Integral Equations and Their Applications

For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles.Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eight chapters, pedagogically organized. This book is specially designed for those who wish to understand integral equations without having extensive mathematical background.Some knowledge of integral calculus, ordinary differential equations, partial differential equations, Laplace transforms, Fourier transforms, Hilbert transforms, analytic functions of complex variables and contour integrations are expected on the part of the reader.

Professor Matiur Rahman is Professor of Applied Mathematics and Fluid Mechanics in the Department of Engineering Mathematics at Dalhousie University in Halifax, Canada. He has taught mathematical methods in many universities aroudn the world, including Jorhat Engineering College in Assam, Imperial College of Science, Technology and Medicine in UK, Windsor, Moncton, Ottawa and Manitoba Universities in Canada. He received his PhD (1973) from Windsor University, Canada and his DSc (Eng) (1992) from London University, UK. His other academic achievements include a BSc (Hons) (1962) from Cotton College, India; an MSc (1964) from Gauhati University, India; a DIC (1969) from Imperial College, UK and a MPhil (1969) from London University, UK. In 1990, he was elected a Fellow of the Institute of Mathematics and Its Applications (FIMA), in 1991, a Chartered Mathematician of IMA, and in 1992 the American Biographical Institute selected him as Man of the Year. Professor Rahman earned a WIT (UK) Eminent Scientists Award for his outstanding research contributions in Fluid Mechanics Science and a medal was presented at the Fourth International Conference on Advances in Fluid Mechanics held at Ghent, Belgium on 15 May 2002. He is the first Canadian Scientist to receive such a medal. At the International Conference on Advances in Fluid Mechanics held at Lisbon, Portugal 22-24 March 2004, Professor Rahman was admitted as a Fellow of Wessex Institute of Great Britain (FWIGB). He was also presented with a certificate for his outstanding research and leadership in the field of Fluid Mechanics. He was also recognized for his outstanding research and teaching accomplishments by the Assam Sahitya Sabha at its 68th Open Session held at Sipajhar, Assam, India on 19 February 2005. Professor Rahman has published 16 textbooks and research monographs and over 200 research papers in refereed journals and proceedings. His graduate textbook Water Waves: Relating Modern Theory to Advanced Engineering Applications brought considerable accolades from the scientific community, was reviewed in the SIAM Reviews, and received an award from the Natural Sciences and Engineering Research Council of Canada (NSERC) in 1996. Professor Rahman was awarded the 2001 Outstanding Academic Title Award by CHOICE Magazine for his book Mathematical Methods with Applications. In 2006, Professor Rahman founded the journal International Journal of Applied Mathematics and Engineering Sciences . Professor Rahman's main research interests are in areas of waves and hydrodynamic loading, fluid-structure interaction, natural convection flows with diffusion and reaction, stability of tubular chemical flow reactors, temperature stratification in large bodies of water, and non-linear ocean waves. Professor Rahman is currently Managing Editor of the international series on Advances in Fluid Mechanics, published by WIT Press, UK, 32 volumes of which has been published since it was created by him in 1993. The main aim of the Series is to exchange new research findings and ideas on modern fluid mechanics between scientists and engineers. Professor Rahman has been an external and internal examiner of over 30 MSc and PhD theses in Applied Mathematics and Engineering disciplines, and has supervised several MSc(12) and PhD(8) theses in Fluid Mechanics. Many Postdoctoral Fellows have worked with him. Because of his outstanding research accomplishments and the high-standard training he provides, NSERC has been funding Professor Rahman research grants continuously since 1981. Professor Rahman is presently one of the recepients of a $2.7 million grant for Oil and Gas recovery and production research.