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Topology, calculus and approximation, Komornik, Vilmos

Автор: Komornik, Vilmos
Название:  Topology, calculus and approximation   (Вилмос Коморник: Топология, математический анализ и прогнозирование)
Издательство: Springer
Классификация:
Дифферунциально и интегральное исчисление и математический анализ

ISBN: 1447173155
ISBN-13(EAN): 9781447173151
ISBN: 1-447-17315-5
ISBN-13(EAN): 978-1-447-17315-1
Обложка/Формат: Paperback
Страницы: 382
Вес: 0.592 кг.
Дата издания: 10.04.2017
Серия: Springer undergraduate mathematics series
Язык: ENG
Издание: 1st ed. 2017
Иллюстрации: 63 black & white illustrations, 1 colour illustrations, 9 colour tables, biography
Размер: 23.39 x 15.60 x 2.06 cm
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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, Fejer, Stieltjes, and Turan.

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 Caratheodorys 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.


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Approximation Theory and Approximation Practice

Автор: Trefethen
Название: Approximation Theory and Approximation Practice
ISBN: 1611972396 ISBN-13(EAN): 9781611972399
Издательство: Cambridge Academ
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Цена: 3724 р.
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Описание: This book presents a twenty-first century approach to classical polynomial and rational approximation theory. The reader will find a strikingly original treatment of the subject, completely unlike any of the existing literature on approximation theory, with a rich set of both computational and theoretical exercises for the classroom. There are many original features that set this book apart: the emphasis is on topics close to numerical algorithms; every idea is illustrated with Chebfun examples; each chapter has an accompanying Matlab file for the reader to download; the text focuses on theorems and methods for analytic functions; original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. This textbook is ideal for advanced undergraduates and graduate students across all of applied mathematics.

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Approximation Theory

Автор: Christensen
Название: Approximation Theory
ISBN: 0817636005 ISBN-13(EAN): 9780817636005
Издательство: Springer
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Цена: 2474 р.
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Описание: Gives an elementary introduction to approximation theory. This work demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. It is useful for students and instructors in pure and applied mathematics, mathematical physics, and engineering.

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Entropy, Compactness and the Approximation of Operators

Автор: Carl
Название: Entropy, Compactness and the Approximation of Operators
ISBN: 0521090946 ISBN-13(EAN): 9780521090940
Издательство: Cambridge Academ
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Цена: 3352 р.
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Описание: Entropy quantities are connected with the `degree of compactness` of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces.

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Numerical approximation of partial differential equations

Автор: Quarteroni, Alfio M. Valli, Alberto
Название: Numerical approximation of partial differential equations
ISBN: 3540852670 ISBN-13(EAN): 9783540852674
Издательство: Springer
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Цена: 6352 р.
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Описание: Deals with the numerical approximation of partial differential equations. This work provides an illustration of numerical methods, carries out their stability and convergence analysis, derives error bounds, and discusses the algorithmic aspects relative to their implementation.

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Constructive Approximation

Автор: DeVore
Название: Constructive Approximation
ISBN: 3540506276 ISBN-13(EAN): 9783540506270
Издательство: Springer
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Цена: 10721 р.
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Описание: The purpose of this text is to provide a unified exposition of approximation theory for functions of one real variable. It develops the basic properties of polynomials, splines and linear operators, emphasizing the logical selection of material and the avoidance of superfluous details.

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Fourier Analysis and Approximation of Functions

Автор: Trigub
Название: Fourier Analysis and Approximation of Functions
ISBN: 1402023413 ISBN-13(EAN): 9781402023415
Издательство: Springer
Цена: 8249 р.
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Описание: Presents the basics of classical Fourier Analysis as well as those of approximation by polynomials, splines and entire functions of exponential type. This work includes theorems on convergence. It discusses basic properties of simple and multiple Fourier series.

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Numerical Approximation of Hyperbolic Systems of Conservation Laws

Автор: Godlewski
Название: Numerical Approximation of Hyperbolic Systems of Conservation Laws
ISBN: 0387945296 ISBN-13(EAN): 9780387945293
Издательство: Springer
Цена: 8246 р.
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Описание: This work is devoted to the theory and approximation of nonlinear hyperbolic systems of conservation laws in one or two spaces variables. It concentrates on the systems and theoretical aspects which are needed in the applications, such as the solution of the Riemann problem.

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Asymptotic Approximation of Integrals

Автор: R. Wong
Название: Asymptotic Approximation of Integrals
ISBN: 0898714974 ISBN-13(EAN): 9780898714975
Издательство: Cambridge Academ
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Цена: 5681 р.
Наличие на складе: Поставка под заказ.

Описание: Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In this book, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, with references provided. Asymptotic Approximations of Integrals contains the ‘distributional method’, not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as ‘exponential asymptotics’. Expositions of these new theories are available in papers published in various journals, but not yet in book form.

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Approximation by Algebraic Numbers

Автор: Yann Bugeaud
Название: Approximation by Algebraic Numbers
ISBN: 0521045673 ISBN-13(EAN): 9780521045674
Издательство: Cambridge Academ
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Цена: 4283 р.
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Описание: Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine’s theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler’s conjecture on S-numbers, the Jarnik–Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references.

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Iterative Approximation of Fixed Points

Автор: Berinde Vasile
Название: Iterative Approximation of Fixed Points
ISBN: 3540722335 ISBN-13(EAN): 9783540722335
Издательство: Springer
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Цена: 4698 р.
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Описание: The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.

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Algorithms for Approximation / Proceedings of the 5th International Conference, Chester, July 2005

Автор: Iske A., Levesley J.
Название: Algorithms for Approximation / Proceedings of the 5th International Conference, Chester, July 2005
ISBN: 3540332839 ISBN-13(EAN): 9783540332831
Издательство: Springer
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Цена: 12787 р.
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Описание: Approximation methods are vital in many challenging applications of computational science and engineering.This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing.It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems.An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales.Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.

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Approximation, Complex Analysis, and Potential Theory

Автор: Arakelian Norair, Gauthier Paul M., Sabidussi Gert
Название: Approximation, Complex Analysis, and Potential Theory
ISBN: 1402000286 ISBN-13(EAN): 9781402000287
Издательство: Springer
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Цена: 11958 р.
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Описание: Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here. Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures. A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.

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