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Consortium for Mathematics and its Applications

Product ID: 99345
Supplementary Print
Undergraduate

Population Projection (UMAP)

Author: Edward L. Keller


This unit examines a model developed by P.H. Leslie and others that uses matrix multiplication to make population projections from one time period to another. The emphasis is on understanding the role of eigenvalues and eigenvectors. Proofs are not emphasized. There are computer exercises in an appendix for those who wish to use them. Students see how a knowledge of eigenvalues and eigenvectors is useful in studying powers of a matrix, and are birefly exposed to some interesting theorems of linear algebra.

Table of Contents:

1. INTRODUCTION

2. THE MODEL
2.1 Population Projection -- An Example
2.2 Extending the Projection
2.3 Powers of the Leslie Matrix
2.4 Another Example

3. THEORETICAL BACKGROUND
3.1 Some Observations
3.2 The Perron-Frobenius Theorem
3.3 An Example with Oscillations
3.4 Summary
3.5 A Simplification Using Left and Right Eigenvectors

4. A HUMAN POPULATION EXAMPLE

5. REFERENCES

6. ANSWERS TO EXERCISES

APPENDIX A

APPENDIX B

©1980 by COMAP, Inc.
UMAP Module
33 pages

Mathematics Topics:

Abstract & Linear Algebra

Application Areas:

Life Sciences & Medicine , Social Studies , Population Studies

Prerequisites:

Matrix algebra; ability to find eigenvalues and eigenvectors of a matrix

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