Differentiation of real functions / Andrew M. Bruckner

This collection of notes is essential reading for anyone interested in the historic or recent developments of differentiation of real functions, many of which are results of the author. The style is excellent. Further, the author provides throughout the book a series of insightful problems which are currently open. It is clear that the author has surpassed his stated purpose of creating a book that (1) provides a relatively efficient development of the present state of knowledge on the subject, (2) discusses some of the open problems which are worth investigating, and (3) provides references to work on topics which the book does not develop in detail. ... Table of contents: I: Darboux functions; II; Darboux functions in the first class of Baire; III: Continuity and approximate continuity of derivatives; IV: The extreme derivates of a function; V: Reconstruction of the primitive; VI: The Zahorski classes; VII: The problem of characterizing derivatives; VIII: Derivatives a.e. and generalizations; IX: Transformations via homeomorphisms; X: Generalized derivatives; XI: Monotonicity; XII: Stationary and determining sets; XIII: Behavior of typical continuous functions; XIV: Miscellaneous topics. (MathSciNet)