Functional Analysis for Physics and Engineering 1st Edition by Hiroyuki Shima (PDF)

Description

This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials, making it accessible for those unfamiliar with graduate-level mathematics. Topics include topology, vector spaces, tensor spaces, Lebesgue integrals, and operators, to name a few. Each chapter explains, concisely, the purpose of the specific topic and the benefit of understanding it. Researchers and graduate students in physics, mechanical engineering, and information science will benefit from this view of functional analysis.

User’s Reviews

Editorial Reviews: About the Author Hiroyuki Shima

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is indeed a unique book. Its uniqueness consists of making clear and explicit the subtle issues in passing from the finite dimensions to infinite dimensions, that is, passing from linear algebra to functional analysis. These subtle issues are often glossed over by authors in a hurry to impress you with dry formalism. This book will serve as a very good introduction to standard books like Kreyszig’s Functional Analysis which is a quite good text book but does not make the subtle distinctions between finite and infinite dimensions so clear and explicit.Another field which badly needs a teacher and author like Hiroyuki Shima San is the theory of infinite dimensional representations, because this field very badly needs a very good introduction to works of Gelfand and Harish-chandra. Again the difficulty is the subtle issues in passing from finite to infinite dimensional representations.Rattan Mann,Rattan Mann Films,[…]

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⭐I have a background in computer science and ive been trying to approach functional analysis for sometime. This book gives a crystal clear birds eye view of the subject. After reading a few times, now im going through functional analysis books knowing what the hell they are talking about: topology spaces, Banach spaces, Hilbert Spaces, l and L norms and spaces, Lebesgue integral, measure, operator theory, distribution etcAfter this book i want to read every functional analysis book that exists!

⭐Good if you already know some of the material. The definitions are rather precise, but the discussions lack some of the depth of the subject. For instance, on the chapter on topology, he mentions the axiomatic definition, but doesn’t do anything with it. I’ve read most of the text at this point, and I imagine another more rigorous text is needed to follow up if having to use the stuff a lot.Overall, the physical examples are a bit hand wavey, but the content is nice light reading for grad students in physics (with a moderate math background).The chapter on distributions is a bit lack-luster. Lighthill’s book on generalized functions and Fourier transforms is much nicer in terms of actual use.

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