Appropriate for undergraduates and even high school students, 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. Unabridged republication of the edition published by Holt, Rinehart and Winston, New York, 1961.
Here's a sample of other books in this Dover category
Lectures on Functional Equations and Their Applications by J. Aczel Numerous detailed proofs highlight this treatment, which examines equations for functions of a single variable and those for functions of several variables. Also includes composite equations, vector and matrix equations, more. 1966 edition.
Theory of Approximation by N. I. Achieser Graduate-level text by a pioneer of modern developments in approximation theory approaches the subject from the standpoint of functional analysis. Clear treatments of classical topics and an extensive section of problems and applications.
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.
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.
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.
