Anatolii Podkorytov's Books

Real Analysis: Measures, Integrals and Applications

By: Boris Makarov,Anatolii Podkorytov

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Real Analysis: Measures, Integrals and Applications

By: Boris Makarov,Anatolii Podkorytov

Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications both classical and those rarely covered in literature. This book provides a detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines the concept of the Hausdorff measure, the properties of the area on smooth and Lipschitz surfaces, the divergence formula, and Laplace's method for finding the asymptotic behavior of integrals. The general theory is then applied to harmonic analysis, geometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of independent random variables. The book contains more than 600 examples and exercises. The reader who has mastered the first third of the book will be able to study other areas of mathematics that use integration, such as probability theory, statistics, functional analysis, partial probability theory, statistics, functional analysis, partial differential equations and others. Real Analysis: Measures, Integrals and Applications is intended for advanced undergraduate and graduate students in mathematics and physics. It assumes that the reader is familiar with basic linear algebra and differential calculus of functions of several variables.

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Page Count

780

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447151224

ISBN 13

9781447151227

Smooth Functions and Maps

By: Boris M. Makarov,Anatolii N. Podkorytov

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Smooth Functions and Maps

By: Boris M. Makarov,Anatolii N. Podkorytov

The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus. The scope of notions includes, among others, Lagrange inequality, Taylor’s formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings. In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor’s formula in a nonconvex area (Chapter I, §8), Whitney's extension theorem for smooth function (Chapter I, §11) and some of its corollaries, global diffeomorphism theorem (Chapter II, §5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV). The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.

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Page Count

296

Publisher

Springer Nature

Published Date

ISBN 10

3030794385

ISBN 13

9783030794385

Real Analysis: Measures, Integrals and Applications

By: Boris Makarov,Anatolii Podkorytov

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Real Analysis: Measures, Integrals and Applications

By: Boris Makarov,Anatolii Podkorytov

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Solve jigsaw puzzle

Age

Page Count

780

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447151224

ISBN 13

9781447151227

Smooth Functions and Maps

By: Boris M. Makarov,Anatolii N. Podkorytov

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Smooth Functions and Maps

By: Boris M. Makarov,Anatolii N. Podkorytov

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N/A

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Solve jigsaw puzzle

Age

Page Count

296

Publisher

Springer Nature

Published Date

ISBN 10

3030794385

ISBN 13

9783030794385

Book's by Anatolii Podkorytov

Real Analysis: Measures, Integrals and Applications

Real Analysis: Measures, Integrals and Applications

Smooth Functions and Maps

Smooth Functions and Maps

Real Analysis: Measures, Integrals and Applications

Real Analysis: Measures, Integrals and Applications

Smooth Functions and Maps

Smooth Functions and Maps

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