PREFACE

# Introduction

This electronic book are intended to serve as a text for the course in multivariable analysis that usually taken by second year students who study mathematics and computer sciences.

Despite the fact that these are our “class notes”, they should be accessible to anyone wanting to learn multivariable analysis or needing a refresher in some of the topics from the class. These notes do assume that the reader has a good working knowledge of mathematical analysis I topics including limits, derivatives and integration. It also assumes that the reader has a good knowledge of several mathematical analysis II topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space.

The brief theoretical material on following sections of Mathematical Analysis of many variables is presented in the given methodical instructions: the limits and continuity of functions of many variables, the partial derivatives of first order and high order, differentials of first order and high order, differentiation of implicit functions, the extreme value of a function of several variables, double and triple integrals and their properties, the curvilinier integrals, the integrals over the surfaces, Gauss-Ostrogradsky's theorem, Green's theorem, the elements of a field‘s theory. The examples, control tasks and questions are given in the above-named sections.

THESE NOTES ARE NOT A SUBSTITUTION FOR ATTENDING CLASS!!