Designed for a first course in real variables, this text encourages intuitive thinking and offers background for more advanced mathematical work. Topics include complex variables, measure theory, differential equations, functional analysis, and probability. Detailed solutions to the problems appear at the back of the book, making it ideal for independent study. 1993 edition. Reprint of the Institute of Electrical and Electronics Engineers Press, 1992 edition.
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Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
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.
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.
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.
Theory of the Integral by Stanislaw Saks An excellent introduction to modern real variable theorem, this volume covers all the standard topics such as theory, theory of measure, functions with general properties, and theory of integration.
Foundations of Analysis: Second Edition by David F Belding, Kevin J Mitchell Unified and highly readable, this introductory approach develops the real number system and the theory of calculus, extending its discussion of the theory to real and complex planes. 1991 edition.
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.
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.
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.
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.
