
Population Models in Biology and Demography (UMAP)
George Ashline, Joanna EllisMonaghan

Mathematics Topic: Calculus 
Application Areas: Demography, Biology 
Prerequisites: None. 

This module presents applications from microbiology and demography that give a physical context for critical concepts in a firstsemester calculus course. Elementary models of population growth are developed using data collected from biological experiments conducted during the course. Then, proceeding from "microcosm to macrocosm," the tools of calculus, demographic software, and the Maple computer algebra system (CAS) are used to address questions of human population projections. Included are discussion materials, sample models using exponential and logistic curves, projects, complete biology labs for generating raw data, exercises for developing facility with Maple, and resource lists (including software and Internet sites) for studying demographic questions.
Table of Contents:
INTRODUCTION
MODELING EXAMPLES
Raw Data
Bacteria colony
Population of Italy
Exponential and Logistic Functions
Modeling Bacteria Growth
Modeling the Population of Italy
MODELING ACTIVITIES
Examples with Given Data
Exponential growth
Logistic growth
Laboratory Analysis
Human Populations
Analyzing the population of a specific country
DEVELOPING FACILITY WITH MAPLE
Examples and Discussion
Graphing
Solving
Differentiating
The Shapes of Graphs
Exponential and Logarithmic Functions
Maple Exercises
RESOURCES
Laboratory Notes
Exponential growth with slime molds and flour beetles
Exponential/logistic growth with a yeast culture
Logistic growth with a bacteria culture
Population crash with ciliated protistans
Population Internet Sites
Additional Resources
Early works
Biology
Demography
Curve fitting and the logistic model
A few pertinent journals
TEACHING NOTES
REFERENCES
ACKNOWLEDGMENTS
ABOUT THE AUTHORS
