Classical Analysis of Real-Valued Functions

V.S. Serov

ISBN 10: 1611977665 / ISBN 13: 9781611977660

Published by Society for Industrial and Applied Mathematics,U.S., US, 2023

About this Item

Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential equations, and other subjects. The first section of Classical Analysis of Real-Valued Functions covers the theorems of existence of supremum and infimum of bounded sets on the real line and the Lagrange formula for differentiable functions. Applications of these results are crucial for classical mathematical analysis, andmany are threaded through the text. In the second part of the book, the implicit function theorem plays a central role, while the Gauss-Ostrogradskii formula, surface integration, Heine-Borel lemma, the Ascoli-Arzelą theorem, and the one-dimensional indefinite Lebesgue integral are also covered. This book is intended for students in the first and second years of classical universities majoring in pure and applied mathematics, but students of engineering disciplines will also gain important and helpful insights. It is appropriate for courses in mathematical analysis, functional analysis, real analysis, and calculus and can be used for self-study as well.

Seller Inventory # LU-9781611977660

Bibliographic Details

• Title: Classical Analysis of Real-Valued Functions
• Publisher: Society for Industrial and Applied Mathematics,U.S., US
• Publication Date: 2023
• Language: English
• ISBN 10: 1611977665
• ISBN 13: 9781611977660
• Binding: Paperback
• Condition: New
• Weight: 445 grams

About this title

Synopsis

Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential equations, and other subjects. The first part of Classical Analysis of Real-Valued Functions covers the theorems of existence of supremum and infimum of bounded sets on the real line and the Lagrange formula for differentiable functions. Applications of these results are crucial for classical mathematical analysis, and many are threaded through the text. In the second part of the book, the implicit function theorem plays a central role, while the Gauss–Ostrogradskii formula, surface integration, Heine–Borel lemma, the Ascoli–Arzelą theorem, and the one-dimensional indefinite Lebesgue integral are also covered. This book is intended for first and second year students majoring in mathematics although students of engineering disciplines will also gain important and helpful insights. It is appropriate for courses in mathematical analysis, functional analysis, real analysis, and calculus and can be used for self-study as well.

About the Author

V. S. Serov is Professor Emeritus at the University of Oulu in Finland, where he teaches courses focusing on various aspects of inverse problems. In 2008, he helped establish an annual scientific seminar on inverse problems. Earlier in his career, he taught at Moscow Lomonosov State University for many years.