ENGLISH

Several Real Variables

By Shmuel Kantorovitz (auth.)

Book information

Publisher
Springer International Publishing
Year
2016
ISBN
978-3-319-27955-8, 978-3-319-27956-5
DOI
10.1007/978-3-319-27956-5
Language
english
Format
PDF
Filesize
3 MB (3339473 bytes)
Series
Springer Undergraduate Mathematics Series
Edition
1
Pages
XII, 307\315
Time added
2016-03-14 21:35:01
Real Functions

Description

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.

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