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INTEGRAL EQUATIONS KopyKitab
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INTEGRAL EQUATIONS, BOUNDARY VALUE PROBLEMS, with Green s function technique and its applications. For M A M Sc Mathematics and M Sc Physics students of all Indian. Universities Institutions according to latest U G C model curriculum and. various engineering and professional examinations such as. GATE C S I R NET JRF and SLET etc, Dr M D RAISINGHANIA. Formerly Head of Mathematics Department, S D Postgraduate College. Muzaffarnagar U P, S CHAND COMPANY PVT LTD, AN ISO 9001 2008 COMPANY. RAM NAGAR NEW DELHI 110 055, S CHAND COMPANY PVT LTD.
An ISO 9001 2008 Company, Head Office 7361 RAM NAGAR NEW DELHI 110 055. Phone 23672080 81 82 9899107446 9911310888, Fax 91 11 23677446. Shop at schandgroup com e mail info schandgroup com. AHMEDABAD 1st Floor Heritage Near Gujarat Vidhyapeeth Ashram Road Ahmedabad 380 014. Ph 27541965 27542369 ahmedabad schandgroup com, BENGALURU No 6 Ahuja Chambers 1st Cross Kumara Krupa Road Bengaluru 560 001. Ph 22268048 22354008 bangalore schandgroup com, BHOPAL Bajaj Tower Plot No 2 3 Lala Lajpat Rai Colony Raisen Road Bhopal 462 011. Ph 4274723 4209587 bhopal schandgroup com, CHANDIGARH S C O 2419 20 First Floor Sector 22 C Near Aroma Hotel Chandigarh 160 022.
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Ph 22690881 22610885 mumbai schandgroup com, NAGPUR Karnal Bagh Near Model Mill Chowk Nagpur 440 032 Ph 2720523 2777666. nagpur schandgroup com, PATNA 104 Citicentre Ashok Mahima Palace Govind Mitra Road Patna 800 004 Ph 2300489. 2302100 patna schandgroup com, PUNE 291 Flat No 16 Ganesh Gayatri Complex IInd Floor Somwarpeth Near Jain Mandir. Pune 411 011 Ph 64017298 pune schandgroup com Marketing Office. RAIPUR Kailash Residency Plot No 4B Bottle House Road Shankar Nagar Raipur 492 007. Ph 2443142 Mb 09981200834 raipur schandgroup com Marketing Office. RANCHI Flat No 104 Sri Draupadi Smriti Apartments Near of Jaipal Singh Stadium Neel Ratan Street. Upper Bazar Ranchi 834 001 Ph 2208761 ranchi schandgroup com Marketing Office. SILIGURI 122 Raja Ram Mohan Roy Road East Vivekanandapally P O Siliguri Siliguri 734001. Dist Jalpaiguri W B Ph 0353 2520750 Marketing Office siliguri schandgroup com. VISAKHAPATNAM No 49 54 15 53 8 Plot No 7 1st Floor Opp Radhakrishna Towers. Seethammadhara North Extn Visakhapatnam 530 013 Ph 2782609 M 09440100555. visakhapatnam schandgroup com Marketing Office, Copyright Reserved. All rights reserved No part of this publication may be reproduced or copied in any material form including. photo copying or storing it in any medium in form of graphics electronic or mechanical means and whether. or not transient or incidental to some other use of this publication without written permission of the copyright. owner Any breach of this will entail legal action and prosecution without further notice. Jurisdiction All disputes with respect to this publication shall be subject to the jurisdiction of the Courts. tribunals and forums of New Delhi India only, First Edition 2007.
Subsequent Editions 2009 2010 2011 2012, Sixth Revised Edition 2013. ISBN 81 219 2805 2 Code 14C 544, PRINTED IN INDIA, By Rajendra Ravindra Printers Pvt Ltd 7361 Ram Nagar New Delhi 110 055. and published by S Chand Company Pvt Ltd 7361 Ram Nagar New Delhi 110 055. PREFACE TO THE SIXTH EDITION, Reference to the latest papers of GATE and various universities have been inserted at proper. places Solutions of some new problems are also given. Suggestions for further improvement of the book will be gratefully received. M D Raisinghania, PREFACE TO THE FOURTH EDITION, New matter and latest questions of various universities have been added at appropriate places. In addition to this the following new useful topics have been added. Appendix A Boundary value problems and Green s identities. Appendix B Two and three dimensional Dirac delta functions. Appendix C Additional topics and problems based on Green s functions. I hope that these changes will make the material of this book more useful to the reader. Suggestions for further improvement of the book will be gratefully received. M D Raisinghania, PREFACE TO THE THIRD EDITION, Reference to the latest papers of various universities and GATE have been inserted at proper.
