Texts in Applied Mathematics

An Introduction to Delay Differential Equations with Applications to the Life Sciences

Authors: Smith, Hal

  • Focuses on the key tools needed to understand delay equations
  • Begins with a survey of mathematical models involving delay equations
  • Includes a wealth of examples, exercises and illustrations
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About this Textbook

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a good background in ordinary differential equations and would like to learn about the applications. It may also be of interest to applied mathematicians, computational scientists, and engineers. It focuses on key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models. Aside from standard well-posedness results for the initial value problem, it focuses on stability of equilibria via linearization and Lyapunov functions and on Hopf bifurcation. It contains a brief introduction to abstract dynamical systems focused on those generated by delay equations, introducing limit sets and their properties. Differential inequalities play a significant role in applications and are treated here, along with an introduction to monotone systems generated by delay equations. The book contains some quite recent results such as the Poincare-Bendixson theory for monotone cyclic feedback systems, obtained by Mallet-Paret and Sell. The linear chain trick for a special family of infinite delay equations is treated. The book is distinguished by the wealth of examples that are introduced and treated in detail. These include the delayed logistic equation, delayed chemostat model of microbial growth, inverted pendulum with delayed feedback control, a gene regulatory system, and an HIV transmission model. An entire chapter is devoted to the interesting dynamics exhibited by a chemostat model of bacteriophage parasitism of bacteria. The book has a large number of exercises and illustrations. Hal Smith is a Professor at the School of Mathematical and Statistical Sciences at Arizona State University. 

About the authors

Hal Smith is a Professor at the School of Mathematical and Statistical Sciences at Arizona State University.

Reviews

From the reviews:

“This text is designed to be an introduction to the theory of differential equations with delay for advanced undergraduates and beginning graduate students.” (William J. Satzer, The Mathematical Association of America, November, 2010)

“This textbook would serve as an excellent reference text to help a mathematics faculty develop an introductory mathematics course on DDEs … . This textbook clearly places the study of DDEs firmly within the standard curriculum of a graduate program in mathematics and well within the scope of a strong final-year undergraduate mathematics major. … this text will have a positive impact on biomathematics education and be a welcome addition. We certainly find it so.” (John G. Milton and Michael C. Mackey, Mathematical Reviews, Issue 2011 k)

“This book gives a first introduction to delay differential equations that is intended for mathematics students. Thanks to the emphasis on applications to life sciences, it can be recommended also to scientists from this discipline that wish to get a deeper understanding of the theoretical aspects for this widely used class of models.” (Matthias Wolfrum, Zentralblatt MATH, Vol. 1227, 2012)


Table of contents (8 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4419-7646-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-1-4419-7645-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA
  • ISBN 978-1-4614-2697-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Delay Differential Equations with Applications to the Life Sciences
Authors
Series Title
Texts in Applied Mathematics
Series Volume
57
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-7646-8
DOI
10.1007/978-1-4419-7646-8
Hardcover ISBN
978-1-4419-7645-1
Softcover ISBN
978-1-4614-2697-4
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XI, 172
Topics