“divergence theorem”的概念、定义、翻译、参考文献-科学参考

divergence theorem

Physics

A theorem that gives the relation between the total flux of a vector F out of a surface S, which surrounds the volume V, to the vector inside the volume. The divergence theorem states that
$\int_{v} div FdV = \int_{s} F \cdot ds .$

The divergence theorem is also known as Gauss’ theorem and Ostrogradsky’s theorem (named after the Russian mathematician Michel Ostrogradsky (1801–61), who stated it in 1831). Gauss’ law for electric fields is a particular case of the divergence theorem.

Mathematics

For a bounded region R in ℝ³ with smooth boundary Ʃ, and for a continuously differentiable vector field F on R,

$\int \int \int_{R} div F d V = \int \int_{Σ} F \cdot d S .$

Here dS = n dS, where S denotes surface area and n is the outward-pointing unit normal. As the divergence divF represents the local expansion/contraction of the field F, then the theorem states that the sum of such expansions equals the flux of F over the boundary Ʃ. See Stokes’ theorem (generalized form).

单词	divergence theorem
释义	divergence theorem Physics A theorem that gives the relation between the total flux of a vector F out of a surface S, which surrounds the volume V, to the vector inside the volume. The divergence theorem states that $\int_{v} div FdV = \int_{s} F \cdot ds .$ The divergence theorem is also known as Gauss’ theorem and Ostrogradsky’s theorem (named after the Russian mathematician Michel Ostrogradsky (1801–61), who stated it in 1831). Gauss’ law for electric fields is a particular case of the divergence theorem. Mathematics For a bounded region R in ℝ³ with smooth boundary Ʃ, and for a continuously differentiable vector field F on R, $\int \int \int_{R} div F d V = \int \int_{Σ} F \cdot d S .$ Here dS = n dS, where S denotes surface area and n is the outward-pointing unit normal. As the divergence divF represents the local expansion/contraction of the field F, then the theorem states that the sum of such expansions equals the flux of F over the boundary Ʃ. See Stokes’ theorem (generalized form).
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