<p>Originally published in two volumes, this long out-of-print work by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics, the treatment offers a clear account of integration theory and a practical introduction to functional analysis. Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series. <br>Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations, the Stieltjes integral, absolutely contiguous functions, and the indefinite Lebesgue integral. Volume II addresses singular integrals, trigonometric series, convex functions, point sets in two-dimensional space, measurable functions of several variables and their integration, set functions and their applications in the theory of integration, transfinite numbers, the Baire classification, certain generalizations of the Lebesgue integral, and some ideas from functional analysis. Many chapters feature challenging exercises.</p>

Theory of Functions of a Real Variable (Dover Books on Mathematics)

Science & Math

Natanson, I.P.

Mathematics

Dover Publications

<p><div>Translated and adapted from a popular Russian educational series, this concise book requires only some background in high school algebra and elementary trigonometry. It explores the fundamental concept of the integral calculus: the limit of the sum of an infinitely increasing number of infinitely decreasing quantities. Mastery of this concept enables the solution of geometry and physics problems, and is an excellent introduction to the systematic study of higher mathematics.<br /> Starting with some algebraic formulas, the treatment proceeds to the determination of the pressure of a liquid on a vertical wall and the calculation of the work done in pumping liquid from a container. Subsequent chapters explore finding the volumes of a cone, pyramid, sphere, and other geometric forms and the measurement of the parabola, ellipse, and sinusoid. The text concludes with a selection of practice problems.<br /> For advanced high school students and college undergraduates.</div></p>

Summation of Infinitely Small Quantities (Dover Books on Mathematics)

<p>Contents: Infinite Sets; Point Sets; Measurable Sets; Measurable Functions; The Lebesgue Integral of a Bounded Function; Summable Functions; Square-Summable Functions; Functions of Finite Variation - The Stieltjes Integral; Absolutely Continuous Functions - The Indefinite Lebesgue Integral; Index. Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, smoothness and related properties of real-valued functions.</p>

Theory of Functions of a Real Variable, Vol. 1

Frederick Ungar

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Books by Natanson, I.P.

See the best price to sell, buy, or rent books by Natanson, I.P.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Theory of Functions of a Real Variable (Dover Books on Mathematics)

Summation of Infinitely Small Quantities (Dover Books on Mathematics)

Theory of Functions of a Real Variable, Vol. 1