Book Description
This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.
This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Customer Reviews:
As a reference, this is nice, but as a book for first-time learners..........2007-08-28
I enjoy perusing Rudin's "Functional Analysis" at this stage in my life. It is fairly nice tome for functional analysis, and its general treatment of topological vector spaces (as opposed to the standard Banach space examples studied in a typical functional analysis class) is now well-received.
However, as a student, I was put off by this book. At times, I found it difficult to tie the theory present to the basic examples which were relevant at the time (such as L^{p} spaces). For a first time learner, I would suggest the book of Kolmogorov and Fomin (which is a Dover book, by the way), and would wait until later for this book.
Outstanding.......2007-05-30
Hardly can I find words to highlight the goodness of this book. As mentioned by other readers ,it provides elegant, direct and powerfool proofs of the three theorems which constitute the cornserstones of functional analysis (Hanh-Banach, Banach-Steinhaus and Open mapping). These theorems are, in addition, studied in their most general context, namely topological vector spaces.
Specially appealing is its treatment of distributions' theory. It is, as far as I know, the only text which start by defining the rigurous topology on the set of test functions and then obtains the convergence and continuity of functionals (distributions) in terms of this topolgy, which is, indeed, the only way to present and gain insight into these concepts and to reach some results such as completness. In doing otherwise one risk definitions can emerge as artificial and rather arbitrary.
It is, without any doubt, a must have book for those with interest in pure mathematics as well as for those who, eventually, realize that the only way to dominate their area is saling through mathematics.
Modern topics in math........2003-04-05
"Modern analysis" used to be a popular name for the subject of this lovely book. It is as important as ever, but perhaps less "modern". The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. In the beginning it generated awe in its ability
to provide elegant proofs of classical theorems that otherwise were thought to be both technical and difficult. The beautiful idea that makes it all clear as daylight: Wiener's theorem on absolutely convergent(AC) Fourier series of 1/f if you can divide, and if f has the AC Fourier series, is a case in point. The new subject gained from there because of its many sucess stories,- in proving new theorems, in unifying old ones, in offering a framework for quantum theory, for dynamical systems, and for partial differential equations. And offering a language that facilitated interdisiplinary work in science! The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor in theories surprisingly far from the original roots of the subject. The topics in Rudin's book are inspired by harmonic analysis. The later part offers one of the most elegant compact treatment of the theory of operators in Hilbert space, I can think of. Its approach to unbounded operators is lovely.
The Bible on Distributions.......1999-06-15
No other book covers the elements of distributions and the fourier transform quite like Rudin's Functional Analysis. This is a must for every budding PDE-er!
Uno de los mejores en Análisis Funcional.......1998-02-05
De los excelentes textos en Análisis Funcional que existen en el mercado, éste es de los mejores. Tiene una excelente presentación de la Teoría de Distribuciones, en los capítulos 6, 7 y 8. La teoría espectral como se trata aca es magnifica. Tambien tiene un desarrollo muy completo sobre espacios vectoriales topológicos. Termina con una reseña bibliográfica muy completa.
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Linear Processes in Function Spaces: Theory and Applications (Lecture Notes in Statistics)
D. Bosq
Manufacturer: Springer
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ASIN: 0387950524 |
Book Description
The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces.The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).
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- Differential Geometry review
- Good as a basic textbook and a source of solve problems
- Differential Geometry - A Schaum's Outline Series
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Schaum's Outline of Differential Geometry (Schaum's)
Martin M. Lipschutz
Manufacturer: McGraw-Hill
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Differential Geometry
ASIN: 0070379858 |
Book Description
Students will find all the information covered in the standard textbooks--and more--explained clearly and concisely in this powerful study tool. Unusually detailed, it elucidates all the most difficult-to-grasp concepts that class studies and texts sometimes gloss over. The hundreds of problems with fully explained solutions illuminate important points and teach students sound problem-solving skills. Ideal, also, for independent study.
Customer Reviews:
Differential Geometry review.......2007-01-04
I have found this to be an excellent addition to my library.
Good as a basic textbook and a source of solve problems.......2006-06-05
This book is intended to assist upper level undergraduate and graduate students in their understanding of differential geometry, which is the study of geometry using calculus. Usually students study differential geometry in reference to its use in relativity. I personally have a rather oddball application for the subject - modeling of curved geometry for computer graphics applications. The fundamental concepts are presented for curves and surfaces in three-dimensional Euclidean space to add to the intuitive nature of the material.
