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Erschienen in:
2015 | OriginalPaper | Buchkapitel
8. Integral calculus in several variables
verfasst von : Claudio Canuto, Anita Tabacco
Erschienen in: Mathematical Analysis II
Verlag: Springer International Publishing
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Abstract
The definite integral of a function of one real variable allowed us, in Vol. I, to define and calculate the area of a sufficiently regular region in the plane. The present chapter extends this notion to multivariable maps by discussing multiple integrals; in particular, we introduce double integrals for dimension 2 and triple integrals for dimension 3. These new tools rely on the notions of a measurable subset of ℝ
n
and the corresponding n-dimensional measure; the latter extends the idea of the area of a plane region (n = 2), and the volume of a solid (n = 3) to more general situations.