Smooth Functions and Maps

Boris M. Makarov, Professor of the Saint Petersburg State University, Mathematics and Mechanics Faculty, Department of Mathematical Analysis. In 1996-2006, he was a member of the Editorial Board of the journal Functional Analysis and Its Applications of the Russian Academy of Sciences. In 2014, received the Saint Petersburg State University ‘Pedagogic Excellency’ award. In 2010, co-authored (with Anatolii N. Podkorytov) a book Lectures on Real Analysis published in English by Springer in 2013 under the title of Real Analysis: Measures, Integrals and Applications. Co-authored (with Maria G. Goluzina, Andrei A. Lodkin, and Anatolii N. Podkorytov) a book of problems Problems in Real Analysis published in Russian (two editions: 1992 and 2004), English (AMS, 1992), and French (Cassini, 2010). Anatolii N. Podkorytov, Associate Professor of the Saint Petersburg State University, Mathematics and Mechanics Faculty, Department of Mathematical Analysis. Author of anumber of published works and frequent deliverer of talks on properties of series and Fourier transform of functions of several variables. In 2014, received the Saint Petersburg State University ‘Pedagogic Excellency’ award. In 2010, co-authored (with Boris M. Makarov) a book Lectures on Real Analysis published in English by Springer in 2013 under the title of Real Analysis: Measures, Integrals and Applications. Co-authored (with Maria G. Goluzina, Andrei A. Lodkin, and Boris M. Makarov) a book of problems Problems in Real Analysis published in Russian (two editions: 1992 and 2004), English (AMS, 1992), and French (Cassini, 2010).

• Introduction.- Differentiable functions.- Smooth maps.-  Implicit function theorem and some its applications.- Critical values of smooth maps.- Appendix.- References.- Names Index.- Subject Index.

“This textbook is a thorough exposition of the theory of smooth mappings in Euclidean spaces. … the book is addressed to undergraduate students who want to become familiar with the theory of smooth maps, as well as to university teachers in mathematical analysis. … For the more advanced topics, the authors provide motivations for the pertinent problems at the beginning of the sections. All these sections are supplemented with a collection of well-presented examples and exercises.” (Carlos Mudarra, Mathematical Reviews, November, 2022)