© 2009

Mathematical Physiology

II: Systems Physiology

  • James Keener
  • James Sneyd

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 8/2)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Pages 471-522
  3. Pages 523-626
  4. Pages 627-681
  5. Pages 683-716
  6. Pages 717-772
  7. Pages 773-819
  8. Pages 821-850
  9. Pages 893-942
  10. Pages 943-974
  11. Back Matter

About this book


There has been a long history of interaction  between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. 

In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina.


Owing to this extensive coverage,  the second edition is published in two volumes. This second volume deals with the physiology of systems and the first volume with the fundamental principles of cell physiology.

The book includes detailed illustrations and  numerous excercises with selected solutions. The emphasis throughout is on the applications; because of this interdisciplinary  approach, this book  will be of  interest to students and researchers, not only in mathematics, but also in bioengineering, physics, chemistry, biology, statistics and medicine.

James Keener is a Distinguished Professor of Mathematics at the University of Utah. He and his wife live in Salt Lake City, but don't be surprised if he moves to the mountains.

James Sneyd is the Professor of Applied Mathematics at the University of Auckland in New Zealand, where he has worked for the past six years. He lives with his wife and three children beside a beach, and would rather be swimming.

Reviews of the first edition:

...probably the best book ever written on the interdisciplinary field of mathematical physiology. Mathematical Reviews, 2000

In addition to being good reading, excellent pedagogy, and appealing science, the exposition is lucid and clear, and there are many good problem sets to choose from... Highly recommended. Mathematical Biosciences, 1999

Both authors are seasoned experts in the field of mathematical physiology and particularly in the field of excitability, calcium dynamics and spiral waves. It directs students to become not merely skilled technicians in biological research but masters of the science. SIAM, 2004

The first edition was the winner of the 1998 Association of American Publishers "Best New Title in Mathematics."


Mathematical Physiology biology cells physiology smooth muscle

Editors and affiliations

  • James Keener
    • 1
  • James Sneyd
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

Bibliographic information

  • Book Title Mathematical Physiology
  • Book Subtitle II: Systems Physiology
  • Authors James Keener
    James Sneyd
  • Series Title Interdisciplinary Applied Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-79387-0
  • Softcover ISBN 978-1-4939-3709-7
  • eBook ISBN 978-0-387-79388-7
  • Series ISSN 0939-6047
  • Edition Number 2
  • Number of Pages XXV, 549
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published in one volume
  • Topics Mathematical and Computational Biology
    Human Physiology
  • Buy this book on publisher's site


From the reviews:

"Probably the best book ever written on the subject of mathematical physiology … It contains numerous exercises, enough to keep even the most diligent student busy, and a comprehensive list of approximately 600 references … highly recommended to anybody interested in mathematical or theoretical physiology." Mathematical Reviews

"In addition to being good reading, excellent pedagogy, and appealing science, the exposition is lucid and clear, and there are many good problem sets to choose from … Highly recommended." Journal of the Society of Mathematical Biology

From the reviews of the second edition:

"This massive new edition … offers an introduction to mathematical physiology that emphasizes work conducted by Keener (Univ. of Utah), Sneyd (Univ. of Auckland, New Zealand), and others over the past 20 years. It is designed as a course resource for beginning graduate students who have … some mathematical background. … Keener and Sneyd have made very reasonable choices in their subject selections. This work is an admirable resource for students with the appropriate prerequisites. Chapters include exercises … . Summing Up: Recommended. Graduate students." (P. Cull, Choice, Vol. 46 (10), June, 2009)

"The texts provide a comprehensive summary of the important concepts in mathematical physiology. … For those actively working in the field of mathematical physiology … is a must have. The new edition includes updated descriptions, new models, and new figures adding to the breadth of the first edition. One of the most beneficial aspects … is the addition of about a decade’s worth of work and references (over 350!). … more advanced questions were added giving more flexibility when used as a course textbook." (Joe Latulippe, The Mathematical Association of America, July, 2009)

“This second edition of Mathematical physiology, ten years after the first one … provides information on recent works in mathematical physiology. … It is a very interesting book dealing with the interdisciplinary field of mathematical physiology. … Mathematical physiology, with the consequent number of exercises given at the end of each chapter, could be used in particular for a full-year course in mathematical physiology. It is also suitable for researchers and graduate students in applied mathematics, bioengineering and physiology.” (Fabien Crauste, Mathematical Reviews, Issue 2010 b)