Several Real Variables

Several Real Variables
Springer | Analysis, Undergraduate Textbook | March 12, 2016 | ISBN-10: 3319279556 | 307 pages | pdf | 3.18 mb

Authors: Kantorovitz, Shmuel
A modern, self-contained exposition of the basic analysis of functions of several real variables
An easy-to-read introduction to first-order logic and model theory
Presents the essential aspects of model theory needed to understand model theoretic algebra
Includes interesting and profound applications of model theory to algebra

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

Number of Illustrations and Tables
16 b/w illustrations
Topics
Real Functions

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