Integral Equations and Integral Transforms

This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert–Schmidt theorem, and the solution of Abel integral equations by using an elementary method.  In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green’s function of a Sturm–Liouville type ordinary differential equation and its applications to physical problems.  The book is divided into two parts: integral equations and integral transforms.Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.

Table of Contents:
Integral Equations: An Introduction.- Fredholm integral equation of the second kind with degenerate kernel.- Integral equations of second kind with more general form of kernel.- Integral equations with symmetric kernel.- Abel integral equations.- Fourier Transform.- Laplace Transform.- Mellin Transform.- Hankel Transform.- Z Transform.- Formal Construction of Integral Transforms and TheirInverses.

About the Author :
Sudeshna Banerjea is Professor at the Department of Mathematics, Jadavpur University, Kolkata. She obtained her M.Sc. degree and Ph.D. degree in Applied Mathematics from the University of Calcutta, respectively, in 1985 and 1992. She was NBHM Post-Doctoral Fellow at the Indian Statistical Institute, Kolkata, in 1993, before joining Jadavpur University as Lecturer in 1993. She is Fellow of the West Bengal Academy of Sciences since 2011. Her research interest includes integral equations, theory of water waves, and associated mathematical methods. With more than 68 research papers, she has supervised more than 8 Ph.D. students. Earlier, she was Principal Investigator for a number of major research projects sanctioned by NBHM, DST, and CSIR.  B. N. Mandal is former NASI Senior Scientist Platinum Jubilee Fellow at the Indian Statistical Institute (ISI), Kolkata (from 2009 to 2014), where he has been Honorary Professor (from 2006 to 2008), and Faculty (from 1989 to 2005). He also had taught at the University of Calcutta (from 1970 to 1989). He earned his M.Sc. degree and Ph.D. degree in Applied Mathematics, respectively, in 1966 and 1973, from the University of Calcutta. He was Postdoctoral Commonwealth Fellow at Manchester University, England, from 1973 to 1975. His research work comprises several areas of applied mathematics including water waves, integral transforms, integral equations, inventory problems, wavelets, etc. He has supervised 27 Ph.D. students and published more than 300 research papers. He was also Chief Editor of the OPSEARCH journal (Springer) and is on the editorial board of a number of reputed journals. He co-authored and co-edited a number of advanced level research monographs published by reputed publishers.  

Review :
“Textbook material is intended for students with different levels of training. The authors tried to present it in such a way as to help the reader master the basics of the subject as much as possible. In this regard, the text provides numerous examples, exercises and test problems. Undoubtedly, this textbook will be useful for getting some initial acquaintance with the theory of integral equations and integral transforms and will give students some idea of this theory as a whole.” (Vitaliy Volchkov, zbMATH 1540.44001, 2024)