hi, I have just read Apostol' Mathematical Analysis months ago, but the second edition. The Green's Theorem does not appear in the second edition, maybe because the author thought these knowledges (Stokes' type of theorems or vector integral calculus) do not belong to entrance mathematical analysis, or not satisfied with his exposition (just guess:-)). I recommend the following two books for Green's Theorem: 1) Spivak's "Calculus on Manifolds", 2)Munkres' "Analysis on Manifolds", if you need to study it in depth for your major, or just skip it if your specialty don't need it at all.