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Product No. 99766 Supplementary Print Price: FREE with membership
 

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 S-shaped 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