An Introduction to Ordinary Differential Equations by Ravi P. Agarwal, Donal O'Regan.

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Agarwal, Ravi P. (Author, http://id.loc.gov/vocabulary/relators/aut), O'Regan, Donal. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2008.
Edition:1st ed. 2008.
Series:Universitext,
Springer eBook Collection.
Subjects:
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.