Integral Equations and Boundary Value Problems, 10/e

Integral Equations and Boundary Value Problems, 10/e

Authors : Dr. M.D. Raisinghania

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About the Author

Dr. M.D. Raisinghania :-
Former Reader and Head of the Mathematics Department, S.D. College, Muzaffarnagar. He obtained his Ph.D. in Mathematics on the thesis entitled "An Analytical Study of Some Non-Newtonian Fluid Flow Problems". He has 38 years of teaching experience. Dr. Raisinghania has published several research papers in the area of Fluid Mechanics in reputed journals.
 

About the Book

The tenth edition of Integral Equations and Boundary Value Problems continues to offer an in-depth presentation of integral equations for the solution of boundary value problems. The book provides a plethora of examples and step-by-step presentation of definitions, proofs of the standard results and theorems which enhance students' problem-solving skills. Solved examples and numerous problems with hints and answers have been carefully chosen, classified in various types and methods, and presented to illustrate the concepts discussed. With the author's vast experience of teaching mathematics, his approach of providing a one-stop solution to the students' problems is engaging which goes a long way for the reader to retain the knowledge gained.

This book has been specifically designed for postgraduate students of Mathematics and Physics. It would also be equally useful for undergraduate students of applied mathematics as well as for the aspirants of GATE, CSIR-UGC (NET/JRF), SLET and other competitive examinations.

 

Contents

1. Preliminary Concepts

2. Conversion of Ordinary Differential Equations into Integral Equations
3. Homogeneous Fredholm Integral Equations of the Second Kind with Separable or Degenerate Kernels

4. Fredholm Integral Equations of the Second Kind with Separable (or Degenerate) Kernels

5. Method of Successive Approximations

6. Classical Fredholm Theory

7. Integral Equations with Symmetric Kernels

8. Singular Integral Equations

9. Integral Transform Methods

10. Self Adjoint Operator, Dirac Delta Function and Spherical Harmonics

11. Applications of Integral Equations and Green's Function to Ordinary Differential Equations

12. Applications of Integral Equations to Partial Differential Equations

13. Applications of Integral Equations to Mixed Boundary Value Problems

14. Integral Equation Perturbation Techniques

Appendix A: Boundary Value Problems and Green's Identities

Appendix B: Two and Three Dimensional Dirac Delta Functions

Appendix C: Beta and Gamma Functions

Appendix D: Cramer's Rule for Solving a System of Two Linear Algebraic Equations in Two Variables

Index

 

Key Features

  1. Thorough revision of chapters on Integral Transform Methods, Applications of Integral Equations and Green's Function to Ordinary Differential Equations and Applications of Integral Equations to Partial Differential Equations as per the latest curriculum requirement 
  2. Latest questions from various universities, GATE (2006-2020) and CSIR-UGC NET (2011-2019)
  3. Enhanced pedagogy comprising:

           -  a set of "Additional results and problems" at the end of each                          chapter

            - a list of useful results of integration for direct applications along                      with contents and notations

       ​4.  Inclusion of two new appendices:

             -  Appendix C: Beta and Gamma functions

             -  Appendix D: Cramer's rule for solving a system of Two Linear                       Algebraic Equations

                                in Two Variables