Topology Calculus And Approximation

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Topology, Calculus and Approximation

Author : Vilmos Komornik
Publisher : Springer
ISBN 13 : 1447173163
Total Pages : 382 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Topology, Calculus and Approximation by : Vilmos Komornik

Download or read book Topology, Calculus and Approximation written by Vilmos Komornik and published by Springer. This book was released on 2017-04-04 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure and applied mathematics, as well as physics and engineering should find this textbook useful. Only basic results of one-variable calculus and linear algebra are used, and simple yet pertinent examples and exercises illustrate the usefulness of most theorems. Many of these examples are new or difficult to locate in the literature, and so the original sources of most notions and results are given to help readers understand the development of the field.

Ten Mathematical Essays on Approximation in Analysis and Topology

Author : Juan Ferrera
Publisher : Elsevier
ISBN 13 : 0080459196
Total Pages : 283 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Ten Mathematical Essays on Approximation in Analysis and Topology by : Juan Ferrera

Download or read book Ten Mathematical Essays on Approximation in Analysis and Topology written by Juan Ferrera and published by Elsevier. This book was released on 2005-04-26 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects 10 mathematical essays on approximation in Analysis and Topology by some of the most influent mathematicians of the last third of the 20th Century. Besides the papers contain the very ultimate results in each of their respective fields, many of them also include a series of historical remarks about the state of mathematics at the time they found their most celebrated results, as well as some of their personal circumstances originating them, which makes particularly attractive the book for all scientist interested in these fields, from beginners to experts. These gem pieces of mathematical intra-history should delight to many forthcoming generations of mathematicians, who will enjoy some of the most fruitful mathematics of the last third of 20th century presented by their own authors. This book covers a wide range of new mathematical results. Among them, the most advanced characterisations of very weak versions of the classical maximum principle, the very last results on global bifurcation theory, algebraic multiplicities, general dependencies of solutions of boundary value problems with respect to variations of the underlying domains, the deepest available results in rapid monotone schemes applied to the resolution of non-linear boundary value problems, the intra-history of the the genesis of the first general global continuation results in the context of periodic solutions of nonlinear periodic systems, as well as the genesis of the coincidence degree, some novel applications of the topological degree for ascertaining the stability of the periodic solutions of some classical families of periodic second order equations, the resolution of a number of conjectures related to some very celebrated approximation problems in topology and inverse problems, as well as a number of applications to engineering, an extremely sharp discussion of the problem of approximating topological spaces by polyhedra using various techniques based on inverse systems, as well as homotopy expansions, and the Bishop-Phelps theorem. Key features: - It contains a number of seminal contributions by some of the most world leading mathematicians of the second half of the 20th Century. - The papers cover a complete range of topics, from the intra-history of the involved mathematics to the very last developments in Differential Equations, Inverse Problems, Analysis, Nonlinear Analysis and Topology. - All contributed papers are self-contained works containing rather complete list of references on each of the subjects covered. - The book contains some of the very last findings concerning the maximum principle, the theory of monotone schemes in nonlinear problems, the theory of algebraic multiplicities, global bifurcation theory, dynamics of periodic equations and systems, inverse problems and approximation in topology. - The papers are extremely well written and directed to a wide audience, from beginners to experts. An excellent occasion to become engaged with some of the most fruitful mathematics developed during the last decades.

Approximation Theory in Tensor Product Spaces

Author : William A. Light
Publisher : Springer
ISBN 13 : 3540397418
Total Pages : 164 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Approximation Theory in Tensor Product Spaces by : William A. Light

Download or read book Approximation Theory in Tensor Product Spaces written by William A. Light and published by Springer. This book was released on 2006-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topology in Process Calculus

Author : Mingsheng Ying
Publisher : Springer Science & Business Media
ISBN 13 : 1461301238
Total Pages : 226 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Topology in Process Calculus by : Mingsheng Ying

Download or read book Topology in Process Calculus written by Mingsheng Ying and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to establish a theory of approximate correctness and infinite evolution of concurrent programs by employing some notions and tools from point-set topology. Professionals, researchers and graduate students in theoretical computer science and formal methods will find this presentation helpful in understanding new concepts for concurrent and real-time systems, especially methods for describing approximation of systems.

A Course in Approximation Theory

Author : Elliott Ward Cheney
Publisher : American Mathematical Soc.
ISBN 13 : 0821847988
Total Pages : 379 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Course in Approximation Theory by : Elliott Ward Cheney

Download or read book A Course in Approximation Theory written by Elliott Ward Cheney and published by American Mathematical Soc.. This book was released on 2009-01-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.

