math 32b discussion session week 7 notes february 21 and 23 2017 in last week s notes we introduced surface integrals integrating scalar valued functions over parametrized surfaces as with ...
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...Math b discussion session week notes february and in last s we introduced surface integrals integrating scalar valued functions over parametrized surfaces as with our previous used a transformation namely the parametrization to rewrite integral more familiar domain picked up fudge factor along way this want integrate vector elds of fields suppose have r eld f dened on such those seen following gure wewanttomakesense what it means that is dene symbol z ds when dening integration curves set things so would measure work done by curve doesn t lift very nicely which direction should be considered positive instead measuring extent pushing ll through ux can pointwise contribution much same measured for line focus xed point p at tangent plane indicated here blue associated only part perpendicular making any decomposed sum two vectors one not thus makes no all data encoded its projection onto normal then magnitude see kf nk where n unit pointing reason make denition let whose contains zzsf zzs ...