Principles of Differential Equations

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John Wiley & Sons, Jun 11, 2004 - Mathematics - 352 pages
An accessible, practical introduction to the principles of differential equations

The field of differential equations is a keystone of scientific knowledge today, with broad applications in mathematics, engineering, physics, and other scientific fields. Encompassing both basic concepts and advanced results, Principles of Differential Equations is the definitive, hands-on introduction professionals and students need in order to gain a strong knowledge base applicable to the many different subfields of differential equations and dynamical systems.

Nelson Markley includes essential background from analysis and linear algebra, in a unified approach to ordinary differential equations that underscores how key theoretical ingredients interconnect. Opening with basic existence and uniqueness results, Principles of Differential Equations systematically illuminates the theory, progressing through linear systems to stable manifolds and bifurcation theory. Other vital topics covered include:

  • Basic dynamical systems concepts
  • Constant coefficients
  • Stability
  • The Poincaré return map
  • Smooth vector fields

As a comprehensive resource with complete proofs and more than 200 exercises, Principles of Differential Equations is the ideal self-study reference for professionals, and an effective introduction and tutorial for students.

 

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Contents

Classical Themes
49
Linear Differential Equations
84
Constant Coefficients
109
Stability
146
The Poincare Return Map
184
Smooth Vector Fields
213
Hyperbolic Phenomenon
250
Bifurcations
298
Bibliography
334
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About the author (2004)

NELSON G. MARKLEY, PhD, was a faculty member in the Mathematics Department at the University of Maryland before moving to Lehigh University where he served as Provost and then Senior Vice President. He has published numerous research papers including recent work in the Journal of Differential Equations, and is the author of an elementary text on probability used by thousands of university students over some twenty years. He received his doctoral degree from Yale University.

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