This book started its life as a series of lectures given by the
second author from the 1970's onwards to students in their third
and fourth years in the Department of Mechanics and Mathematics at
Rostov State University. For these lectures there was also an
audience of engineers and applied mechanicists who wished to
understand the functional analysis used in contemporary research in
their fields. These people were not so much interested in
functional analysis itself as in its applications; they did not
want to be told about functional analysis in its most abstract
form, but wanted a guided tour through those parts of the analysis
needed for their applications. The lecture notes evolved over the
years as the first author started to make more formal typewritten
versions incorporating new material. About 1990 the first author
prepared an English version and submitted it to Kluwer Academic
Publishers for inclusion in the series Solid Mechanics and its
Applications. At that state the notes were divided into three long
chapters covering linear and nonlinear analysis. As Series Editor,
the third author started to edit them. The requirements of lecture
notes and books are vastly different. A book has to be complete (in
some sense), self contained, and able to be read without the help
of an instructor.
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