Customer Reviews

Applied Functional Analysis: A First Course for Students of Mechanics and Engineering Science (Civil engineering and engineering mechanics series)

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Written by two experts in the area of computational and applied mathematics, this book is ideal for first/second year graduate students in engineering who wish to use concepts from functional analysis in their work. On one hand, the treatment is mathematically precise and yet the authors use their extensive engineering experience to present examples that are highly intuitive.

The introduction is greatly self-contained and serves as an appetizer for further chapters. Having worked in matrix methods for a while, I found the chapter on linear algebra especially interesting and informative. It explains the underlying concepts behind results that are generally taken for granted otherwise. The next few chapters consist of material that is, in general, not easy to explain and yet the style of the authors significantly simplifies the flow of the book. The topics covered in these chapters are at a level of abstraction higher than that encountered in engineering mathematics. This is evident, for example in the chapter on Lebesgue Integration. The heavy notation that is used sometimes makes it necessary to pay close attention while reading but this is perhaps a small price to pay for precision. The chapters on Banach and Hilbert spaces should be of special interest to people who wish to study the solution of variational boundary value problems.

In all, the book is an excellent text for the beginner and a very useful reference for the advanced user.

A very good first book on functional analysis. The book starts with preliminary set theory, logic, functions, and concepts of abstract algebra and moves on to the big convergence theorems in the Lebesgue integration and onto topological and metric spaces. The book ends with basic theory of Hilbert space. Each section concludes with exercises. The author takes great pains to include a lot of detail in the proofs. I would recommend this book to an advanced undergraduate or beginning graduate student.

I took Functional Analysis from professor Demkowicz. Actually the course is a misnomer, since you learn very little functional analysis and quite a bit more about set theory, Lebesgue measure theory, and topology (through Ch. 4 in the book). While I feel that the book is very meticulously written, it tries to cover in too much detail everything starting from the most basic laws of logic. The proofs and explanations are concise and clear but for my taste I also appreciate a bit of "plain English" explanation before tackling a proof, so I at least have some idea of what is going on. Only get this book if you want an *extremely* detailed development of basic theory and don't care much about applications.

Yet another book that resulted out of Class Notes ! Don't waste your money buying this book if you want to learn applied functional analysis. This book is meant solely for those students who have registered for Leszek's Class at UT, Austin.