The book presumes very little in the way of background and thus starts out with the basic theory of vectors and vector calculus of a single variable in the first two chapters. The following three chapters discuss the concept and theory of curves in three dimensions including selected topics in the theory of contact.
Great care is given to the definition of a surface so that the reader has a firm foundation in preparation for further study in modern differential geometry. Thus, there is some background material in analysis and in point set topology in Euclidean spaces presented in chapters 6 and 7. The definition of a surface is detailed in chapter eight. Chapters 9 and 10 are devoted to the theory of the non-intrinsic geometry of a surface. This includes an introduction to tensor methods and selected topics in the global geometry of surfaces. The last chapter of the outline presents the basic theory of the intrinsic geometry of surfaces in three-dimensional Euclidean space.
Exercises are primarily in the form of proofs, and there are plenty of worked examples. Since the examples are kept to no more than three dimensions, the outline contains plenty of good instructive diagrams that illustrate key concepts. This Schaum's outline has quite a bit of instruction in it past the bare required minimum, but you might still want a good primary textbook. My personal favorite is Pressley's "Elementary Differential Geometry". Overall I find this to be a very good outline and source of solved problems on the subject and I highly recommend it.
Differential Geometry - A Schaum's Outline Series.......2000-06-25
As with all of the Schaum's Outline Series, this book is particularly useful if the readers intent is to gain a working knowledge of the subject. The subject of Differential Geometry is no exception. Dr. Lipschultz has done an excellent job of communicating the essential aspects of differential geometry to the reader. The book assumes a fairly low level of mathematical ability having calculus as the primary prerequisite. From this humble beginning, Dr. Lipschultz takes the reader through the necessary discussions of vector functions, curvature, fundamental forms, and tensor analysis. Given the theoretical nature of the subject, Dr. Lipschultz has included most of the theorems and associated proofs necessary for a general understanding of the subject. However, this book is not a substitute for a serious study of differential geometry. In addition most of the problems are limited to two dimensional surfaces and this reader would have enjoyed a more adventurous investigation of higher dimensional spaces. Like all Schaum's series, the text is chock full of problems and their solution. I recommend this book for anyone interested in quickly gaining a working knowledge of the subject.
Average customer rating:
- An excellent introduction to Relativity
|
Relativity: An introduction to space-time physics
Steve Adams
Manufacturer: CRC
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ASIN: 0748406212 |
Book Description
Provides the essential principles and results of special relativity as required by undergraduates. The text uses a geometric interpretation of space-time so that a general theory is seen as a natural extension of the special theory. Although most results are derived from first principles, complex and distracting mathematics is avoided and all mathematical steps and formulae are fully explained and interpreted, often with explanatory diagrams.; The emphasis throughout the text is on understanding the physics of relativity. The structure of the book is designed to allow students of different courses to choose their own route through the short self-contained sections in each chapter. The latter part of the book shows how Einstein's theory of gravity is central to unraveling fundamental questions of cosmology.
Customer Reviews:
An excellent introduction to Relativity.......2003-05-21
If you are a ambitious highshool student or a physics freshman this is the best place to get started on special realtivity.
It is far less mathematically demanding then many books out there and clear on physical concepts.
(ch.1) Good review of classical ideas.
(ch.2) Need for special relativity, good explanations of
galaian and lorentz transformation, and uses of the latter.
(ch.3) Good introductions to spacetime geometry (the invariant
interval) and relativistic mechanics.
(ch.4) Good introduction to basis of general relativity and cosmmology.
One of the great things about the book is that it takes the common 'popular' accounts one step further by intoducing physics in precise languge and formulas. So that you can apply your knowldege to actully solve some problems and gain further understanding. There are problems at end of each chapter and they are (mostly) supplemented by answers in an appendix.
One thing that is left out completely is relativistic electrodynamics, of course that's only sutibale for a more advanced book. I would've liked to see the power of four vectors utilized more and see the role of tensors.
