CRM Monograph Series 1994; 195 pp; hardcover Volume: 5 ISBN10: 0821869906 ISBN13: 9780821869901 List Price: US$65 Member Price: US$52 Order Code: CRMM/5
 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. Readership Graduate students and researchers in the differentiation theory of real functions and related subjects. Table of Contents  Darboux functions
 Darboux functions in the first class of Baire
 Continuity and approximate continuity of derivatives
 The extreme derivatives of a function
 Reconstruction of the primitive
 The Zahorski classes
 The problem of characterizing derivatives
 Derivatives a.e. and generalizations
 Transformations via homeomorphisms
 Generalized derivatives
 Monotonicity
 Stationary and determining sets
 Behavior of typical continuous functions
 Miscellaneous topics
 Recent developments
 Bibliography
 Supplementary bibliography
 Terminology index
 Notational index
