Multidimensional Real Analysis I Differentiation [Hardcover]

Part one of a comprehensive text on multidimensional real analysis, including numerous exercises with partial solutions.Two-volume set of the authors' comprehensive and innovative work on multidimensional real analysis. These books give a thorough account of analysis in multidimensional Euclidean space. They are an ideal preparation for students who wish to go on to more advanced study. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the books ideal as either the text for a course, a source of problems for a seminar or for self study.Two-volume set of the authors' comprehensive and innovative work on multidimensional real analysis. These books give a thorough account of analysis in multidimensional Euclidean space. They are an ideal preparation for students who wish to go on to more advanced study. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the books ideal as either the text for a course, a source of problems for a seminar or for self study.Volume 1 provides a comprehensive review of differential analysis in multidimensional Euclidean space.Preface; Acknowledgements; Introduction; 1. Continuity; 2. Differentiation; 3. Inverse function and implicit function theorems; 4. Manifolds; 5. Tangent spaces; Exercises; Notation; Index.'Throughout the notation is carefully organized and all proofs are complete and rigorous. The text is completed by carefully worked examples, many of them are illustrated by drawings. A special feature of the book is the extensive collection of exercises & The book is a good preparation for readers who wish to go on to more advanced studies in analysis. It can be also highly recommended as a text for a course or for self study.' Zentralblatt fur Mathematik