PREFACE
Purpose of the book. Functional analysis plays an increasing role in
the applied sciences as well as in mathematics itself. Consequently, it
becomes more and more desirable to introduce the student to the field
at
an early stage of study. This book
is
intended to familiarize the
reader with the basic concepts, principles and methods of functional
analysis and its applications.
Since a textbook should be written for the student, I have sought
to bring basic parts of the field and related practical problems within
the comfortable grasp of senior undergraduate students
or
beginning
graduate students of mathematics and physics. I hope that graduate
engineering students may also profit from the presentation.
Prerequisites. The book
is
elementary. A background in under-
graduate mathematics, in particular, linear algebra and ordinary cal-
culus,
is
sufficient as a prerequisite. Measure theory
is
neither assumed
nor
discussed. No knowledge in topology
is
required; the few consider-
ations involving compactness are self-contained. Complex analysis
is
not
needed, except in one of the later sections (Sec. 7.5), which
is
optional, so that it can easily be omitted. Further help
is
given in
Appendix 1, which contains simple material for review and reference.
The
book should therefore be accessible to a wide spectrum of
students and may also facilitate the transition between linear algebra
and advanced functional analysis.
Courses. The book
is
suitable for a one-semester course meeting five
hours
per
week
or
for a two-semester course meeting three hours
per
week.
The book can also be utilized for shorter courses. In fact, chapters
can be omitted without destroying the continuity
or
making the rest of
the book a torso (for details see below).
For
instance:
Chapters 1 to 4
or
5 makes a very short course.
Chapters 1 to 4 and 7
is
a course that includes spectral theory and
other
topics.
Content and arrangement. Figure 1 shows that the material has
been
organized into
five
major blocks.
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