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Full Description
The dynamic development of various processes is a central problem of biology and indeed of all the sciences. The mathematics describing that development is, in general, complicated, because the models that are realistic are usually nonlinear. Consequently many biologists may not notice a possible application of theory. They may be unable to decide whether a particular model captures the essence of a system, or to appreciate that analysis of a model can reveal important aspects of biological problems and may even describe in detail how a system works. The aim of this textbook is to remedy the situation by adopting a general approach to model analysis and applying it several times to problems (drawn primarily from molecular and cellular biology) of gradually increasing biological and mathematical complexity. Although material of considerable sophistication is included, little mathematical background is required - only some exposure to elementary calculus; appendixes supply the necessary mathematics and the author concentrates on concepts rather than techniques. He also emphasizes the role of computers in giving a full picture of model behavior and complementing more qualitative analysis. Some problems suitable for computer analysis are also included. This is a class-tested textbook suitable for a one-semester course for advanced undergraduate and beginning graduate students in biology or applied mathematics. It can also be used as a source book for teachers and a reference for specialists.
Contents
Preface; Note to the instructor; Conventions and notations; 1. Optimal strategies for the metabolism of storage materials; 2. Recursion relations in ecological and cellular population dynamics; 3. Population genetics: separate generations; 4. Enzyme kinetics; 5. The chemostat; 6. A model of the cellular slime mold cAMP signaling system; 7. Diffusion; 8. Developmental pattern formation and stability theory; 9. A mechanical basis for morphogenesis; Mathematical appendixes; Hints and answers for selected exercises; References; Index.
