462 pages, illus
The conjoining of mathematics and biology has brought about significant advances in both areas, with mathematics providing a tool for modelling and understanding biological phenomena and biology stimulating developments in the theory of nonlinear differential equations. The continued application of mathematics to biology holds great promise and in fact may be the applied mathematics of the 21st century. Differential Equations and Mathematical Biology provides a detailed treatment of both ordinary and partial differential equations, techniques for their solution, and their use in a variety of biological applications.
The presentation includes the fundamental techniques of nonlinear differential equations, bifurcation theory, and the impact of chaos on discrete time biological modelling. The authors provide generous coverage of numerical techniques and address a range of important applications, including heart physiology, nerve pulse transmission, chemical reactions, tumour growth, and epidemics. This book is the ideal vehicle for introducing the challenges of biology to mathematicians and likewise delivering key mathematical tools to biologists. Carefully designed for such multiple purposes, it serves equally well as a professional reference and as a text for coursework in differential equations, in biological modelling, or in differential equation models of biology for life science students.
!Much progress by these authors and others over the past quarter century in modeling biological and other scientific phenomena make this differential equations textbook more valuable and better motivated than ever. !The writing is clear, though the modeling is not oversimplified. Overall, this book should convince math majors how demanding math modeling needs to be and biologists that taking another course in differential equations will be worthwhile. The coauthors deserve congratulations as well as course adoptions. --SIAM Review, Sept. 2010, Vol. 52, No. 3 ! Where this text stands out is in its thoughtful organization and the clarity of its writing. This is a very solid book ! The authors succeed because they do a splendid job of integrating their treatment of differential equations with the applications, and they don't try to do too much. ! Each chapter comes with a collection of well-selected exercises, and plenty of references for further reading. --MAA Reviews, April 2010 Praise for the First Edition A strength of [this book] is its concise coverage of a broad range of topics. ! It is truly remarkable how much material is squeezed into the slim book's 400 pages. --SIAM Review, Vol. 46, No. 1 It is remarkable that without the classical scheme (definition, theorem, and proof) it is possible to explain rather deep results like properties of the Fitz--Hugh--Nagumo model ! or the Turing model ! . This feature makes the reading of this text pleasant business for mathematicians. ! [This book] can be recommended for students of mathematics who like to see applications, because it introduces them to problems on how to model processes in biology, and also for theoretically oriented students of biology, because it presents constructions of mathematical models and the steps needed for their investigations in a clear way and without references to other books. --EMS Newsletter The title precisely reflects the contents of the book, a valuable addition to the growing literature in mathematical biology from a deterministic modeling approach. This book is a suitable textbook for multiple purposes ! Overall, topics are carefully chosen and well balanced. !The book is written by experts in the research fields of dynamical systems and population biology. As such, it presents a clear picture of how applied dynamical systems and theoretical biology interact and stimulate each other--a fascinating positive feedback whose strength is anticipated to be enhanced by outstanding texts like the work under review. --Mathematical Reviews, Issue 2004g
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