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...Vectorcalculusintwodimensions by peter j olver university of minnesota introduction the purpose these notes is to review basics vector calculus in two dimen sions we will assume you are familiar with partial derivatives including equality mixed partials assuming they continuous chain rule implicit dieren tiation addition some familiarity multiple integrals assumed although highlights proofs and full details can be found most texts begin a discussion plane curves domains many physical quantities force velocity determined elds basic concepts key dierential operators planar gradient divergence operations along jacobian matrix for maps from r itself there three types line respect arc length computing lengths masses wires center mass etc ordinary work uid circulation ux uids forces next double scalar functions over connected justly famous green s theorem which our collecting together facts concerning geometry curve c parametrized pair x t y where parameter varies an open or closed interval ...