Differential Equations and Mathematical Biology. This item is unavailable.Differential Equations and Mathematical Biology

Over the past decade, mathematics has made a considerable impact as a tool with which to model and understand biological phenomena. In return, biology has confronted the mathematician with a variety of challenging problems which have stimulated developments in the theory of nonlinear differential equations. This book is the outcome of the need to introduce undergraduates of mathematics, the physical and biological sciences to some of those developments. It is primarily directed towards students with a mathematical background up to and including that normally taught in a first-year physical science degree of a British university (sophomore year in a North American university) who are interested in the application of mathematics to biological and physical situations. Chapter 1 is introductory, showing how the study of first-order ordinary differential equations may be used to model the growth of a population, monitoring the administration of drugs and the mechanism by which living cells divide. In Chapter 2, a fairly comprehensive account of linear ordinary differential equations with constant coefficients is given. Such equations arise frequently in the discussion of the biological models encountered throughout the text. Chapter 3 is devoted to modelling biological pheno mena and in particular includes (i) physiology of the heart beat cycle, (ii) blood flow, (iii) the transmission of electrochemical pulses in the nerve, (iv) the Belousov-Zhabotinskii chemical reaction and (v) predator-prey models."

"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 theoretical 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 text like the work under review." -Mathematical Reviews, Issue 2004g