Stability Theory of Differential Equations (Paperback)

Richard Bellman

ISBN 10: 0486462730 / ISBN 13: 9780486462738

Editore: Dover Publications Inc., New York, 2008

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Paperback. Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincare and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit. Suitable for advanced undergraduates and graduate students, this text introduces the stability theory and asymptotic behavior of solutions of linear and nonlinear differential equations. 1953 edition. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Codice articolo 9780486462738

Dati bibliografici

• Titolo: Stability Theory of Differential Equations (Paperback)
• Editore: Dover Publications Inc., New York
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 0486462730
• ISBN 13: 9780486462738
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.
The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.

Contenuti

Preface 1. Properties of Linear Systems 2. Stability, Boundedness, and Asymptotic Behavior of Solutions of Linear Systems 3. The Existence and Uniqueness of Solutions of Nonlinear Systems 4. The Stability of Solutions of Nonlinear Differential Equations 5. The Asymptotic Behavior of the Solutions of Some Nonlinear Equations of the First Order 6. The Second-order Linear Differential Equation 7. The Emden-Fowler Equation Index