vector algebra and calculus 2nd year a1 course 8 lectures michaelmas 2013 stephen roberts sjrob robots ox ac uk vector calculus scalar fields 0 2 think about some scalar quantities ...
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...Vector algebra and calculus nd year a course lectures michaelmas stephen roberts sjrob robots ox ac uk scalar fields think about some quantities massm length l time t temperature etc if r is position in space eld might be varying the z keep y constant what when you move x but suppose moved of direction n would multiply does exist it or quantity v that has value at every region examples are theelectric e around stationary charges theunsteady uid velocity stream local can viewed using laser doppler anemometry by dropping twigs diving ll interested weirs acceleration vortices curls contents revision product triple products multiple applications to geometry dierentiation functions mechanics elds line surface volume integrals curvilinear co ordinates operators grad div curl identities ordinate systems gauss stokes theorems extensions engineering...