Some Mathematical Tools

  • Edward K. Yeargers
  • Ronald W. Shonkwiler
  • James V. Herod


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. A model must capture the essence of an event or process but at the same time not be so complicated that it is intractable or dilutes the event’s most important features. In this regard, the field of differential equations is the most widely invoked branch of mathematics 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.


Direction Field Mathematical Tool Maximum Heart Rate Order Differential Equation Asymptotic Limit 
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References and Suggested Further Reading

  1. 1.
    AIDS cases in the U.S.: HIV/AIDS Surveillance Report, U. S Department of Health and Human Services, Centers for Disease Control, Division of HIV/AIDS, 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. Natl. Acad. Sci. USA, vol. 86, pp. 4793–4797, 1989.CrossRefGoogle Scholar
  3. 3.
    Ideal height and weight: Sue Rodwell Williams, Nutrition and Diet Therapy, 2nd ed., The C. V. Mosby Company, Saint Louis, p. 655, 1973.Google Scholar
  4. 4.
    Georgia Tech Exercise Laboratory: Philip B. Sparling, Melinda Millard-Stafford, Linda B. Rosskopf, Linda Dicarlo, and Bryan T. Hinson, “Body composition by bioelectric impedance and densitometry in black women,” American Journal of Human Biology 5, pp. 111–117, 1993.CrossRefGoogle Scholar
  5. 5.
    Classical differential equations: E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen, Chelsea Publishing Company, New York, NY, 1948.zbMATHGoogle Scholar
  6. 6.
    The Central Limit Theorem: Robert Hogg and Allen Craig, Intro. to Math. Statistics, Macmillan, New York, NY, 1965.Google Scholar
  7. 7.
    Mortality tables for Alabama: “Epidemiology Report,” Alabama Department of Public Health, IX (number 2), February, 1994.Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Edward K. Yeargers
    • 1
  • Ronald W. Shonkwiler
    • 2
  • James V. Herod
    • 2
  1. 1.School of BiologyGeorgia Institute of TechnologyAtlantaUSA
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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