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This third part is known as the Laplacian part or the relaxed part and is contained in the other parts.
Linera operator entirna tha deuh mai chu Laplacian kha a ni a.
We can rewrite (1a) as ∆u = ut − f (x) and, noting that the Laplacian ∆ ≡ ∇ · ∇, take volume integrals over D on all terms such that Z Z Z ∇ · (∇u) dx = ut dx − f (x) dx D D D Z Z f (x) dx ut dx − 0= D Z ZD f (x) dx = ut dx .
if A is a constant vector, show that grad (A · r) = A 3.for any ortogonal curvilinear coordinate system find the gradient, divergence, laplacian and curl.
Expression of grad, div, curl and Laplacian in Spherical and Cylindrical co-ordinates.