Preface to the English Edition
This book started about 30 years ago as a course of lectures on functional analysis given by a youthful Prof. I.I. Vorovich to his students in the Department of Mathematics and Mechanics (division of Mechanics) at Rostov State University. That course was subsequently extended through the offering, to those same students, of another course called Applications of Functional Analysis. Later, the courses were given to pure mathematicians, and even to engineers, by both coauthors. Although experts in mechanics are quick to accept results concerning uniqueness or non-uniqueness of solutions, many of these same practitioners seem to hold a rather negative view concerning theorems of existence. Our goal was to overcome this attitude of reluctance toward existence theorems, and to show that functional analysis does contain general ideas that are useful in applications. This book was written on the basis of our lectures, and was then extended by the inclusion of some original results which, although not very new, are still not too well known.
We mentioned that our lectures were given to students of the Division of Mechanics. It seems that only in Russia are such divisions located within departments of mathematics. The students of these divisions study mathematics on the level of mathematicians, but they are also exposed to much material that is normally given at engineering departments in the West. So we expect that the book will be useful for western engineering departments as well.
This book is a revised and extended translation of the Russian edition of the book, and is published by permission of editor house Vuzovskskaya Kniga, Moscow. We would like to thank Prof. Michael Cloud of Lawrence Technological University for assisting with the English translation, for producing the LaTeX files, and for contributing the problem hints that appear in the Appendix.
Department of
Mechanics and Mathematics
Rostov State University, Russia L.P. Lebedev
&
Department of Mathematics
National University of Colombia, Colombia
Department of
Mechanics and Mathematics
Rostov State University, Russia I.I. Vorovich