FUNCTIONS OF SEVERAL VARIABLES

This chapter focuses on the functions of several variables and also describes the concept of limits. It presents an assumption in which the function f ( x , y ) is defined either in the whole plane or in a certain domain. A definite value f ( x , y ), thus, corresponds to every point ( x, y ) of this domain. If interior points only of the domain are considered, the domain is said to be open. If the domain includes its boundary, it is said to be closed. The chapter explains the concepts of the partial derivatives and the total differential of a function of two variables. These concepts are extended to the case of functions of any number of variables. In the case of a function of a single variable, the expression for its first differential does not depend on the choice of the independent variable. A function of any number of variables is called a homogeneous function of degree m of these variables if multiplication of all the variables by an arbitrary magnitude t results in multiplication of the function by t m .