Differential Equations and Mathematical Biology
2nd Edition
Published on 9. November 2009
Book
Hardback
462 pages
978-1-4200-8357-6 (ISBN)
Description
Deepen students' understanding of biological phenomena
Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material.
New to the Second Edition
A section on spiral waves
Recent developments in tumor biology
More on the numerical solution of differential equations and numerical bifurcation analysis
MATLAB (R) files available for download online
Many additional examples and exercises
This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincare phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator-prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases.
Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material.
New to the Second Edition
A section on spiral waves
Recent developments in tumor biology
More on the numerical solution of differential equations and numerical bifurcation analysis
MATLAB (R) files available for download online
Many additional examples and exercises
This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincare phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator-prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases.
Reviews / Votes
"... 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
More details
Series
Edition
2nd edition
Language
English
Place of publication
Boca Raton
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Undergraduate
Product notice
Paper over boards
Illustrations
100 s/w Abbildungen, 3 s/w Tabellen
3 Tables, black and white; 100 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 29 mm
Weight
857 gr
ISBN-13
978-1-4200-8357-6 (9781420083576)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
D.S. Jones | Michael Plank | B.D. Sleeman
Differential Equations and Mathematical Biology
E-Book
11/2009
2nd Edition
Chapman & Hall/CRC
€125.99
Available for download
D.S. Jones | Michael Plank | B.D. Sleeman
Differential Equations and Mathematical Biology
E-Book
11/2009
2nd Edition
Chapman and Hall
€125.99
Available for download
Previous edition
D.S. Jones | B.D. Sleeman
Differential Equations and Mathematical Biology
Book
02/2003
1st Edition
CRC Press
€91.91
Article exhausted; check for reprint
Persons
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.
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.
Content
Introduction. Linear Ordinary Differential Equations with Constant Coefficients. Systems of Linear Ordinary Differential Equations. Modelling Biological Phenomena. First-Order Systems of Ordinary Differential Equations. Mathematics of Heart Physiology. Mathematics of Nerve Impulse Transmission. Chemical Reactions. Predator and Prey. Partial Differential Equations. Evolutionary Equations. Problems of Diffusion. Bifurcation and Chaos. Numerical Bifurcation Analysis. Growth of Tumors. Epidemics. Answers to Selected Exercises. Index.