{"product_id":"smooth-functions-and-maps-9783030794408","title":"Smooth Functions and Maps","description":"\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003e\n\u003cbr\u003eThe 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. \u003c\/blockquote\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 244 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 26 July 2022\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer Nature Switzerland AG\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cbr\u003eThe 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.\u003cbr\u003e\u003cbr\u003eTo 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.\u003cbr\u003e\u003cbr\u003eThe 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 468g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 235 x 155 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783030794408\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2021\u003c\/p\u003e","brand":"Boris M. Makarov,Anatolii N. Podkorytov","offers":[{"title":"Paperback \/ softback","offer_id":44103279608058,"sku":"9783030794408","price":41.64,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_1dab401e-4e9c-472e-b0fe-e363f21e9f24.jpg?v=1669971303","url":"https:\/\/shulphink.com\/products\/smooth-functions-and-maps-9783030794408","provider":"Shulph Ink","version":"1.0","type":"link"}