Evaluating Double Integrals.

Although the definition of the integral reflects its origins in scientific problems, its evaluation relies on a considerable range of mathematical concepts and tools. Most fundamental is the change of variables formula; the single-variable version (˵u-substitution″) is perhaps the core technique of integration in the introductory calculus course. By contrast, the method of iterated integrals has no singlevariable analogue; it evaluates a double integral by ˵partial integration″ of one variable at a time. This chapter connects double and iterated integrals, establishes the change of variables formula, and discusses Green΄s theorem as a tool for evaluating double integrals and as a reason for orienting them. [ABSTRACT FROM AUTHOR]