The Laplacian operator, denoted ∇2, is the second order partial differential operator defined by
(a) Explain why it makes sense to think of ∇2 as∇ ·∇.
(b) Show that if f and g are functions of class C2, then ∇2( f g) = f ∇2g + g∇2 f + 2(∇ f ·∇g).
(c) Show that ∇ · ( f ∇g − g∇ f ) = f ∇2g − g∇2 f.
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