Several Real Variables by Shmuel KantorovitzSeveral Real Variables by Shmuel Kantorovitz

Several Real Variables

byShmuel Kantorovitz

Paperback | February 19, 2016

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This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as:

•The p-norms on vector space and their equivalence

•The Weierstrass and Stone-Weierstrass approximation theorems

•The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables

•The Implicit Function Theorem for a system of equations, proved via Banach's Fixed Point Theorem

•Applications to Ordinary Differential Equations

•Line integrals and an introduction to surface integrals

This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study.

Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in linear algebra and analysis of one real variable.

The author is an expert in Spectral Theory and semigroups of operators, researching in this area for 50 years, publishing numerous papers and three monographs.  
Title:Several Real VariablesFormat:PaperbackDimensions:307 pagesPublished:February 19, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319279556

ISBN - 13:9783319279558


Table of Contents

Continuity.- Derivation.- Implicit Functions.- Integration.- Solutions.

Editorial Reviews

"The book elegantly explores the core concepts in several real variables and introduces accessible methods for both students and instructors. . Ideal for either classroom use or self-study, Several real variables is an excellent textbook for both students discovering real analysis in many variables for the first time and for anyone who looks for a useful resource for reference or review." (Grigore Ciurea, Mathematical Reviews, February, 2017) "Kantorovitz's work is derived from a fourth semester course in mathematics. . this text will be appropriate for potential mathematics majors. . This title offers mature coverage of the subject area, along with a diverse viewpoint of advanced undergraduate mathematics for the serious student. Summing Up: Recommended. Lower- and upper-division undergraduates." (D. Z. Spicer, Choice, Vol. 54 (3), November, 2016)