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  3. A Primer of Real Functions
  • This book is no longer available to purchase from Cambridge Core
  • Cited by 25
Publisher:
Mathematical Association of America
Online publication date:
January 2012
Print publication year:
1996
Online ISBN:
9781614440130
DOI:
https://doi.org/10.5948/UPO9781614440130
Subjects:
Mathematics, Mathematical Modeling and Methods
Series:
Carus Mathematical Monographs
Information

Book description

This is a revised, updated and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is thus suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: for example, the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series.

Reviews

It is a great pleasure to see the … fourth edition of this gem, which is well-known all over the world.... This is an important work, especially for teachers and even for (trained) students.

Source: Acta Sci. Math (Szeged)

I highly recommend this monograph to mathematics majors who wish to review or extend their knowledge of real analysis, and to workers in other fields who wish to learn of the major results of analysis.

Source: The Mathematics Teacher

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