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To understand vector-valued functions, it's common to either think parametrically, in which you think of the function as drawing a curve or surface in the output space, or with a vector field, in which you plop a vector on various points in space.

6653_3d_vector_fields_introduction.html

6654_3d_vector_field_example.html

6652_Fluid_flow_and_vector_fields.html

6650_Parametric_surfaces.html

6649_Parametric_curves.html

6651_Vector_fields_introduction.html

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