A First Course in Functional Analysis 1st edition by Promislow, S. David (2008) Hardcover

by S. David Promislow

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.

Hardcover

First published January 1, 2008

Reviews

[meadow · Rating 3 out of 5]

not a bad introduction to functional analysis, though it contains a lot of typos, some of which are very confusing. i understand why measure theory was avoided for the most part, and i am kind of grateful for it, but it made the parts of the book that did involve measure theory both tough and unfulfilling. maybe a chapter 0 about the necessary measure theory would be good? it covers the material in the appendix but doesn't do too great of a job. i'm also not completely sure on the idea of talking so much about banach spaces before talking about hilbert spaces. i get that banach spaces are "simpler" in the sense of being more general, but that just makes them more tricky to deal with. additionally, hilbert spaces are already kind of familiar to anyone who's had a linear algebra class, so it seems strange not to start from there. the exercises are good but not great. one thing the author did particularly well was explaining the motivation for the development of certain ideas, and occasionally briefly mentioning applications. all in all i feel it's given me a good grounding for when i more properly study functional analysis.

note: i only read about the first half.