Multiple Integrals

Abstract

Differentiation and operations with derivatives for functions of several variables are directly reducible to their anologues for functions of one variable. Integration and its relation to differentiation are more involved, since the concept of integral can be generalized for functions of several variables in a variety of ways. Thus, for a function f(x, y, z) of three independent variables, we have to consider integrals over surfaces and lines, as well as integrals over regions of space. Nonetheless, all questions of integration will be related to the original concept of the integral of a function of a single independent variable.