The first two lemmas involve surface integrals over a small sphere of radius b and taking the limit as b goes to zero [Transparancies 2 and 3]. The third lemma involves the Laplacian of 1/R.
Using these lemmas, when considering a region which excludes a small sphere of radius b at the origin, and taking the limit as b goes to zero, one arrives at the Third Green Formula [Transparancy 4]. The Third Green Formula can be used to obtain an expression which clearly indicates how the Laplacian of a scalar field is related to the difference between a scalar field and its average value over the surface of a small sphere [Transparancy 5]. This justifies our previous intuition (lecture 15) about the Laplacian!
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