ISBN 9788132206736,An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations

Publisher:

Springer

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ISBN 9788132206736
Publisher

Springer

Publication Year 2012
ISBN-13

ISBN 9788132206736

ISBN-10 8132206738
Binding

Paperback

Number of Pages 326 Pages
Language (English)
Subject

Educational: Mathematics & numeracy

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.

Salient Features

Effectively organizes the subject into easily manageable sections in the form of 42 class-tested lectures.
Provides a theoretical treatment by organizing the material around theorems and proofs. Uses detailed examples to drive the presentation.
Includes numerous exercise sets that encourage pursuing extensions of the material, each with an 'answers or hints' section.
Covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics.
Provides excellent grounding and inspiration for future research contributions to the field of ODEs and related areas.
This book is ideal for a senior undergraduate or a graduate-level course on ordinary differential equations. Prerequisites include a course in calculus.
Table of Contents

Preface
Introduction
Historical Notes
Exact Equations
Elementary First Order Equations
First Order Linear Equations
Second Order Linear 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 Non-Autonomous 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
References
Index
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