Book Description
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Customer Reviews:
A superb classic in harmonic analysis........2000-05-31
This book deals with the extension of real and complex methods in harmonic analysis to the many-dimensional case. So, its pre-requisites are a strong background in real and complex analysis and some acquaintance with elementary harmonic analysis, that is, this book is intended for graduate students and working mathematicians. Maybe some advanced undergraduates could cover certain parts of the material.
This book is one component of the Stein trilogy on harmonic analysis (together with "Singular Integrals and Differentiability Properties of Functions" and "Harmonic Analysis", both also reviewed by myself), and as such it must be regarded as an authoritative reference on the subject since Elias Stein and Guido Weiss are two of the leading experts in the field, and the material they selected was taken from their teaching and research experience.
The contents of the book are: The Fourier Transform; Boundary Values of Harmonic Functions; The Theory of H^p Spaces on Tubes; Symmetry Properties of the Fourier Transform; Interpolation of Operators; Singular Integrals and Systems of Conjugate Harmonic Functions; Multiple Fourier Series.
Includes motivation and full explanations for each topic, excercises for each chapter, called "further results", and extensive references. Outstanding printing quality and nice clothbound.
These three volumes should be present in every analyst's library.
Please take a look to the rest of my reviews (just click on my name above).
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Gaussian Hilbert Spaces (Cambridge Tracts in Mathematics)
Svante Janson
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The Malliavin Calculus and Related Topics (Probability and its Applications)
ASIN: 0521561280 |
Book Description
This book treats the very special and fundamental mathematical properties of a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, statistics and theoretical physics. The book concentrates on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.
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Univalent Functions and Teichmüller Spaces (Graduate Texts in Mathematics)
O. Lehto
Manufacturer: Springer
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ASIN: 0387963103 |
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This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the later chapters of Bourbaki's
Topologie générale. It completes the treatment of general topology begun in Part I (Ch. 1-4, also available in English in softcover). The real numbers having been introduced in Ch. 4, the first chapters of this volume study subgroups and quotients of R (with applications to the 'measurement of magnitudes' and to the log and exp functions), then real vector spaces and projective spaces, then the additive groups Rn (subgroups, quotients, homomorphisms, infinite sums and products). Analogous properties are then studied for complex numbers, in Ch.8. Chapter 9 illustrates the use of real numbers in general topology, studying different important kinds of topological spaces: uniformizable, metric, normal Baire, Polish, Borel spaces.The final chapter deals with the various topologies of function spaces,ending with a section on approximation of functions.
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Theory of Function Spaces III (Monographs in Mathematics)
Hans Triebel
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ASIN: 3764375817 |
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Digital Control Systems: Design, Identification and Implementation (Communications and Control Engineering)
Ioan D. Landau , and
Gianluca Zito
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ASIN: 1846280559 |
Book Description
The extraordinary development of microprocessors and their extensive use in control systems in all fields of application has brought about important changes in the design of control systems. Their performance and low cost make them much more capable, in many circumstances, than analog controllers.
In order to take full advantage of this potential,
Digital Control Systems demonstrates in detail how to design and implement high-performance model-based controllers combining system identification and control design techniques extensively tested in industrial milieux. The effective use of these techniques is illustrated in the context of various systems including: d.c. motors, flexible transmissions, air heaters, distillation columns and hot-dip galvanizing. Topics covered include:
• essentials of computer-based control systems;
• controller design methods (robust pole placement, long-range-predictive control, state space, digital PID, etc.);
• system identification techniques;
• practical aspects of system identification and digital control.
A number of recent methodological developments in control design and system identification, driven by applications, are presented, including:
• robust digital control design using sensitivity function shaping;
• plant identification in closed loop operation;
• reduction of controller complexity.
The text of
Digital Control Systems is enhanced, for practical and tutorial purposes, by the use of software which illustrates the various concepts and algorithms and gives a feeling for the phenomena, discussed. The MATLAB
®/Scilab routines used for this purpose can be downloaded from the textbook’s website where additional material for teaching is available (slide presentations of the chapter material, data files for additional laboratory sessions and example files).
Graduate students in courses on digital control will find this text to be most helpful in learning the essential techniques of computer-based control while the wealth of additional material will make the tutor’s tasks of teaching and preparation quicker and easier. The book also provides practising engineers wishing to enhance their skills in this area with efficient and co-ordinated methods for the design and implementation of computer-based controllers.
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