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Green's third identity derives from the second identity by choosing ... For example, in R 3, a solution ... the third term vanishes to yield Green's vector identity: ...
The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:
Green's functions are also useful tools in solving wave equations and diffusion equations. In quantum mechanics, Green's function of the Hamiltonian is a key concept with important links to the concept of density of states. The Green's function as used in physics is usually defined with the opposite sign, instead.
Beware that unit does not mean identity in this context, i.e. in general there are non-identity elements in H 1. The "unit" terminology comes from ring theory.) For example, in the transformation monoid on n elements, T n, the group of units is the symmetric group S n. Finally, D is defined: a D b if and only if there exists a c in S such that ...
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in ) bounded by C. It is the two-dimensional special case of Stokes' theorem (surface in R 3 {\displaystyle \mathbb {R} ^{3}} ).
Their identity may vary depending on the circumstances and the context of their lives at a given point. They may wish to, at any one time, identify with one gender, but over time they don't want ...
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Elementary vector and tensor algebra in curvilinear coordinates is used in some of the older scientific literature in mechanics and physics and can be indispensable to understanding work from the early and mid 1900s, for example the text by Green and Zerna. [1]