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Recommendations... Elementary Real and Complex Analysis
by Georgi E. Shilov
Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition.
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| |  Counterexamples in Analysis
by Bernard R. Gelbaum, John M. H. Olmsted
These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
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 Introductory Real Analysis
by A. N. Kolmogorov, S. V. Fomin, Richard A. Silverman
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.
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| |  Introduction to Real Analysis
by Michael J. Schramm
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.
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 A Second Course in Complex Analysis
by William A. Veech
Geared toward upper-level undergraduates and graduate students, this clear, self-contained treatment of important areas in complex analysis is chiefly classical in content and emphasizes geometry of complex mappings. 1967 edition.
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| |  Real Variables with Basic Metric Space Topology
by Robert B. Ash
Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.
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 Real Analysis
by Norman B. Haaser, Joseph A. Sullivan
Clear, accessible text for 1st course in abstract analysis. Explores sets and relations, real number system and linear spaces, normed spaces, Lebesgue integral, approximation theory, Banach fixed-point theorem, Stieltjes integrals, more. Includes numerous problems.
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Products in Real and Complex Analysis | | |  | Applied Algebra and Functional Analysis
by Anthony N. Michel, Charles J. Herget
Graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, more. Exercises. 1981 edition.
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|  | Applied Complex Variables
by John W. Dettman
Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.
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|  | Applied Functional Analysis
by D.H. Griffel
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.
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|  | Applied Nonstandard Analysis
by Prof. Martin Davis
This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.
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|  | Approximate Calculation of Integrals
by V. I. Krylov, Arthur H. Stroud
This introduction to approximate integration approaches its subject from the viewpoint of functional analysis. The 3-part treatment covers concepts and theorems from the theory of quadrature, calculation of definite integrals, and calculation of indefinite integrals. 1962 edition.
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|  | Approximation of Elliptic Boundary-Value Problems
by Jean-Pierre Aubin
A marriage of the finite-differences method with variational methods for solving boundary-value problems, this self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis.
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|  | Asymptotic Expansions of Integrals
by Norman Bleistein, Richard A, Handelsman
Excellent introductory text by two experts presents a coherent, systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. 1975 edition.
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|  | Banach Spaces of Analytic Functions
by Kenneth Hoffman
This rigorous investigation of Hardy spaces and the invariant subspace problem is suitable for advanced undergraduates and graduates, covering complex functions, harmonic analysis, and functional analysis. 1962 edition.
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|  | Basic Methods of Linear Functional Analysis
by John D. Pryce
Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973 edition.
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|  | A Collection of Problems on Complex Analysis
by L. I. Volkovyskii, G. L. Lunts, I. G. Aramanovich
Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Answers and solutions.
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|  | Complex Analysis with Applications
by Richard A. Silverman
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.
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|  | Complex Integration and Cauchy's Theorem
by G.N. Watson
Brief monograph by a distinguished mathematician offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Includes applications to the calculus of residues. 1914 edition.
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|  | Complex Variable Methods in Elasticity
by A. H. England
Plane strain and generalized plane stress boundary value problems of linear elasticity are discussed as well as functions of a complex variable, basic equations of 2-dimensional elasticity, plane and half-plane problems, more. 1971 edition. Includes 26 figures.
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|  | Complex Variables
by Francis J. Flanigan
Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Numerous problems and solutions. 1972 edition.
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|  | Complex Variables: Second Edition
by Stephen D. Fisher
Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.
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|  | Complex Variables: Second Edition
by Robert B. Ash, W. P. Novinger
Suitable for advanced undergraduates and graduate students, this newly revised treatment covers Cauchy theorem and its applications, analytic functions, and the prime number theorem. Numerous problems and solutions. 2004 edition.
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|  | The Concept of a Riemann Surface
by Hermann Weyl, Gerald R. MacLane
This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.
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|  | Conformal Mapping
by Zeev Nehari
Combined theoretical and practical approach covers harmonic functions, analytic functions, the complex integral calculus, families of analytic functions, conformal mapping of simply-connected domains, and more.
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|  | Conformal Mapping on Riemann Surfaces
by Harvey Cohn
Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.
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|  | Constructive Real Analysis
by Allen A. Goldstein
This text introduces students of mathematics, science, and technology to the methods of applied functional analysis and applied convexity. Topics include iterations and fixed points, metric spaces, nonlinear programming, applications to integral equations, and more. 1967 edition.
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