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 edition:
"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)
