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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Agarwal, Ravi P. (Autor), O'Regan, Donal (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2008.
Edición:1st ed. 2008.
Colección:Universitext,
Temas:
Differential equations.
Engineering mathematics.
Engineering-Data processing.
Differential Equations.
Mathematical and Computational Engineering Applications.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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