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- W73767630 abstract "With this chapter we conclude the study of multivariable integral calculus. In the first part we define integrals along curves in ℝ m and over surfaces in space, by considering first real-valued maps, then vector-valued functions. Integrating a vector field's tangential component along a curve, or its normal component on a surface, defines line and flux integrals respectively; these are interpreted in Physics as the work done by a force along a path, or the flow across a membrane immersed in a fluid. Curvilinear integrals rely, de facto, on integrals over real intervals, in the same way as surface integrals are computed by integrating over domains in the plane. A certain attention is devoted to how integrals depend upon the parametrisations and orientations of the manifolds involved." @default.
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- W73767630 date "2015-01-01" @default.
- W73767630 modified "2023-09-27" @default.
- W73767630 title "Integral calculus on curves and surfaces" @default.
- W73767630 doi "https://doi.org/10.1007/978-3-319-12757-6_9" @default.
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