Principles of Differential Equations

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 Poincar 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.

An accessible, practical introduction to the principles ofdifferential equationsThe field of differential equations is a keystone of scientificknowledge today, with broad applications in mathematicsengineering, physics, and other scientific fields. Encompassingboth basic concepts and advanced results, Principles ofDifferential Equations is the definitive, hands-on introductionprofessionals and students need in order to gain a strong knowledgebase applicable to the many different subfields of differentialequations and dynamical systems.Nelson Markley includes essential background from analysis andlinear algebra, in a unified approach to ordinary differentialequations that underscores how key theoretical ingredientsinterconnect. Opening with basic existence and uniqueness resultsPrinciples of Differential Equations systematically illuminates thetheory, progressing through linear systems to stable manifolds andbifurcation theory. Other vital topics covered include:* Basic dynamical systems concepts* Constant coefficients* Stability* The Poincaré return map* Smooth vector fieldsAs a comprehensive resource with complete proofs and more than200 exercises, Principles of Differential Equations is the idealself-study reference for professionals, and an effectiveintroduction and tutorial for students.

Preface.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.Bibliography.Index.