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Lectures on Integral Equations

Harold Widom
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
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This is a charming book. In the space of 125 pages it provides a modern (but pleasingly concrete) introduction to integral equations, as well as a concise introduction to Banach and Hilbert spaces and to orthogonal expansions.The present book is a 2016 Dover corrected reprint of the 1969 Van Nostrand edition. It is a polished set of lecture notes from a 1963 course at Cornell, prepared by David Drasin and Anthony J. Tromba.

As you would expect from this description, the emphasis is on integral operators more than integral equations, and in fact it has only a moderate amount of material on integral equations. The capstone (about 1/5 of the book) is a thorough look at second-order linear differential equations, after rewriting them as integral equations, and covers both existence theorems and solution methods. The book deals with a number of specific integral and differential equations, but does not deal with applications to physics or other areas. It has one excursion into more classical areas, which is a brief chapter outlining Fredholm’s approach to integral equations.

Another modern introductory book, that I have not seen but is well-regarded, is Kress’s Linear Integral Equations (Springer, 3rd edition, 2014). It has a more applied slant and includes some numerical work. A more traditional book (going back to 1957 but still in print from Dover) is Tricomi’s Integral Equations.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is His mathematical interests are number theory and classical analysis.


I. Banach Spaces

II. Completely Continuous Operators

III. The Fredholm Theory

IV. Hilbert Space Theory

V. Applications to Ordinary Differential Equations

VI. Singular Integral Operators