Abstract
In this chapter, we define and discuss volume integrals in \(\, D\)-dimensional space, curvilinear, and surface integrals of the first and second types in 3D.
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Notes
- 1.
Reminder: \(\,\mathrm{diam}\,(V_i)\,\) is a maximal (supremum) of the distances between the two points of the figure \(\,(V_i)\).
- 2.
In Exercise 2, we ask to verify that \(\, dx^{i}\,\) really transform as contravariant vector components.
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Shapiro, I.L. (2019). Curvilinear, Surface, and D-Dimensional Integrals. In: A Primer in Tensor Analysis and Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26895-4_8
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DOI: https://doi.org/10.1007/978-3-030-26895-4_8
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