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Hardcover ISBN:  9780821869901 
Product Code:  CRMM/5 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
eBook ISBN:  9781470438517 
Product Code:  CRMM/5.E 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 
Hardcover ISBN:  9780821869901 
eBook ISBN:  9781470438517 
Product Code:  CRMM/5.B 
List Price:  $225.00 $170.00 
MAA Member Price:  $202.50 $153.00 
AMS Member Price:  $180.00 $136.00 

Book DetailsCRM Monograph SeriesVolume: 5; 1994; 195 ppMSC: Primary 26
Topics related to the differentiation of real functions have received considerable attention during the last few decades. This book provides an efficient account of the present state of the subject. Bruckner addresses in detail the problems that arise when dealing with the class \(\Delta '\) of derivatives, a class that is difficult to handle for a number of reasons. Several generalized forms of differentiation have assumed importance in the solution of various problems. Some generalized derivatives are excellent substitutes for the ordinary derivative when the latter is not known to exist; others are not. Bruckner studies generalized derivatives and indicates “geometric” conditions that determine whether or not a generalized derivative will be a good substitute for the ordinary derivative. There are a number of classes of functions closely linked to differentiation theory, and these are examined in some detail. The book unifies many important results from the literature as well as some results not previously published. The first edition of this book, which was current through 1976, has been referenced by most researchers in this subject. This second edition contains a new chapter dealing with most of the important advances between 1976 and 1993.
Titles in this series are copublished with the Centre de recherches mathématiques.
ReadershipGraduate students and researchers in the differentiation theory of real functions and related subjects.

Table of Contents

Chapters

Introduction

Preliminaries

Chapter 1. Darboux functions

Chapter 2. Darboux functions in the first class of Baire

Chapter 3. Continuity and approximate continuity of derivatives

Chapter 4. The extreme derivatives of a function

Chapter 5. Reconstruction of the primitive

Chapter 6. The Zahorski classes

Chapter 7. The problem of characterizing derivatives

Chapter 8. Derivatives a.e. and generalizations

Chapter 9. Transformations via homeomorphisms

Chapter 10. Generalized derivatives

Chapter 11. Monotonicity

Chapter 12. Stationary and determining sets

Chapter 13. Behavior of typical continuous functions

Chapter 14. Miscellaneous topics

Chapter 15. Recent developments


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Topics related to the differentiation of real functions have received considerable attention during the last few decades. This book provides an efficient account of the present state of the subject. Bruckner addresses in detail the problems that arise when dealing with the class \(\Delta '\) of derivatives, a class that is difficult to handle for a number of reasons. Several generalized forms of differentiation have assumed importance in the solution of various problems. Some generalized derivatives are excellent substitutes for the ordinary derivative when the latter is not known to exist; others are not. Bruckner studies generalized derivatives and indicates “geometric” conditions that determine whether or not a generalized derivative will be a good substitute for the ordinary derivative. There are a number of classes of functions closely linked to differentiation theory, and these are examined in some detail. The book unifies many important results from the literature as well as some results not previously published. The first edition of this book, which was current through 1976, has been referenced by most researchers in this subject. This second edition contains a new chapter dealing with most of the important advances between 1976 and 1993.
Titles in this series are copublished with the Centre de recherches mathématiques.
Graduate students and researchers in the differentiation theory of real functions and related subjects.

Chapters

Introduction

Preliminaries

Chapter 1. Darboux functions

Chapter 2. Darboux functions in the first class of Baire

Chapter 3. Continuity and approximate continuity of derivatives

Chapter 4. The extreme derivatives of a function

Chapter 5. Reconstruction of the primitive

Chapter 6. The Zahorski classes

Chapter 7. The problem of characterizing derivatives

Chapter 8. Derivatives a.e. and generalizations

Chapter 9. Transformations via homeomorphisms

Chapter 10. Generalized derivatives

Chapter 11. Monotonicity

Chapter 12. Stationary and determining sets

Chapter 13. Behavior of typical continuous functions

Chapter 14. Miscellaneous topics

Chapter 15. Recent developments