Geodesic
Flow of a vector field through a smooth surface and its representation by a surface integral of the 2nd kind
Matematičeskoe obrazovanie, Tome 104 (2022) no. 4, pp. 39-46.

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The article proposes a refinement of the requirements for the parametrization of a smooth two-dimensional surface in three-dimensional space, so that it would be possible to correctly determine the flow of a vector field through the surface. 
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S. V. Shvedenko. Flow of a vector field through a smooth surface and its representation by a surface integral of the 2nd kind. Matematičeskoe obrazovanie, Tome 104 (2022) no. 4, pp. 39-46. http://geodesic.mathdoc.fr/item/MO_2022_104_4_a5/

[1] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya, v. III, Nauka, M., 1966

[2] S. V. Shvedenko, “Prostoi vyvod formuly ploschadi gladkoi poverkhnosti”, Matematicheskoe obrazovanie, 2021, no. 4 (100), 96–98