An Introduction to Delay Differential Equations with Applications to the Life Sciences (Texts in Applied Mathematics, 57, Band 57) - Hardcover

Buch 17 von 55: Texts in Applied Mathematics

Smith, Hal

 
9781441976451: An Introduction to Delay Differential Equations with Applications to the Life Sciences (Texts in Applied Mathematics, 57, Band 57)
Hardcover
ISBN 10: 1441976450 ISBN 13: 9781441976451
Verlag: Springer, 2010

Inhaltsangabe

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.

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Über die Autorin bzw. den Autor

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

Von der hinteren Coverseite

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.

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Verlag
Springer
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
1441976450
ISBN 13 
9781441976451
Einband
Gebundene Ausgabe
Anzahl der Seiten
183
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Weitere beliebte Ausgaben desselben Titels

9781461426974: An Introduction to Delay Differential Equations with Applications to the Life Sciences (Texts in Applied Mathematics, Band 57)

Vorgestellte Ausgabe

ISBN 10:  1461426979 ISBN 13:  9781461426974
Verlag: Springer, 2012
Softcover