Synopsis
This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects. This second edition includes more extended coverage of the classical and abstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added. The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics. Reviews of first "This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. … Detailed solutions of the exercises are provided in an appendix." (L’Enseignment Mathematique, Vol. 49 (1-2), 2003) "The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises … test the reader’s comprehension at every stage. Summing Recommended." (F. E. J. Linton, Choice, September, 2003)
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Review
From the reviews: "The material in this book is a mixture of functional analysis, presented at the level of a mathematics students, and (mechanical) engineering applications. ... It is a concise but complete treatment of the abstract notions underlying problems in continuum mechanics. It grew out of 30 years of experience of the authors and it is a welcome translation of Russian edition. It will be highly appreciated by graduate students in mathematics, physics and engineering." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 12 (1), 2005) "The book is a revised and extended translation of the Russian edition. ... The book is suitable for readers in continuum mechanics and can be recommended to graduate students and researchers in mathematics, physics and engineering." (EMS – European Mathematical Society Newsletter, March, 2004) "This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. ... Detailed solutions of the exercises are provided in an appendix." (L’Enseignment Mathematique, Vol. 49 (1-2), 2003) "The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises ... test the reader’s comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003) "The formulated applications are by all means interesting. It is also very good that more complicated problems have been included. ... The book gives a survey of material which every worker in applications of functional analysis to various parts of mechanics should know." (Rudolf Kodnár, Zentralblatt MATH, Vol. 1014, 2003) "This textbook is based on the course of lectures on functional analysis ... . General ideas and algorithms are clear and understandable. There is a good index attached. ... This skillfully-written book is a reader friendly and well-organized textbook in the field of Mathematical Mechanics. It can be highly recommended for students of technology universities as well as for researchers in Mechanics. ... The book is recommended for purchase by university libraries and for individuals interested in the mathematical problems of Mechanics." (I Andrianov, Applied Mechanics Reviews, Vol. 56 (4), 2003)
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