Multivariate Calculus

Chapter 2 Functions of Several Variables: Differentiation - I

2.1 Introduction

The details of multivariate functions, its different kinds of limits, continuities etc. have been discussed in Chapter 1 along with few topological aspects of subsets of ℝ² and ℝ³. In this chapter, we are going to discuss the analytical definitions of first and higher order partial derivatives, the total differentiations and directional derivatives etc. The inter relations among the limits, continuities and different kinds of derivatives of functions of several variables have also been discussed with numerous appropriate examples in analytical point of view.

2.2 Partial Derivatives

The partial derivatives of a function of several variables with respect to one of ...