Green's First Identity
This identity is derived from the divergence theorem applied to the vector field : Let φ and ψ be scalar functions defined on some region U in R3, and suppose that φ is twice continuously differentiable, and ψ is once continuously differentiable. Then
where is the Laplace operator, is the boundary of region U and n is the outward pointing unit normal of surface element dS. This theorem is essentially the higher dimensional equivalent of integration by parts with ψ and the gradient of φ replacing u and v.
Note that Green's first identity above is a special case of the more general identity derived from the divergence theorem by substituting :
Read more about this topic: Green's Identities
Famous quotes containing the words green and/or identity:
“Your hooves have stamped at the black margin of the wood,
Even where horrible green parrots call and swing.
My works are all stamped down into the sultry mud.”
—William Butler Yeats (1865–1939)
“Personal change, growth, development, identity formation—these tasks that once were thought to belong to childhood and adolescence alone now are recognized as part of adult life as well. Gone is the belief that adulthood is, or ought to be, a time of internal peace and comfort, that growing pains belong only to the young; gone the belief that these are marker events—a job, a mate, a child—through which we will pass into a life of relative ease.”
—Lillian Breslow Rubin (20th century)