Introductory Real Analysis

Author: A. N. Kolmogorov
Publisher: Courier Corporation
ISBN: 0486134741
Format: PDF, ePub, Mobi
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Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

Introduction to Real Analysis

Author: Michael J. Schramm
Publisher: Courier Corporation
ISBN: 0486131920
Format: PDF, Mobi
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This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

Introduction to Analysis

Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Format: PDF, ePub, Docs
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Introductory Complex Analysis

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 0486318524
Format: PDF, ePub, Mobi
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Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Elements of Real Analysis

Author: David A. Sprecher
Publisher: Courier Corporation
ISBN: 0486153258
Format: PDF, Mobi
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Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.

Foundations of Modern Analysis

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Format: PDF, Mobi
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Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

Functional Analysis

Author: R.E. Edwards
Publisher: Courier Corporation
ISBN: 0486145107
Format: PDF
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Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.

Complex Analysis with Applications

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 9780486647623
Format: PDF, ePub
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The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

Theorems and Problems in Functional Analysis

Author: A. A. Kirillov
Publisher: Springer Science & Business Media
ISBN: 1461381533
Format: PDF, ePub, Mobi
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Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.

Introductory Real Analysis

Author: Frank Dangello
Publisher: Houghton Mifflin College Division
ISBN: 9780395959336
Format: PDF, Docs
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This text for courses in real analysis or advanced calculus is designed specifically to present advanced calculus topics within a framework that will help students more effectively write and analyze proofs. The authors' comprehensive yet accessible presentation for one- or two-term courses offers a balanced depth of topic coverage and mathematical rigor.