An Introduction to Ordinary Differential Equations
This textbook provides a rigorous and lucid introduction to the theory of ordinary differential equations (ODEs), which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines. Key Features of this textbook: Effectively organizes the subject...
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Serier: | Universitext
|
| Fag: | |
| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Kommentar: |
L'impression du document génère 338 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to ordinary differential equations, Ravi P. Agarwal, Donal O'Regan, New York, Springer, 2008, 1 vol. (XII-321 p.), Universitext, 978-0-387-71275-8 |
Indholdsfortegnelse:
- Historical Notes Exact Equations Elementary First-Order Equations First-Order Linear Equations Second-Order Linera Equations Preliminaries to Existence and Uniqueness of Solutions Picard#x0027;s Method of Successive Approximations Existence Theorems Uniqueness Theorems Differential Inequalities Continuous Dependence on Initial Conditions Preliminary Results from Algebra and Analysis Preliminary Results from Algebra and Analysis (Contd.) Existence and Uniqueness of Solutions of Systems Existence and Uniqueness of Solutions of Systems (Contd.) General Properties of Linear Systems Fundamental Matrix Solution Systems with Constant Coefficients Periodic Linear Systems Asymptotic Behavior of Solutions of Linear Systems Asymptotic Behavior of Solutions of Linear Systems (Contd.) Preliminaries to Stability of Solutions Stability of Quasi-Linear Systems Two-Dimensional Autonomous Systems Two-Dimensional Autonomous Systems (Contd.) Limit Cycles and Periodic Solutions Lyapunov#x0027;s Direct Method for Autonomous Systems Lyapunov#x0027;s Direct Method for Nonautonomous Systems Higher-Order Exact and Adjoint Equations Oscillatory Equations Linear Boundary Value Problems Green#x0027;s Functions Degenerate Linear Boundary Value Problems Maximum Principles Sturm#x2014;Liouville Problems Sturm#x2013;Liouville Problems (Contd.) Eigenfunction Expansions Eigenfunction Expansions (Contd.) Nonlinear Boundary Value Problems Nonlinear Boundary Value Problems (Contd.) Topics for Further Studies