Dérivation, intégration / Claude Wagschal

The book is divided into two large chapters. Chapter 1, of 115 pages, does the basics of differential calculus in Banach spaces, plus an introduction to differential geometry. The four sections are headed: Differentiable mapping, Derivatives of higher order, Implicit function theorems, and Varieties (manifolds). Chapter 2, pages 116-462, on integration, is divided into 11 sections: Measure theory, Lebesgue integral, Vector integration, Radon measure, Products of measure spaces, Lp -spaces, Absolutely continuous functions, Stokes theorem, Fourier series, Fourier transforms, and Fredholm integral equations. The book is in basic “definition, theorem, proof, remark” format, with exercises and problems of varying levels of difficulty scattered liberally throughout. There is a short bibliography, a four-page index of notations and a short general alphabetical index (which one could wish were more complete). Although there is neither a preface nor remarks of any kind about intended use, the content and style of treatment make clear that this is a textbook for a course which might follow a standard introductory undergraduate real analysis course. There are two small separate volumes with solutions to the exercises and problems. (Zentralblatt)

Bibliogr. p. 463-464. Index