Integral Equations by Harry Hochstadt (PDF)

Description

This classic work is now available in an unabridged paperback edition. Hochstatdt’s concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of the Schauder fixed point theorem to nonlinear equations.

User’s Reviews

Editorial Reviews: About the Author Harry Hochstadt is the author of Integral Equations, published by Wiley.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The following is an exact quote from the book under a section called “Kernels with Weak Singularities”- In general, integral equations with singular kernels are very difficult to handle. For the moment, we shall not offer a precise definition for a singular kernel. Loosely speaking, these are kernels that do not satisfy the previously discussed conditions (which encompass the past 30 of 35 pages).It’s a great book if you already know a lot about the most popular integral equations and need some supplemental material to go a little bit deeper or if you have the desire to continue the study of integral equations, but it’s not a good book to learn about I.E. because it follows the basic format outlined above; it’s not that hard or that time consuming to add a paragraph explaining what weak singularities are and how they will be expressed in the book. And considering the price of the book, I expected much more than I was given. Courant and Hilbert’s Methods of Mathematical Physics Volume I, by the same publisher, does an equivalent job in about 60 pages; but it is by no means a complete explanation of the subject.There are better books at better prices. But it is accurate despite the lousy format of “no time for a short explanation, we’ve got to differentiate or this bus is going to explode!”

⭐The theory of Integral Equations (IE) is exposed in the framework of Hilbert spaces. The book is mainly oriented towards the theory of compact integral operators, partial differential operators and boundary value problems. It provides a complete treatment of numerous transform techniques (Fourier, Laplace, Mellin, Hankel, Hilbert). The classical Fredholm theory makes the object of a full chapter. The last chapter deals with the nonlinear IE. The book is written is a very nice way, very simple. Numerous examples and exercises are provided. Each chapter begins with an overview of the goals and of the results, which is really nice!This book is intended to be simple, dedicated to students. It provides a good introduction to the world of IE (see also Jerry, Introduction to IE with applications). Applications of the IE are to be found in other, more specialized books.

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