Boris M. Makarov,Anatolii N. Podkorytov
Smooth Functions and Maps
Smooth Functions and Maps
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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: Hardback
Length: 244 pages
Publication date: 25 July 2021
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, a novel technical approach is employed in several chapters, allowing the authors to clarify and simplify complex proofs while maintaining their integrity. Additionally, the book provides complete proofs of significant results that have previously been published in scholarly literature or scientific journals. These include remainder estimates of Taylors formula in a nonconvex area, Whitney's extension theorem for smooth functions, 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 contains over 150 problems and 19 illustrations, providing further opportunities for the reader to explore and deepen their knowledge in this field.
By reading this book, readers will gain a solid foundation in smooth functions and maps, enabling them to delve deeper into any literature based on multivariable calculus.
Weight: 623g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030794378
Edition number: 1st ed. 2021
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