INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION
This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem, Green’s function, the Picard’s theorem, and the Sturm–Picone theorem. The text is supported by a number of worked-out examples to make the concepts clear, and it also provides a number of exercises help students test their knowledge and improve their skills in solving differential equations. The book is intended to serve as a text for the postgraduate students of mathematics and applied mathematics. It will also be useful to the candidates preparing to sit for the competitive examinations such as NET and GATE.
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INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION
This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem, Green’s function, the Picard’s theorem, and the Sturm–Picone theorem. The text is supported by a number of worked-out examples to make the concepts clear, and it also provides a number of exercises help students test their knowledge and improve their skills in solving differential equations. The book is intended to serve as a text for the postgraduate students of mathematics and applied mathematics. It will also be useful to the candidates preparing to sit for the competitive examinations such as NET and GATE.
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INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION

INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION

by V. DHARMAIAH
INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION

INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION

by V. DHARMAIAH

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Overview

This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem, Green’s function, the Picard’s theorem, and the Sturm–Picone theorem. The text is supported by a number of worked-out examples to make the concepts clear, and it also provides a number of exercises help students test their knowledge and improve their skills in solving differential equations. The book is intended to serve as a text for the postgraduate students of mathematics and applied mathematics. It will also be useful to the candidates preparing to sit for the competitive examinations such as NET and GATE.

Product Details

ISBN-13: 9788120346666
Publisher: PHI Learning
Publication date: 09/19/2012
Sold by: Barnes & Noble
Format: eBook
File size: 8 MB

About the Author

<TABLE border=0 width="100%"><TBODY><TR><TD class=normal><STRONG>V. DHARMAIAH</STRONG>, PhD, is Professor of Mathematics in Osmania University, Hyderabad. He has over 30 years of teaching experience and 20 years of research experience. Professor Dharmaiah has published several research articles in reputed journals. His areas of research include Functional Analysis, Theory of Operators, Theory of Ordinary Differential Equations and Integral Equations.&nbsp;</TD></TR><TR><TD>&nbsp;</TD><TD>&nbsp;</TD></TR></TBODY></TABLE>

Table of Contents

Preface1. PRELIMINARIES2. EXISTENCE THEOREMS3. ANALYTICAL METHODS4. FIRST ORDER EQUATIONS5. SYSTEMS OF EQUATIONS6. LINEAR SYSTEMS7. LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS8. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS9. LINEAR EQUATIONS WITH REGULAR SINGULAR POINTS10. GENERALIZATION OF VARIATION OF PARAMETERS FORMULA11. ADJOINT EQUATIONS12. RICCATI EQUATION13. BOUNDARY VALUE PROBLEMS14. OSCILLATION THEORY (FOR LINEAR DIFFERENTIAL EQUATIONS OF ORDER TWO)15. STABILITY THEORY16. DELAY DIFFERENTIAL EQUATIONSIndex
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