Some Mathematical Tools

  • Ronald W. Shonkwiler
  • James Herod
Part of the Undergraduate Texts in Mathematics book series (UTM)


This book is about biological modeling—the construction of mathematical abstractions intended to characterize biological phenomena and the derivation of predictions from these abstractions under real or hypothesized conditions. Amodel must capture the essence of an event or process but at the same time not be so complicated as to be intractable or to otherwise dilute its most important features. In this regard, differential equations have been widely invoked across the broad spectrum of biological modeling. Future values of the variables that describe a process depend on their rates of growth or decay. These in turn depend on present, or past, values of these same variables through simple linear or power relationships. These are the ingredients of a differential equation. We discuss linear and power laws between variables and their derivatives in Section 2.1 and differential equations in Section 2.4.


Difference Equation Mathematical Tool Maximum Heart Rate Asymptotic Limit Bench Press 
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References and Suggested Further Reading

  1. [1] AIDS Cases in The U.S.:
    HIV/AIDS Surveillance Report, Division of HIV/AIDS, Centers for Disease Control, U.S. Department of Health and Human Services, Atlanta, GA, July, 1993.Google Scholar
  2. [2] Cubic Growth of AIDS:
    S.A. Colgate, E.A. Stanley, J.M. Hyman, S.P. Layne, and C. Qualls, Risk-behavior model of the cubic growth of acquired immunodeficiency syndrome in the United States, Proc. Nat. Acad. Sci. USA, 86 (1989), 4793–4797.CrossRefGoogle Scholar
  3. [3] Ideal Height And Weight:
    S. R. Williams, Nutrition and Diet Therapy, 2nd ed., Mosby, St. Louis, 1973, 655.Google Scholar
  4. [4] Georgia Tech Exercise Laboratory:
    P. B. Sparling, M. Millard-Stafford, L. B. Rosskopf, L. Dicarlo, and B. T. Hinson, Body composition by bioelectric impedance and densitometry in black women, Amer. J. Human Biol., 5 (1993), 111–117.CrossRefGoogle Scholar
  5. [5] Classical Differential Equations:
    E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen, Chelsea, New York, 1948.MATHGoogle Scholar
  6. [6] The Central Limit Theorem:
    R. Hogg and A. Craig, Introduction to Mathematical Statistics, Macmillan, New York, 1965.MATHGoogle Scholar
  7. [7] Mortality Tables For Alabama:
    Epidemiology Report IX (Number 2) Alabama Department of Public Health, Montgomery, AL, February, 1994.Google Scholar
  8. [8] Basic Combinatorics:
    R. P. Grimaldi, Discrete and Combinatorial Mathematics, Addison–Wesley, New York, 1998.Google Scholar

Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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