INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATIONS------PHI
Description:
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.
Contents:
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
