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An introduction to ordinary differential equations

Author: Ravi P Agarwal; Donal O'Regan
Publisher: New York ; London : Springer, 2008.
Series: Universitext.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 into easily manageable sections in the form of 42 class-tested lectures Provides a theoretical treatment by organizing  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Agarwal, Ravi P.
Introduction to ordinary differential equations.
New York ; London : Springer, 2008
(DLC) 2007935982
(OCoLC)181090518
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ravi P Agarwal; Donal O'Regan
ISBN: 9780387712765 0387712763 6611926879 9786611926878
OCLC Number: 325025473
Language Note: English.
Description: 1 online resource (xii, 321 pages) : illustrations
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'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's Direct Method for Autonomous Systems --
Lyapunov's Direct Method for Nonautonomous Systems --
Higher-Order Exact and Adjoint Equations --
Oscillatory Equations --
Linear Boundary Value Problems --
Green's Functions --
Degenerate Linear Boundary Value Problems --
Maximum Principles --
Sturm-Liouville Problems --
Sturm-Liouville Problems (Contd.) --
Eigenfunction Expansions --
Eigenfunction Expansions (Contd.) --
Nonlinear Boundary Value Problems --
Nonlinear Boundary Value Problems (Contd.) --
Topics for Further Studies.
Series Title: Universitext.
Responsibility: Ravi P. Agarwal, Donal O'Regan.

Abstract:

Ordinary differential equations serve as mathematical models for many exciting real world problems. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures  Read more...

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From the reviews:"Presents a thorough treatment of the classical material traditionally covered in an advanced book on ordinary differential equations, including a number of interesting historical Read more...

 
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