Change is the nature of things in biology and differential equations are used to model change. The concentrations of some bio-chemicals present in an organism change over time, sometimes dramatically, in response to the changes in the concentrations of other chemicals. Other systems make up a steady-state system, where the concentrations of reactants are damped within fairly rigid bounds. Segments of organisms change due to dynamic feedback with other segments of the same organism, actions in one location can propagate throughout the entire creature. Organisms of one species interact with others of the same species, sometimes in cooperation, and other times in competition. The same thing applies to populations of different species, in some circumstances, all species benefit or suffer and in other circumstances the advantage to one species is based on harm to the other(s). All of these situations are examined in a thorough manner; the models are based on differential equations started from some basic, logical assumptions.
It has been over a decade since the release of the now classic original edition of Murray’s Mathematical Biology. Since then mathematical biology has grown at an astonishing rate and is well established as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biomedical sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems that arise in biology and gives some indication of the wide spectrum of questions that modeling can address. Due to the tremendous development in the field this book is being published in two volumes. This first volume is an introduction to the field, the mathematics mainly involves ordinary differential equations that are suitable for undergraduate and graduate courses at different levels. For this new edition Murray is covering certain items in depth, giving new applications such as modeling marital interactions and temperature dependence sex determination.
SIAM, 2004: “Murray’s Mathematical Biology is a classic that belongs on the shelf of any serious student or researcher in the field. Together the two volumes contain well over 1000 references, a rich source of material, together with an excellent index to help readers quickly find key words. … I recommend the new and expanded third edition to any serious young student interested in mathematical biology who already has a solid basis in applied mathematics.”
Author: James D. Murray
Publisher: Springer Science & Business Media
Genre: Mathematics / Applied
Date Published: 2011-02-02
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