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Analysis In Vector Spaces Set
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Book Synopsis Analysis in Vector Spaces by : Mustafa A. Akcoglu
Download or read book Analysis in Vector Spaces written by Mustafa A. Akcoglu and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined withrelated computational methods are essential to understanding nearlyall areas of quantitative science. Analysis in Vector Spacespresents the central results of this classic subject throughrigorous arguments, discussions, and examples. The book aims tocultivate not only knowledge of the major theoretical results, butalso the geometric intuition needed for both mathematicalproblem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology,and notation and also provide a basic introduction to set theory,the properties of real numbers, and a review of linear algebra. Anelegant approach to eigenvector problems and the spectral theoremsets the stage for later results on volume and integration.Subsequent chapters present the major results of differential andintegral calculus of several variables as well as the theory ofmanifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter toreinforce new concepts and to illustrate how results can be appliedto additional problems. Furthermore, proofs and examples arepresented in a clear style that emphasizes the underlying intuitiveideas. Counterexamples are provided throughout the book to warnagainst possible mistakes, and extensive appendices outline theconstruction of real numbers, include a fundamental result aboutdimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra andsingle variable calculus, Analysis in Vector Spaces is anexcellent book for a second course in analysis for mathematics,physics, computer science, and engineering majors at theundergraduate and graduate levels. It also serves as a valuablereference for further study in any discipline that requires a firmunderstanding of mathematical techniques and concepts.
Book Synopsis Analysis in Vector Spaces Set by : Mustafa A. Akcoglu
Download or read book Analysis in Vector Spaces Set written by Mustafa A. Akcoglu and published by Wiley. This book was released on 2009-04-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This set includes: Analysis in Vector Spaces ISBN 978-0-470-14824-2 and Analysis in Vector Spaces, Student Solutions Manual ISBN 978-0-470-14825-9. rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology, and notation and also provide a basic introduction to set theory, the properties of real numbers, and a review of linear algebra. An elegant approach to eigenvector problems and the spectral theorem sets the stage for later results on volume and integration. Subsequent chapters present the major results of differential and integral calculus of several variables as well as the theory of manifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra and single variable calculus, Analysis in Vector Spaces is an excellent book for a second course in analysis for mathematics, physics, computer science, and engineering majors at the undergraduate and graduate levels. It also serves as a valuable reference for further study in any discipline that requires a firm understanding of mathematical techniques and concepts.
Book Synopsis Convex Analysis in General Vector Spaces by : C. Zalinescu
Download or read book Convex Analysis in General Vector Spaces written by C. Zalinescu and published by World Scientific. This book was released on 2002 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions.
Book Synopsis A Vector Space Approach to Geometry by : Melvin Hausner
Download or read book A Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.
Book Synopsis Optimization by Vector Space Methods by : David G. Luenberger
Download or read book Optimization by Vector Space Methods written by David G. Luenberger and published by John Wiley & Sons. This book was released on 1997-01-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
Book Synopsis Calculus in Vector Spaces, Second Edition, Revised Expanded by : Lawrence Corwin
Download or read book Calculus in Vector Spaces, Second Edition, Revised Expanded written by Lawrence Corwin and published by CRC Press. This book was released on 1994-12-08 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus in Vector Spaces addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This second edition introduces, among other topics, the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space, allowing for Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting. Mathematical analysts, algebraists, engineers, physicists, and students taking advanced calculus and linear algebra courses should find this book useful.
Book Synopsis Solutions Manual to accompany Analysis in Vector Spaces by : Mustafa A. Akcoglu
Download or read book Solutions Manual to accompany Analysis in Vector Spaces written by Mustafa A. Akcoglu and published by Wiley. This book was released on 2009-04-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology, and notation and also provide a basic introduction to set theory, the properties of real numbers, and a review of linear algebra. An elegant approach to eigenvector problems and the spectral theorem sets the stage for later results on volume and integration. Subsequent chapters present the major results of differential and integral calculus of several variables as well as the theory of manifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra and single variable calculus, Analysis in Vector Spaces is an excellent book for a second course in analysis for mathematics, physics, computer science, and engineering majors at the undergraduate and graduate levels. It also serves as a valuable reference for further study in any discipline that requires a firm understanding of mathematical techniques and concepts.
Book Synopsis From Vector Spaces to Function Spaces by : Yutaka Yamamoto
Download or read book From Vector Spaces to Function Spaces written by Yutaka Yamamoto and published by SIAM. This book was released on 2012-10-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.
Book Synopsis Finite-Dimensional Vector Spaces by : Paul R. Halmos
Download or read book Finite-Dimensional Vector Spaces written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2017-05-24 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.
Book Synopsis Linear Functional Analysis by : Bryan Rynne
Download or read book Linear Functional Analysis written by Bryan Rynne and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
Book Synopsis Topological Vector Spaces I by : Gottfried Köthe
Download or read book Topological Vector Spaces I written by Gottfried Köthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.
Book Synopsis Topological Vector Spaces, Distributions and Kernels by : François Treves
Download or read book Topological Vector Spaces, Distributions and Kernels written by François Treves and published by Elsevier. This book was released on 2016-06-03 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.
Book Synopsis A Course on Topological Vector Spaces by : Jürgen Voigt
Download or read book A Course on Topological Vector Spaces written by Jürgen Voigt and published by Springer Nature. This book was released on 2020-03-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach’s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein’s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(Ω) and the space of distributions, and the Krein-Milman theorem. The book adopts an “economic” approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians.
Book Synopsis Topological Vector Spaces, Distributions and Kernels by :
Download or read book Topological Vector Spaces, Distributions and Kernels written by and published by Academic Press. This book was released on 1967-01-01 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Vector Spaces, Distributions and Kernels
Book Synopsis Topological Vector Spaces by : Lawrence Narici
Download or read book Topological Vector Spaces written by Lawrence Narici and published by CRC Press. This book was released on 2010-07-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v
Book Synopsis Topological Vector Spaces and Their Applications by : V.I. Bogachev
Download or read book Topological Vector Spaces and Their Applications written by V.I. Bogachev and published by Springer. This book was released on 2017-05-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Book Synopsis Topological Vector Spaces and Algebras by : Lucien Waelbroeck
Download or read book Topological Vector Spaces and Algebras written by Lucien Waelbroeck and published by Springer. This book was released on 2006-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures associated with these notes were given at the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, during the local winter 1970. To emphasize the properties of topological algebras, the author had started out his lecture with results about topological algebras, and introduced the linear results as he went along.
