By Subject > Science and Mathematics > Mathematics > Real and Complex Analysis
Recommendations...
| |  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.
all books in Numerical Analysis
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 Introductory Real Analysis
by A. N. Kolmogorov, S. V. Fomin
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. Features 350 problems.
all books in Real and Complex Analysis
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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.
all books in Real and Complex Analysis
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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.
all books in Real and Complex Analysis
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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.
all books in Real and Complex Analysis
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| Products in Real and Complex Analysis | | |  | Analytic Inequalities
by Nicholas D. Kazarinoff
This text introduces a pair of ancient theorems, explores inequalities and calculus, and covers modern theorems, including Bernstein's proof of the Weierstrass approximation theorem and the Cauchy, Bunyakovskii, Hölder, and Minkowski inequalities. 1961 edition. Includes 28 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 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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|  | 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: 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 Representation
by C. Carathéodory
Comprehensive introduction discusses the Möbius transformation, non-Euclidean geometry, elementary transformations, Schwarz's Lemma, transformation of the frontier and closed surfaces, and the general theorem of uniformization. Detailed proofs.
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|  | The Convolution Transform
by Isidore Isaac Hirschman, David V. Widder
The relation between differential operators and integral transforms is the theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, more.
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|  | Elementary Functional Analysis
by Georgi E. Shilov
Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.
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|  | 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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| |  | Elements of the Theory of Functions and Functional Analysis
by A. N. Kolmogorov, S. V. Fomin
Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque interval, Hilbert Space, more. Exercises. 1957 edition.
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|  | Functional Analysis
by George Bachman, Lawrence Narici
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.
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|  | Functional Analysis
by Frigyes Riesz, Béla Sz.-Nagy
Classic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition.
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|  | General Theory of Functions and Integration
by Angus E. Taylor
Lucid introduction to abstract theories in analysis. Classical theory of points in Euclidean space, continuous functions, ideas of topology, more. For graduate students. 38 diagrams. Introduction. List of Special Symbols. Index.
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|  | Hardy Classes
by Marvin Rosenblum, James Rovnyak
Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Includes general theory of shift operators on a Hilbert space, more. Appendix. Bibliography. 1985 edition.
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|  | Infinite Sequences and Series
by Konrad Knopp
Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
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|  | Intermediate Mathematical Analysis
by Anthony E. Labarre, Jr.
Focusing on concepts rather than techniques, this text deals primarily with real-valued functions of a real variable. Complex numbers appear only in supplements and the last two chapters. 1968 edition.
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|  | Introduction to Analysis
by Maxwell Rosenlicht
Unusually clear, accessible coverage of set theory, real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, more. Wide range of problems. Written for junior and senior undergraduates. Bibliography.
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