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.
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First Sentence:
"This chapter demonstrates that elementary calculus can be used to illuminate some aspects of the general question of how organisms should employ storage materials, given that they have evolved to be ""optimum"" in some sense." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
strong autocatalysis, vertical nullcline, activator peaks, different qualitative behaviors, activator concentration, enzyme adenylate cyclase, heavy dots, instability condition, parameter plane, stable node, positive cooperativity, critical nutrient, steady solutions, phase plane, rest length, phosphodiesterase activity New!
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"This chapter demonstrates that elementary calculus can be used to illuminate some aspects of the general question of how organisms should employ storage materials, given that they have evolved to be ""optimum"" in some sense." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
strong autocatalysis, vertical nullcline, activator peaks, different qualitative behaviors, activator concentration, enzyme adenylate cyclase, heavy dots, instability condition, parameter plane, stable node, positive cooperativity, critical nutrient, steady solutions, phase plane, rest length, phosphodiesterase activity New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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28
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- Mathematical Models in Molecular Cellular Biology by Lee A. Segel in Back Matter (1), and Back Matter (2)
- Mathematical Ideas in Biology by J. Maynard Smith on page 36, and Back Matter
- Modelling Fluctuating Populations by R. M. Nisbet in Back Matter
- Caste and Ecology in the Social Insects. (MPB-12) (Monographs in Population Biology) by George F. Oster in Back Matter
- The Theory of Atomic Spectra by E. U. Condon in Back Matter
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- Mathematical Models in Biology (Classics in Applied Mathematics) by Leah Edelstein-Keshet on page 111, page 162, and page 553
- A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational (Monographs on Mathematical Modeling and Computation) by Gerda de Vries in Back Matter (1), and Back Matter (2)
- Mathematical Models in the Applied Sciences (Cambridge Texts in Applied Mathematics) by A. C. Fowler in Back Matter
- First Signals: The Evolution of Multicellular Development by John Tyler Bonner in Back Matter
- First Signals: The Evolution of Multicellular Development. by John Tyler Bonner in Back Matter
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