Poisson's equation (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Poisson's equation" in English language version.

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Kazhdan, Michael; Bolitho, Matthew; Hoppe, Hugues (2006). "Poisson surface reconstruction". Proceedings of the fourth Eurographics symposium on Geometry processing (SGP '06). Eurographics Association, Aire-la-Ville, Switzerland. pp. 61–70. ISBN 3-905673-36-3.

Poisson (1823). "Mémoire sur la théorie du magnétisme en mouvement" [Memoir on the theory of magnetism in motion]. Mémoires de l'Académie Royale des Sciences de l'Institut de France (in French). 6: 441–570. From p. 463: "Donc, d'après ce qui précède, nous aurons enfin: ${\frac {\partial ^{2}V}{\partial x^{2}}}+{\frac {\partial ^{2}V}{\partial y^{2}}}+{\frac {\partial ^{2}V}{\partial z^{2}}}=0,=-2k\pi ,=-4k\pi ,$ selon que le point M sera situé en dehors, à la surface ou en dedans du volume que l'on considère." (Thus, according to what preceded, we will finally have: ${\frac {\partial ^{2}V}{\partial x^{2}}}+{\frac {\partial ^{2}V}{\partial y^{2}}}+{\frac {\partial ^{2}V}{\partial z^{2}}}=0,=-2k\pi ,=-4k\pi ,$ depending on whether the point M is located outside, on the surface of, or inside the volume that one is considering.) V is defined (p. 462) as $V=\iiint {\frac {k'}{\rho }}\,dx'\,dy'\,dz',$ where, in the case of electrostatics, the integral is performed over the volume of the charged body, the coordinates of points that are inside or on the volume of the charged body are denoted by $(x',y',z')$ , $k'$ is a given function of $(x',y,'z')$ and in electrostatics, $k'$ would be a measure of charge density, and $\rho$ is defined as the length of a radius extending from the point M to a point that lies inside or on the charged body. The coordinates of the point M are denoted by $(x,y,z)$ and $k$ denotes the value of $k'$ (the charge density) at M.

Jackson, Julia A.; Mehl, James P.; Neuendorf, Klaus K. E., eds. (2005), Glossary of Geology, American Geological Institute, Springer, p. 503, ISBN 9780922152766

Calakli, Fatih; Taubin, Gabriel (2011). "Smooth Signed Distance Surface Reconstruction" (PDF). Pacific Graphics. 30 (7).

Oldham, K. B.; Myland, J. C.; Spanier, J. (2008). "The Error Function erf(x) and Its Complement erfc(x)". An Atlas of Functions. New York, NY: Springer. pp. 405–415. doi:10.1007/978-0-387-48807-3_41. ISBN 978-0-387-48806-6.