A primer of real functions / Ralph P. Boas.

Format:

Book

Author/Creator:

Boas, Ralph P. (Ralph Philip), 1912-1992, author.

Boas, Harold P., author.

Series:

Carus mathematical monographs ; no. 13.

The Carus mathematical monographs ; no. 13

Language:

English

Subjects (All):

Functions of real variables.

Physical Description:

1 online resource (xiv, 305 pages) : digital, PDF file(s).

Edition:

Fourth edition.

Place of Publication:

Washington : Mathematical Association of America, 1996.

Language Note:

English

Summary:

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.

Contents:

Preface to the fourth edition

Preface to the third edition

[ch.] 1. 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 theorem

10. Some applications of Baire's theorem

11. Sets of measure zero

[c.h.] 2. Functions

12. Functions

13. Continuous functions

14. Properties of continuous functions

15. Upper and lower limits

16. Sequences of functions

17. Uniform convergence

18. Point wise limits on continuous functions

19. Approximations to continuous functions

20. Linear functions

21. Derivaties

22. Monotonic functions

23. Convex functions

24. Infinitely differentiable functions

[ch.] 3. 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

Index.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-61444-013-1

OCLC:

929120248