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Primer of Real Functions 4TH Edition


Primer of Real Functions 4TH Edition Cover


Synopses & Reviews

Publisher Comments:

This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhere-oscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days.

Book News Annotation:

A revised and updated monograph (first published 1960) on the theory of functions of a real variable. Retaining the informal, conversational style of previous editions, this edition adds a new chapter on integration and its applications. 5.25x7.75".
Annotation c. Book News, Inc., Portland, OR (


Revised edition of a classic Carus monograph with a new chapter on integration and its applications.

Table of Contents

Part I. Sets: 1. Sets; 2. Sets of real numbers; 3. Countable and uncountable sets; 4. Metric spaces; 5. Open and closed sets; 6. Dense and nowhere dense sets; 7. Compactness; 8. Convergence and completeness; 9. Nested sets and Baire's problem; 10. Some applications of Baire's theorem; 11. Sets of measure zero; Part II. Functions: 12. Functions; 13. Continuous functions; 14. Properties of continuous functions; 15. Upper and lower limits; 16. Sequences of functions; 17. Uniform convergence; 18. Pointwise limits of continuous functions; 19. Approximations to continuous functions; 20. Linear functions; 21. Derivatives; 22. Monotonic functions; 23. Convex functions; 24. Infinitely differentiable functions; Part III. Integration: 25. Lebesgue measure; 26. Measurable functions; 27. Definition of the Lebesgue integral; 28. Properties of Lebesgue integrals; 29. Applications of the Lebesgue integral; 30. Stieltjes integrals; 31. Applications of the Stieltjes integral; 32. Partial sums of infinite series; Answers to exercises.

Product Details

The Mathematical Association of America
Boas, Ralph P.
Boas, Harold P.
Watkins, William
Functions of real variables
Probability & Statistics - General
General Mathematics
Edition Number:
Edition Description:
Includes bibliographical references and index.
Carus mathematical monographs ;
Series Volume:
no. 461no. 13
Publication Date:
Grade Level:
College/higher education:
11 line diagrams

Related Subjects

Science and Mathematics » Agriculture » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Real Analysis

Primer of Real Functions 4TH Edition
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Product details 319 pages Mathematical Association of America - English 9780883850299 Reviews:
"Synopsis" by , Revised edition of a classic Carus monograph with a new chapter on integration and its applications.
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