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Principles of Differential Equations

Nelson G. Markley

ISBN: 978-0-471-64956-4 June 2004 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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1. Fundamental Theorems.

2. Classical Themes.

3. Linear Differential Equations.

4. Constant Coefficients.

5. Stability.

6. The Poincare Return Map.

7. Smooth Vector Fields.

8. Hyperbolic Phenomenon.

9. Bifurcations.