An Introduction to Ordinary Differential Equations

• Κύριοι συγγραφείς: Agarwal, Ravi P. (Συγγραφέας), O'Regan, Donal (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2008.
• Σειρά: Universitext
• Θέματα: Mathematics.; Differential equations.; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Ordinary Differential Equations.; Partial Differential Equations.; Appl.Mathematics/Computational Methods of Engineering.

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...

Πίνακας περιεχομένων:

• 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.