No.
99766 
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Using Original Sources to Teach the Logistic Equation (UMAP)
Bonnie Shulman

Mathematics Topic: Calculus, Differential Equations 
Application Areas: Mathematical modeling, biology 
Prerequisites: Calculus (differentiation, integration of elementary functions) 

 ©1998 by COMAP, Inc.  Tools for Teaching 1997  28 pages 

This module uses original data, diagrams, and texts from three original sources to develop the logistic model of growth in natural systems with limited resources. The logistic differential equation and the familiar Sshaped logistic curve have applications in solving problems in ecology, biology, chemistry, and economics. The module illustrates with concrete examples how mathematics develops, and it provides insights into the assumptions that drive the modeling process.
Table of Contents:
INTRODUCTION
THE LOGISTIC EQUATION
Yule's Summary of Malthus's Argument
Verhulst's Argument
Pearl and Reed's Data and Methods
Continuation of Yule's Account
Return to Verhulst's Original Account
Further History and Yule's Own Development
Yule's Appendix
MORAL
SOLUTIONS TO SELECTED EXERCISES
REFERENCES
ABOUT THE AUTHOR



