Some Mathematical Tools

Edward K. Yeargers, Ronald W. Shonkwiler and James V. Herod
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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

Chapter Chapter 2 in An Introduction to the Mathematics of Biology: with Computer Algebra Models, 1996, pp 9-76 from Springer

Abstract: 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.

Keywords: Direction Field; Mathematical Tool; Maximum Heart Rate; Order Differential Equation; Asymptotic Limit (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4757-1095-3_2

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