Smooth Functions and Maps

The book provides a comprehensive theory of smooth functions and maps, including Lagrange inequality, Taylors formula, extrema, smoothness, inverse maps, and diffeomorphism. It uses a new technical approach to clarify proofs and includes complete proofs of important results. It also features examples and problems for further exploration.

Format: Paperback / softback
Length: 244 pages
Publication date: 26 July 2022
Publisher: Springer Nature Switzerland AG

The book is a comprehensive and well-developed theory of smooth functions and maps, particularly in relation to differential calculus. It encompasses a wide range of concepts, including Lagrange inequality, Taylors formula, finding absolute and relative extrema, smoothness of inverse maps, local invertibility conditions, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism, and critical values of smooth mappings.

To enhance the understanding of these topics, the authors employ a novel technical approach that simplifies complex proofs while maintaining their integrity. Additionally, the book provides complete proofs of significant results that were previously available only in scholarly literature or scientific journals. These include remainder estimates of Taylors formula in a nonconvex area, Whitney's extension theorem for smooth functions, the global diffeomorphism theorem, results on sets of critical values of smooth mappings, and the related Whitney example.

The text is accompanied by numerous examples that illustrate the obtained results and validate their accuracy. Furthermore, the book includes over 150 problems and 19 illustrations, providing further opportunities for exploration and application of the material. By reading this book, readers will gain a solid foundation in multivariable calculus and be well-equipped to delve into any literature based on this field.

Weight: 468g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030794408
Edition number: 1st ed. 2021