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

Book Description

This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.

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Thorough, clear and very relevant for engineering students.......2006-06-21

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.

Excellent applied functional analysis text.......2003-04-11

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.

An eminently readable functional analysis book.......2000-06-12

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.

Enlightening for mathematicians, scientists, and engineers.......2000-04-07

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).

Continued Comment.......1999-04-07

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

Linear Operator Theory in Engineering and Science

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Linear Operator Theory in Engineering and Science

Manufacturer: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540907483

Linear Operators and Linear Systems: An Analytical Approach to Control Theory (London Mathematical Society Student Texts)

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Linear Operators and Linear Systems: An Analytical Approach to Control Theory (London Mathematical Society Student Texts)
Jonathan R. Partington
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521546192

Book Description

This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be suitable for a course in functional analysis. The book also includes applications to partial differential equations, the stability and stabilization of linear systems, power signal spaces, and delay systems, treated from an input/output point of view.

Two-Dimensional Linear Systems (Lecture Notes in Control & Information Sciences Vol 68)

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Two-Dimensional Linear Systems (Lecture Notes in Control & Information Sciences Vol 68)
T. Kaczorek
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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An Introduction to the Theory of Piezoelectricity (Advances in Mechanics and Mathematics)

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An excellent book on device analytical techniques

An Introduction to the Theory of Piezoelectricity (Advances in Mechanics and Mathematics)
Jiashi Yang
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Piezoelectric Transducers and Applications

ASIN: 0387235736

Book Description

This volume is intended to provide researchers and graduate students with the basic aspects of the continuum modeling of electroelastic interactions in solids. A concise treatment of linear, nonlinear, static and dynamic theories and problems is presented. The emphasis is on formulation and understanding of problems useful in device applications rather than solution techniques of mathematical problems. The mathematics used in this book is minimal. This volume is suitable for a one-semester graduate course on electroelasticity. It can also be used as a reference for graduate students and researchers in mechanics and acoustics.

Customer Reviews:

An excellent book on device analytical techniques.......2005-03-19

This book by Prof Yang is an excellent book for people want to know more about piezoelectricity and piezoelectric devices.

It starts with a complete theory of piezoelectricity with the intention to get readers familirize with the fundamentals. This part is complicated from its appearance, but there is a purpose. Such formulation is essential in dealing with complicated issues which discussed in detail later, ie the effect of various bias fields like thermo, stress, acceleration and so on.

After descriptions of the basic nonlinear theory, the chapters followed restore to the linear theory for various strctural elements and applications as devices. It touched almost all applications of acosutic devices with simple analytical solutions.

The methods and techniques are not directly related to the engineering solutions of actual problems, but it is the first step you have to take towards the direction.

I highly recommend this book to graduate students and engineers who are interested in advanced knowledge on this subject.

Algebra and Analysis for Engineers and Scientists

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Algebra and Analysis for Engineers and Scientists
Anthony N. Michel , and Charles J. Herget
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Paperback

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Book Description

"This is an intermediate level text, with exercises, whose avowed purpose is to provide the science and engineering graduate student with an appropriate modern mathematical (analysis and algebra) background in a succinct, but nontrivial, manner.... [T]he book is quite thorough and can serve as a text, for self-study, or as a reference." —Mathematical Reviews

Written for graduate and advanced undergraduate students in engineering and science, this classic book focuses primarily on set theory, algebra, and analysis. Useful as a course textbook, for self-study, or as a reference, the work is intended to:

* provide readers with appropriate mathematical background for graduate study in engineering or science;

* allow students in engineering or science to become familiar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor;

* give readers a unified overview of applicable mathematics, enabling them to choose additional, advanced topical courses in mathematics more intelligently.

Whereas these objectives for writing this book were certainly pertinent over twenty years ago when the work was first published, they are even more compelling now. Today’s graduate students in engineering or science are expected to be more knowledgeable and sophisticated in mathematics than students in the past. Moreover, today’s graduate students in engineering or science are expected to be familiar with a great deal of ancillary material (primarily in the computer science area), acquired in courses that did not even exist a couple of decades ago.

