Calculus Without Derivatives

Jean-Paul Penot is an Emeritus Professor at Université Paris 6.  He has taught in Paris, Pau and Canada.

• Preface.- 1 Metric and Topological Tools.- 2 Elements of Differential Calculus.- 3 Elements of Convex Analysis.- 4 Elementary and Viscosity Subdifferentials.- 5 Circa-Subdifferentials, Clarke Subdifferentials.- 6 Limiting Subdifferentials.- 7 Graded Subdifferentials, Ioffe Subdifferentials.- References.- Index​.

"The book collects three different branches of analysis: differential calculus, convex analysis, and nonsmooth analysis. ... What makes Penot's work stand out is his path through the material and the clean and scholarly presentation. It is well suited for individual study or a classroom ... . As preparation for the rough road ahead of us in the coming decades, it might be worth the investment." (Russell Luke, SIAM Review, Vol. 57 (2), June, 2015) "This very good book is an treatise on approximate calculus and justifies the author's claim that the rules of this calculus are as important and useful as those for exact calculus. ... The book is notable not only for its exposition but also for the notes at the end of each chapter explaining the historical and other relevant backgrounds of the material. There are many exercises throughout the book." (Peter S. Bullen, Zentralblatt MATH, Vol. 1264, 2013) "By collecting together a lot of results in nonsmooth analysis and presenting them in a coherent and accessible way, the author rendered a great service to the mathematical community. The book can be considered as an incentive for newcomers to enter this area of research ... . The specialists will find also a lot of systematized information, and ... the first three chapters can be used for independent graduate courses." (S. Cobzas, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 58 (1), 2013)