“Green's Identities”的概念、定义、习题解题方法及翻译-数学辞典

单词

Green's Identities

释义

Green's Identities

Green's identities are a set of three vector derivative/integral identities which can be derived starting with the vectorderivative identities

(1)

and

(2)

where

is the Divergence,

is the Gradient,

is the Laplacian, and

is the Dot Product. From the Divergence Theorem,

(3)

Plugging (2) into (3),

(4)

This is Green's first identity.

Subtracting (2) from (1),

(5)

Therefore,

(6)

This is Green's second identity.

Let have continuous first Partial Derivatives and be Harmonicinside the region of integration. Then Green's third identity is

(7)

(Kaplan 1991, p. 361).

References

Kaplan, W. Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, 1991.

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