Softcover ISBN:  9781470454326 
Product Code:  CAR/13 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614440130 
Product Code:  CAR/13.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Softcover ISBN:  9781470454326 
eBook: ISBN:  9781614440130 
Product Code:  CAR/13.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 
Softcover ISBN:  9781470454326 
Product Code:  CAR/13 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614440130 
Product Code:  CAR/13.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Softcover ISBN:  9781470454326 
eBook ISBN:  9781614440130 
Product Code:  CAR/13.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 

Book DetailsThe Carus Mathematical MonographsVolume: 13; 1996; 305 pp
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 selfstudy 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: e.g., the existence of continuous everywhereoscillating 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.
This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.

Table of Contents

Chapters

Chapter 1. Sets

Chapter 2. Functions

Chapter 3. Integration


Additional Material

Reviews

The fourth edition of this classic introduction to analysis retains the freshness of the first edition as well as its charming conversational style ... This is not in any way a traditional textbook. It is more like a series of informal lectures, wordy, chatty, and not the least bit concise. The author's aim, and the book's great strength, is to bring back a sense of wonder to a subject that, in his opinion, had been lost.
Bill Satzer, MAA Reviews


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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 selfstudy 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: e.g., the existence of continuous everywhereoscillating 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.
This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.

Chapters

Chapter 1. Sets

Chapter 2. Functions

Chapter 3. Integration

The fourth edition of this classic introduction to analysis retains the freshness of the first edition as well as its charming conversational style ... This is not in any way a traditional textbook. It is more like a series of informal lectures, wordy, chatty, and not the least bit concise. The author's aim, and the book's great strength, is to bring back a sense of wonder to a subject that, in his opinion, had been lost.
Bill Satzer, MAA Reviews