The book is divided into three parts: set theory (Chapter 1), algebra (Chapters 2–4), and analysis (Chapters 5–7). The first two chapters deal with the fundamental concepts of sets, functions, relations and equivalence relations, and algebraic structures. Chapters 3 and 4 cover vector spaces and linear transformations, and finite-dimensional vector spaces and matrices. The last three chapters investigate metric spaces, normed and inner product spaces, and linear operators. Because of its flexible structure, Algebra and Analysis for Engineers and Scientists may be used either in a one- or two-semester course by deleting appropriate sections, taking into account the students’ backgrounds and interests.

A generous number of exercises have been integrated into the text, and a section of references and notes is provided at the end of each chapter. Applications of algebra and analysis having a broad appeal are also featured, including topics dealing with ordinary differential equations, integral equations, applications of the contraction mapping principle, minimization of functionals, an example from optimal control, and estimation of random variables.

Supplementary material for students and instructors is available at http://Michel.Herget.net.

Factorization of Matrix and Operator Functions: The State Space Method (Operator Theory: Advances and Applications / Linear Operators and Linear Systems)

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Factorization of Matrix and Operator Functions: The State Space Method (Operator Theory: Advances and Applications / Linear Operators and Linear Systems)
Harm Bart , Israel Gohberg , Marinus A. Kaashoek , and André C.M. Ran
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover

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ASIN: 3764382678

Book Description

The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization.

Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces.

Nonlinear Feedback Control Systems: An Operator Theory Approach

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Nonlinear Feedback Control Systems: An Operator Theory Approach
Rui J. P. Defigueiredo , and Guanrong Chen
Manufacturer: Academic Pr
ProductGroup: Book
Binding: Hardcover

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ASIN: 0122086309

Operator Approach in Linear Problems of Hydrodynamics: Volume 1: Self-adjoint Problems for an Ideal Fluid (Operator Theory: Advances and Applications)

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Operator Approach in Linear Problems of Hydrodynamics: Volume 1: Self-adjoint Problems for an Ideal Fluid (Operator Theory: Advances and Applications)
Nikolay D. Kopachevskii , and Selim G. Krein
Manufacturer: Birkhauser
ProductGroup: Book
Binding: Hardcover

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ASIN: 3764354062

Book Description

This is the first volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The work is a sequel to and at the same time substantially extends the volume "Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems" by N.D. Kopachevsky, S.G. Krein and Ngo Zuy Kan, published in 1989 by Nauka in Moscow. It includes several new problems on the oscillations of partially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The work relies on the authors' and their students' works of the last 30-40 years. The readers are not supposed to be familiar with the methods of functional analysis. In the first part of the present volume, the main facts of linear operator theory relevant to linearized problems of hydrodynamics are summarized, including elements of the theories of distributions, self-adjoint operators in Hilbert spaces and in spaces with an indefinite metric, evolution equations and asymptotic methods for their solutions, the spectral theory of operator pencils. The book is particularly useful for researchers, engineers and students in fluid mechanics and mathematics interested in operator theoretical methods for the analysis of hydrodynamical problems.

Partially Observable Linear Systems Under Dependent Noises (Systems & Control: Foundations & Applications)

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Partially Observable Linear Systems Under Dependent Noises (Systems & Control: Foundations & Applications)
Agamirza E. Bashirov
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover

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ASIN: 376436999X

Book Description

Noise is a rich concept playing an underlying role in human activity. Consideration of the noise phenomenon in arts and sciences, respectively, makes the distinction between both domains more obvious. Artists create "deliberate noise"`; the masterpieces of literature, music, modern fine art etc. are those where a clear idea, traditionally related to such concepts as love, is presented under a skilful veil of "deliberate noise". On the contrary, sciences fight against noise; a scientific discovery is a law of nature extracted from a noisy medium and refined.

This book discusses the methods of fighting against noise. It can be regarded as a mathematical view of specific engineering problems with known and new methods of control and estimation in noisy media.

The main feature of this book is the investigation of stochastic optimal control and estimation problems with the noise processes acting dependently on the state (or signal) and observation systems. While multiple early and recent findings on the subject have been obtained and challenging problems remain to be solved, this subject has not yet been dealt with systematically nor properly investigated. The discussion is given for infinite dimensional systems, but within the linear quadratic framework for continuous and finite time horizon. In order to make this book self-contained, some background material is provided.

Consequently, the target readers of this book are both applied mathematicians and theoretically oriented engineers who are designing new technology, as well as students of the related branches. The book may also be used as a reference manual in that part of functional analysis that is needed for problems of infinite dimensional linear systems theory.

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