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Interdisciplinary Applied Mathematics #8: Mathematical Physiology: I: Cellular Physiologyby James P. Keener
Synopses & Reviews
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 first volume deals with the fundamental principles of cell physiology and the second with the physiology of systems. 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."
This book is an overview of mathematical physiology. It contains a variety of physiological problems and the current and new mathematical techniques used in this area. Numerous exercises and models are included.
Divided into two volumes, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing. New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included. Reviews from first edition: Keener and Sneyd's Mathematical Physiology is the first comprehensive text of its kind that deals exclusively with the interplay between mathematics and physiology. Writing a book like this is an audacious act! -Society of Mathematical Biology Keener and Sneyd's is unique in that it attempts to present one of the most important subfields of biology and medicine, physiology, in terms of mathematical "language", rather than organizing materials around mathematical methodology. -SIAM review
Mathematical Physiology provides an introduction into physiology using the tools and perspectives of mathematical modeling and analysis.
The book is divided in two parts, the first dealing with the fundamental principles of cell physiology, and the second with the physiology of systems.
This second edition provides coverage of more recent models in the chapters, more stochastic approaches, including single channel analysis and Fokker-Plank and Langevin equations.
New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included.
This book will be of interest to researchers, to graduate students and advanced undergraduate students in applied mathematics who wish to learn how to build and analyze mathematical models and become familiar with new areas of applications, as well as to physiologists interested in learning about theoretical approaches to their work.
Bulletin of Mathematical Biology, 2000: Most of the chapters, especially those outined in the second part of the book, can constitute whole monographs by themselves, and Keener and Sneyd have attempted to cover some of the fundamental modeling concepts within the respective areas.
SIAM, 2004: 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.
Winner of the prize for The Best Mathematics book of 1998 from the American Association of Publishers.
Table of Contents
Preface & Acknowledgments. I: Cellular Physiology. 1 Biochemical Reactions. 2 Cellular Homeostasis. 3 Membrane Ion Channels. 4 Passive Electrical Flow in Neurons. 5 Excitability. 6 Traveling Waves of Electrical Excitation. 7 Wave Propagation in Higher Dimensions. 8 Calcium Dynamics. 9 Intercellular Communication. 10 Neuroendocrine Cells. 11 Regulation of Cell Function.
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