Rodney Coleman lives close to Grenoble in France, where he is engaged in teaching and research. His interests include literature, bicycle riding and hiking in the mountains.

• Preface.- 1 Normed Vector Spaces.- 2 Differentiation.- 3 Mean value theorems.- 4 Higher derivatives and differentials.- 5 Taylor theorems and applications.- 6 Hilbert spaces.- 7 Convex functions.- 8 The inverse and implicit mapping theorems.- 9 Vector fields.- 10 The flow of a vector field.- 11 The calculus of variations: an introduction.- Bibliography.- Index​

From the reviews: "Coleman (Laboratoire Jean Kuntzmann, France) generalizes the standard theorems of this subject to an arbitrary, hence possibly infinite, dimensional normed vector space, including the special cases of Banach spaces and Hilbert spaces. ... Best suited for advanced undergraduate or graduate students, the text delivers the level of rigor and mathematical sophistication that one in the discipline expects from a volume published by Springer. Summing Up: Recommended. Upper-division undergraduates, graduate students, and researchers/faculty." (D. S. Larson, Choice, Vol. 50 (10), June, 2013) "It covers all topics of classical calculus in the broad setting of real normed spaces. ... The style used in giving a complete overview of all these topics of differential calculus is a really nice one, introducing concepts whenever they are needed ... . Each chapter contains a variety of interesting exercises which help to complement the material being studied. Therefore, to finish, I highly recommend this book to teachers and researchers on the subject." (Jesus Ferrer, Mathematical Reviews, March, 2013)