places More additional problems have been inserted in the miscellaneous set of problems given. at the end of the book, I hope that these changes will make the material more accessible and attractive to the reader. All valuable suggestions for further improvement of the book will be highly appreciated. M D Raisinghania, Disclaimer While the authors of this book have made every effort to avoid any mistake or omission and have used their skill. expertise and knowledge to the best of their capacity to provide accurate and updated information The author and S Chand does. not give any representation or warranty with respect to the accuracy or completeness of the contents of this publication and are. selling this publication on the condition and understanding that they shall not be made liable in any manner whatsoever S Chand. and the author expressly disclaim all and any liability responsibility to any person whether a purchaser or reader of this publication. or not in respect of anything and everything forming part of the contents of this publication S Chand shall not be responsible for. any errors omissions or damages arising out of the use of the information contained in this publication. Further the appearance of the personal name location place and incidence if any in the illustrations used herein is purely. coincidental and work of imagination Thus the same should in no manner be termed as defamatory to any individual. This book on Linear integral equations and boundary value problems has been specially. written as per latest UGC model carriculum for MA M Sc students of all Indian universities. institutions In addition this book will prove very useful for students preparing for various engi. neering and professional examinations such as GATE C S I R NET JRF and SLET etc. The author possesses a very long and rich experience of teaching mathematics and has first. hand experience of the problems and difficulties that students generally face. The silent features of this book are, The matter has been presented in a simple and lucid language so that students them. selves shall be able to understand the solutions of the problems. Each chapter opens with necessary definitions and complete proofs of the standard. results and theorems These in turn are followed by solved examples which have been. classified in various types and methods This classification will help the students to. revise the subject matter at the time of examination without losing any confidence. Care has been taken not to omit important steps so that the students can understand. every thing without the guidance of a teacher Furthermore a set of unsolved exercises. is given in each chapter to instill confidence in the students. In view of these special features it is sincerely hoped that the book will surely serve its. I am grateful to Shri Ravindra Kumar Gupta Managing Director Shri Navin Joshi General. Manager and Shri R S Saxena Adviser Publishing for showing keen interest throughout the. preparation of the book My sincere thanks are due to Shri Shishir Bhatnagar for bringing the book. in an excellent form, All valuable suggestions for further improvement of the book will be highly appreciated. M D Raisinghania, COMPLETE SYLLABUS FOR, INTEGRAL EQUATIONS AND BOUNDARY VALUE PROBLEMS.
AS PER LATEST U G C MODEL CARRICULUM, FOR M A M SC MATHEMATICS OF ALL INDIAN UNIVERSITIES INSTITUTIONS. Definitions of integral equations and their classification Eigenvalues and eigenfunctions. Fredholm integral equations of second kind with separable kernels Reduction to a system of alge. braic equations An approximate method, Method of successive approximations Iterative schemes for Fredholm integral equations of the. second kind Conditions of uniform convergence and uniqueness of series solution Resolvent kernel. and its results Application of iterative scheme to Volterra integral equations of the second kind. Classical Fredholm theory Fredholm theorems, Integral transform methods Fourier transform Convolution integral Application to Volterra. integral equations with convolution type kernels, Abel s equations Inversion formula for singular integral equation with kernel of the type. h s h t 0 a 1 Cauchy s principal value of singular integrals Solution of Cauchy type integral. equation The Hilber kernel Solution of the Hilbert type singular integral equation. Symmetric kernels Complex Hilbert space Orthonormal system of functions Fundamental. properties of eigenvalues and eigenfunctions for symmetric kernels Expansion in eigenfunction and. bilinear form Hilbert Schmidt theorem and some immediate consequences Solutions of integral. equations with symmetric kernels, Definition of a boundary value problem for an ordinary differential equation of the second.
order and its reduction to a Fredholm integral equation of the second kind Dirac delta function. Green s function approach to reduce boundary value problems of a self adjoint differential equation. with homogeneous boundary conditions to integral equation forms Auxiliary problem satisfied by. Green s function Integral equation formulations of boundary value problems with more general and. inhomogeneous boundary conditions Modified Green s function. Integral representation for the solution of the Laplace s and Poisson s equations Newtonian. single layer and double layer potentials Interior and exterior Dirichelet and Neumann boundary. value problems for Laplace s equation Green s function for Laplace s equation in a space as well as. in a space bounded by a ground vessel Integral equation formulation of boundary value problems for. Laplace s equation Poisson s integral formula Green s function for the space bounded by grounded. two parallel plates or an infinite circular cylinder. Perturbation techniques and its applications to mixed boundary value problems Two part and. three part boundary value probelms, Solutions of electrostatic problems involving a charged circular and annular disc a spherical. cap an annular spherical cap in a free space or a bounded space. REFERENCES, 1 R P Kanwal Linear integral equations Theory and techniques Academic Press NewYork. 2 S G Mikhlin Linear integral equations translated from Russian Hindustan Book Agency. 3 I N Sneddon Mixed boundary value problems in potential theory North Holland 1966. 4 I Stakgold Boundary value probelms of mathematical physics Vol I and II Macmillan 1969. Dedicated to the memory of, my parents, 1 PRELIMINARY CONCEPTS 1 1 1 12. 1 1 Introduction 1 1, 1 2 Abel s problem 1 1, 1 3 Integral equation Definition 1 2. 1 4 Linear and non linear integral equations 1 2, 1 5 Fredholm integral equation 1 3.
i Fredholm integral equation of the first kind 1 3. ii Fredholm integral equation of the second kind 1 3. iii Fredholm integral equation of the third kind 1 3. iv Homogeneous Fredholm integral equation 1 3, 1 6 Volterra integral equation 1 3. i Volterra integral equation of the first kind 1 3. ii Volterra integral equation of the third kind 1 3. iii Volterra integral equation of the second kind 1 4. iv Homogeneous Volterra integral equation 1 4, 1 7 Singular integral equation 1 4. 1 8 Special kinds of kernels 1 4, i Symmetric kernel 1 4. ii Separable or degenerate kernel 1 4, 1 9 Integral equation of the convolution type 1 5. 1 10 Iterated kernels or functions 1 5, 1 11 Resolvent kernel or reciprocal kernel 1 5.
1 12 Eigenvalues or characteristic values or characteristic numbers Eigenfunctions. or fundamental functions 1 6, 1 13 Leibnit z rule of differentiation under integral sign 1 6. 1 14 An important formula for converting a multiple integral into a single ordinary. integral 1 6, 1 15 Regularity conditions 1 7, Square integrable function or 2. function 1 7, 1 16 The inner or scalar product of two functions 1 8. M D Raisinghania Disclaimer While the authors of this book have made every effort to avoid any mistake or omission and have used their skill expertise and knowledge to the best of their capacity to provide accurate and updated information

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