Differential Forms in Algebraic Topology

Author : Raoul Bott
Publisher : Springer Science & Business Media
ISBN 13 : 1475739516
Total Pages : 319 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Differential Forms in Algebraic Topology by : Raoul Bott

Download or read book Differential Forms in Algebraic Topology written by Raoul Bott and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Approximation Theory in Tensor Product Spaces

Author : William A. Light
Publisher :
ISBN 13 : 9783662165409
Total Pages : 168 pages
Book Rating : 4.1/5 (654 download)

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Book Synopsis Approximation Theory in Tensor Product Spaces by : William A. Light

Download or read book Approximation Theory in Tensor Product Spaces written by William A. Light and published by . This book was released on 2014-01-15 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topology from the Differentiable Viewpoint

Author : John Willard Milnor
Publisher : Princeton University Press
ISBN 13 : 9780691048338
Total Pages : 80 pages
Book Rating : 4.0/5 (483 download)

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Book Synopsis Topology from the Differentiable Viewpoint by : John Willard Milnor

Download or read book Topology from the Differentiable Viewpoint written by John Willard Milnor and published by Princeton University Press. This book was released on 1997-12-14 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

Ordered Cones and Approximation

Author : Klaus Keimel
Publisher : Springer
ISBN 13 : 3540470794
Total Pages : 140 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Ordered Cones and Approximation by : Klaus Keimel

Download or read book Ordered Cones and Approximation written by Klaus Keimel and published by Springer. This book was released on 2006-11-15 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

Approximation of Continuously Differentiable Functions

Author : J.G. Llavona
Publisher : Elsevier
ISBN 13 : 9780080872414
Total Pages : 240 pages
Book Rating : 4.8/5 (724 download)

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Book Synopsis Approximation of Continuously Differentiable Functions by : J.G. Llavona

Download or read book Approximation of Continuously Differentiable Functions written by J.G. Llavona and published by Elsevier. This book was released on 1986-11-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book brings together the important results of a rapidly growing area. As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells' theorem and Aron's theorem for the fine topology of order m; extension of Bernstein's and Weierstrass' theorems for infinite dimensional Banach spaces; extension of Nachbin's and Whitney's theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.

Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics

Author : Alejandro Uribe A.
Publisher : American Mathematical Soc.
ISBN 13 : 1470452707
Total Pages : 178 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics by : Alejandro Uribe A.

Download or read book Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics written by Alejandro Uribe A. and published by American Mathematical Soc.. This book was released on 2020-05-21 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.

Functional Analysis, Holomorphy, and Approximation Theory

Author : Guido I. Zapata
Publisher : CRC Press
ISBN 13 : 1000154122
Total Pages : 476 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Functional Analysis, Holomorphy, and Approximation Theory by : Guido I. Zapata

Download or read book Functional Analysis, Holomorphy, and Approximation Theory written by Guido I. Zapata and published by CRC Press. This book was released on 2020-12-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers on complex analysis, function spaces, harmonic analysis, and operators, presented at the International seminar on Functional Analysis, Holomorphy, and Approximation Theory held in 1979. It is addressed to mathematicians and advanced graduate students in mathematics.

Approximation Theory in Tensor Product Spaces

Author : Brian S. Thomson
Publisher :
ISBN 13 : 9780387160573
Total Pages : 227 pages
Book Rating : 4.1/5 (65 download)

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Book Synopsis Approximation Theory in Tensor Product Spaces by : Brian S. Thomson

Download or read book Approximation Theory in Tensor Product Spaces written by Brian S. Thomson and published by . This book was released on 1985 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Analysis, Approximation Theory and Their Applications

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 3319312812
Total Pages : 741 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Mathematical Analysis, Approximation Theory and Their Applications by : Themistocles M. Rassias

Download or read book Mathematical Analysis, Approximation Theory and Their Applications written by Themistocles M. Rassias and published by Springer. This book was released on 2016-06-03 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Advanced Calculus

Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 596 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advanced Calculus by : Lynn Harold Loomis

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Approximation Theory, Sequence Spaces and Applications

Author : S. A. Mohiuddine
Publisher : Springer Nature
ISBN 13 : 9811961166
Total Pages : 277 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Approximation Theory, Sequence Spaces and Applications by : S. A. Mohiuddine

Download or read book Approximation Theory, Sequence Spaces and Applications written by S. A. Mohiuddine and published by Springer Nature. This book was released on 2022-12-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.

Winding Around: The Winding Number in Topology, Geometry, and Analysis

Author : John Roe
Publisher : American Mathematical Soc.
ISBN 13 : 1470421984
Total Pages : 269 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Winding Around: The Winding Number in Topology, Geometry, and Analysis by : John Roe

Download or read book Winding Around: The Winding Number in Topology, Geometry, and Analysis written by John Roe and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra),guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem),explain why every simple closed curve has an inside and an outside (the Jordan curve theorem),relate calculus to curvature and the singularities of vector fields (the Hopf index theorem),allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators),generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem). All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses.