Differential Equations and Mathematical Biology - Hardcover

Jones, D.S., And B.D. Sleeman

Hardcover

ISBN 10: 004515001X ISBN 13: 9780045150014

Publisher: George Allen & Unwin, 1983

Synopsis

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.

About this title

About the Author:

D.S. Jones, FRS, FRSE is Professor Emeritus in the Department of Mathematics at the University of Dundee in Scotland.

M.J. Plank is a senior lecturer in the Department of Mathematics and Statistics at the University of Canterbury in Christchurch, New Zealand.

B.D. Sleeman, FRSE is Professor Emeritus in the Department of Applied Mathematics at the University of Leeds in the UK.

Review:

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

About this edition

• Publisher: George Allen & Unwin
• Publication date: 1983
• ISBN 10: 004515001X
• ISBN 13: 9780045150014
• Binding: Hardcover
• Edition number: 1
• Number of pages: 339