Elements of Real Analysis

Author: David A. Sprecher
Publisher: Courier Corporation
ISBN: 0486153258
Format: PDF
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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.

Introductory Real Analysis

Author: A. N. Kolmogorov
Publisher: Courier Corporation
ISBN: 9780486612263
Format: PDF
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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: 0486469131
Format: PDF, ePub, 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.

Real Analysis

Author: Edward James McShane
Publisher: Courier Corporation
ISBN: 0486165671
Format: PDF, Docs
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This text surveys practical elements of real function theory, general topology, and functional analysis. Discusses the maximality principle, the notion of convergence, the Lebesgue-Stieltjes integral, function spaces and harmonic analysis. Includes exercises. 1959 edition.

Elements of Real Analysis

Author: Herbert S. Gaskill
Publisher: Upper Saddle River, NJ : Prentice Hall
ISBN: 9780138970673
Format: PDF, Mobi
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Comprehensive in coverage, this book explores the principles of logic, the axioms for the real numbers, limits of sequences, limits of functions, differentiation and integration, infinite series, convergence, and uniform convergence for sequences of real-valued functions. Concepts are presented slowly and include the details of calculations as well as substantial explanations as to how and why one proceeds in the given manner. Uses the words WHY? and HOW? throughout; inviting readers to become active participants and to supply a missing argument or a simple calculation. Contains more than 1000 individual exercises. Stresses and reviews elementary algebra and symbol manipulation as essential tools for success at the kind of computations required in dealing with limiting processes.

Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh
Publisher: Courier Corporation
ISBN: 0486134776
Format: PDF, Mobi
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Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Foundations of Modern Analysis

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Format: PDF, ePub
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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.

Applied Functional Analysis

Author: D.H. Griffel
Publisher: Courier Corporation
ISBN: 0486141322
Format: PDF, Mobi
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This introductory text examines applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Covers distribution theory, Banach spaces, Hilbert space, spectral theory, Frechet calculus, Sobolev spaces, more. 1985 edition.

Elements of Point Set Topology

Author: John D. Baum
Publisher: Courier Corporation
ISBN: 0486668266
Format: PDF, Docs
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Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Functional Analysis

Author: George Bachman
Publisher: Courier Corporation
ISBN: 0486136558
Format: PDF, ePub
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Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. 1966 edition.