A concise introduction to the major concepts of functional analysis
Requiring only a preliminary knowledge of elementary linear
algebra and real analysis, A First Course in Functional Analysis
provides an introduction to the basic principles and practical
applications of functional analysis. Key concepts are illustrated
in a straightforward manner, which facilitates a complete and
fundamental understanding of the topic.
This book is based on the author's own class-tested material and
uses clear language to explain the major concepts of functional
analysis, including Banach spaces, Hilbert spaces, topological
vector spaces, as well as bounded linear functionals and operators.
As opposed to simply presenting the proofs, the author outlines the
logic behind the steps, demonstrates the development of arguments,
and discusses how the concepts are connected to one another. Each
chapter concludes with exercises ranging in difficulty, giving
readers the opportunity to reinforce their comprehension of the
discussed methods. An appendix provides a thorough introduction to
measure and integration theory, and additional appendices address
the background material on topics such as Zorn's lemma, the
Stone-Weierstrass theorem, Tychonoff's theorem on product spaces,
and the upper and lower limit points of sequences. References to
various applications of functional analysis are also included
throughout the book.
A First Course in Functional Analysis is an ideal text for
upper-undergraduate and graduate-level courses in pure and applied
mathematics, statistics, and engineering. It also serves as a
valuable reference for practitioners across various disciplines,
including the physical sciences, economics, and finance, who would
like to expand their knowledge of functional analysis.
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