Customer Reviews

Linear Operator Theory in Engineering and Science (Applied Mathematical Sciences)

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At graduate school, I was required to take only 9 credit units in advanced Mathematics. Most of my credits were on Numerical Analysis, Mathematical Optimization and Linear Algebra. However, as I started covering advanced courses in dynamical systems, robust control and nonlinear systems, I found that I really needed strong foundations in Functional Analysis. I audited one course in Functional Analysis where we used the classic Rudin text. However, the pace of that class was too fast for me and I virtually learnt nothing. So I graduated with a handicap that I was unable to handle most rigorous problems. Knowing my handicap, I bought several books on this subject; I did not want to spend too much money, so each book did not cost more than $50 on Amazon marketplace. At first it was very disappointing because each book that I bought was written in the traditional format of Definition-Theorem-Proof without explaining the basic concepts. The last book to buy was this one which I read chapter by chapter from page one to the last page for about four months every evening. I believe this will be my last book on functional analysis, because it has provided what I have been looking for.

The book is well organized, and it provides detailed discussion on each topic followed with numerous and easy to understand examples that are directly related to physical systems. The reader can visualize the concepts by relating to physical systems, which is what engineering students want. After four months of evening reading, it is amazing that now I can tackle all analysis problems that used to intimidate me. This book is a must for all graduate students whose major covers dynamical systems, controls, nonlinear systems or signal processing.

An eminently readable functional analysis book including an appendix on measure theory and probability spaces. The text covers the material without explicit development of the Lebesgue integral. The notation and typesetting are very clean and the section on spectral analysis is unusually good. The proofs are very clean and complete with numerous illustrative engineering examples and diagrams. I recommend this book for graduate level engineering students.

This is a great book for the applied mathematician, scientist, or engineer who wants an applicable and not overly formal introduction to functional analysis. Many examples illustrating the use of the techniques are given throughout. The text is quite readable, with a unique organization introducing algebraic, topological, and combined algebraic-topological structures and their associated theory. The book presents functional analysis without explicitly relying on the Lebesgue integral, although a well-written appendix covers Lebesgue integration and some related concepts from real variable theory. I would have appreciated more discussion of differential equations, but overall this is a very well-written book and a worthy purchase.

This is one of my favourite introductory books on functional analysis because it includes all the fundamental concepts needed to get a thorough understanding of the most important topics in this theory. It stresses which properties come from which structure (set-theoretic, topological, or algebraic), and gives a complete exposition of the main results on bounded and unbounded operators, meanwhile discussing some interesting examples of application. Its appendices on integration, probability and stochastic processes are also valuable. The text is suitable for undergraduate analysis and functional analysis courses. Scientists and engineers will find it very useful also because of its non-pedantic style.

Please check my other reviews in my member page (just click on my name above).

I also recommend the "Optimizaton by vector space" by David Luenberger. It is also a very good book on linear operator with optimization applications.

If your are engineer and want to find an intitutive introduction of functional analysis. That is.

Very Nice Book!
So many examples, almost all the theorems having proofs.
Many graphs, which help comprehension a lot!