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Some Mathematical Tools

In: An Introduction to the Mathematics of Biology: with Computer Algebra Models

Author

Listed:
  • Edward K. Yeargers

    (Georgia Institute of Technology, School of Biology)

  • Ronald W. Shonkwiler

    (Georgia Institute of Technology, School of Mathematics)

  • James V. Herod

    (Georgia Institute of Technology, School of Mathematics)

Abstract

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.

Suggested Citation

  • Edward K. Yeargers & Ronald W. Shonkwiler & James V. Herod, 1996. "Some Mathematical Tools," Springer Books, in: An Introduction to the Mathematics of Biology: with Computer Algebra Models, chapter 0, pages 9-76, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-1095-3_2
    DOI: 10.1007/978-1-4757-1095-3_2
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