Projects for Calculus The Language of Change 2nd ed K Stroyan.pdf

Projects: Calculus: The Language of Change
by Keith D. D. Stroyan



· ISBN: 0126730318
· Pub. Date: December 1998
· Publisher: Elsevier Science & Technology Books
CONTENTS
INTRODUCTION TO THE SCIENTIFIC PROJECTS
What Good Is It? 2
How Much Work Are They? 2
How to Write a Project 2
Help on the World Wide Web 3
PROJECT 1. Linear Approximation of C02 Data 5
EPIDEMIOLOGICAL APPLICATIONS
Review of the S-I-R Model 10
Basic Assumptions 11
Derivation of the Equations of Change 11
PROJECT 2. The 1968-69 New York Hong Kong Flu Epidemic 13
PROJECT 3. ination for Herd Immunity 17
Herd Immunity 18
The Contact Number Data 18
Project Issues 19
ine Failures 19
PROJECT 4. S-I-S Diseases and the Endemic Limit 21
Basic Assumptions 21
The Continuous S-I-S Variables 22
v
Contents
Parameters for the SIS Model 22
The Importance of the Contact Ratio 23
Conjectures 24
Conclusions 25
PROJECT 5. Max-Min in S-I-R Epidemics 27
THE ROLE OF RULES FOR DERIVATIVES
PROJECT 6. The Expanding Economy 33
PROJECT 7. The Expanding House 35
Volume Expansion Explained by Calculus 38
4 APPLICATIONS OF THE INCREMENT APPROXIMATION
f[t + 5t]-f[t] = f'[t]5t +
PROJECT 8. A Derivation of Hubble's law 43
PROJECT 9. Functional Linearity 47
PROJECT 10. Functional Identities 51
Additive Functions 54
DIFFERENTIAL EQUATIONS FROM INCREMENT GEOMETRY
PROJECT 11. The Tractrix 57
PROJECT 12. The Isochrone 59
Conservation of Energy 61
PROJECT 13. The Catenary 63
The Catenary Hypotheses 63
Parameters 63
Variables 64
The Equation for Tension 64
Optimizing Length and Strength 68
VI
Contents
LOG AND EXPONENTIAL FUNCTIONS
PROJECT 14. The Canary Resurrected 73
PROJECT 15. Drug Concentration and "Biexponential" Functions 75
Primary Variables of the Model 76
Parameters of