Normed Spaces.- Bounded and Compact Operators.- Riesz Theory.- Dual Systems and Fredholm Alternative.- Regularization in Dual Systems.- Potential Theory.- Singular Integral Equations.- Sobolev Spaces.- The Heat Equation.- Operator Approximations .-Degenerate Kernel Approximation.- Quadrature Methods.- Projection Methods.- Iterative Solution and Stability.- Equations of the First Kind.- Tikhonov Regularization.- Regularization by Discretization.- Inverse Boundary Value Problems.- References.- Index.
"The book contains 18 well presented chapters with an extensive list of 249 references. ... It also contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear, and in the proper modern framework. ... It is recommended for study to students, teachers, and all others who are interested in the development of this useful, and live area of mathematics." (K. C. Gupta, zbMATH 1328.45001, 2016) "The book being reviewed is the third edition of a well received one on integral equations which combines theory, applications and also numerical methods. ... the book is more suitable for graduate students. The writing is lucid and clear, and the presentation is excellent. ... the book should appeal not just to mathematicians, but also to scientists and engineers who wish to learn the theory of integral equations, the methods used to solve them, and their applications." (Peter Shiu, The Mathematical Gazette, Vol. 99 (544), March, 2015)