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Books : Professional & Technical : Professional Science : Mathematics : Transformations
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The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the field. All the material has been update and several new sections explore the recent progress made in the areas of wavelength modulation, analog information processing, and holography. The book also explores Fourier analysis applications and emphasizes those applications to diffraction, imaging, optical data processing, and holography.
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This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.
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Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis.
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This classic textbook introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
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This classic offers a meticulous account of the theory of finite elasticity. It covers the application of the theory to the solution of boundary-value problems, as well as the analysis of the mechanical properties of solid materials capable of large elastic deformations. Setting is purely isothermal. Problems. References. Appendixes.
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Replete with easy-to-understand examples ranging from the prediction of home runs in baseball using an hierarchical Bayesian statistics model to estimating the expected return at blackjack using control variables, this text functions as a complete consideration of simulation. Sheldon Ross provides broad yet thorough coverage of the subject, presenting the development of a simulation study to analyze models, and demonstrates that by using random variables and the concept of discrete events, it is possible to generate the behavior of a stochastic model over time. Also discussed are questions concerning when to stop a simulation, how much confidence can be placed in the results, and extensive new information on the presentation of the alias method for generating discrete random variables material not found in any other text. Students, practitioners, and researchers alike will find this text to have an important place in their research libraries.
* Presents the statistics needed to analyze simulated data as well as those needed for validating the simulation model
* Stresses variance reduction, including control variables and their relation to regression analysis
* Includes a chapter on Markov chain monte carlo methods
* Emphasizes the use of computers throughout the text -
Broad survey focuses on operators on separable Hilbert spaces. Topics include normal operators, analytic functions of operators, shift operators, invariant subspace lattices, compact operators, invariant and hyperinvariant subspaces, von Neumann algebras, transitive operator algebras, and algebras associated with invariant subspaces. 1973 edition. New Appendix on Recent Developments.
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A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, Taylor coefficients, Hp as a linear space, interpolation theory, the corona theorem, and more. Appropriate for researchers or 2nd- or 3rd-year graduate students. 1970 edition.
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Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.
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Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. 1953 edition.
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Continuing on the success of the previous edition, Introduction to Hilbert Spaces with Applications, Second Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesque integral, and includes an enhanced presentation of results and proofs. Students and researchers benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a new, well-researched chapter on wavelets. Students and researchers agree that this is the definitive text on Hilbert Space theory.
* Systematic exposition of the basic ideas and results of Hilbert space theory
* Introduction to the Lebesgue integral
* New chapter on wavelets
* Improved presentation on results and proof
* Revised examples and updated applications
* Completely updated list of references -
This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. The book is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). The book will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
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From the reviews:
"Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician."
J. Eells in Bulletin of the London Mathematical Society (1980)"Written by two mathematicians who played a crucial role in the development of the modern theory of several complex variables, this is an important book."
J.B. Cooper in Internationale Mathematische Nachrichten (1979) -
This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisite for reading the book is some knowledge of advanced calculus and linear algebra. Throughout the book, examples and applications have been interspersed with the theory. Each chapter concludes with numerous exercises and a section in which the author puts the results of that chapter into a historical perspective. The book is based on lecture notes for a graduate course on best approximation which the author has taught for over 25 years.
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This book studies algebras and linear transformations acting on finite -dimensional vector spaces over arbitrary fields. It is written for students who have prior knowledge of algebra and linear algebra. The goal is to present a balance of theory and example in order for students to gain a firm understanding of the basic theory of finite- dimensional algebras and to provide a foundation for subsequent advanced study in a number of areas of mathematics. As such, the level of exposition is suitable for senior undergraduate students.
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Hardbound.

















