What gradients, fundamental forms, measures of curvature, and the
Jacobian have in common is that they only produce *local *results.
That is, they only provide information about a surface or a coordinate
transformation near a given point. However, it is imperative in
mathematics and science that we be able to work with *global *results,
which are results that hold for an entire surface or for all possible
values of a coordinate transformation.

In single variable calculus, we learned that global results such as area of a region, volume of a solid, and length of a curve are studied using definite integrals. Similarly, in order to determine global results in multivariable calculus, we need to develop a theory of integration of functions of two or more variables. Thus, this chapter is devoted to the development of the theory of multiple integrals.

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