Fusco Mathematical Analysis: Functions of Several Real Variables

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:

Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory.

Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject.

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 self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.