Introduction To Theory Of Ordinary Differential Equations

Introduction To Theory Of Ordinary Differential Equations
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Introduction To Theory Of Ordinary Differential Equations

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Publisher: PHI Learning
ISBN: 9788120346666
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About The Book Introduction To Theory Of Ordinary Differential Equations
Book Summary:

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 SturmLiouville problem, Greens function, the Picards theorem, and the SturmPicone 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.


Table of Contents:
Preface
1. PRELIMINARIES
2. EXISTENCE THEOREMS
3. ANALYTICAL METHODS
4. FIRST ORDER EQUATIONS
5. SYSTEMS OF EQUATIONS
6. LINEAR SYSTEMS
7. LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS
8. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS
9. LINEAR EQUATIONS WITH REGULAR SINGULAR POINTS
10. GENERALIZATION OF VARIATION OF PARAMETERS FORMULA
11. ADJOINT EQUATIONS
12. RICCATI EQUATION
13. BOUNDARY VALUE PROBLEMS
14. OSCILLATION THEORY (FOR LINEAR DIFFERENTIAL EQUATIONS OF ORDER TWO)
15. STABILITY THEORY
16. DELAY DIFFERENTIAL EQUATIONS
Index