Basic Objects
The basic objects in vector calculus are scalar fields (scalar-valued functions) and vector fields (vector-valued functions). These are then combined or transformed under various operations, and integrated. In more advanced treatments, one further distinguishes pseudovector fields and pseudoscalar fields, which are identical to vector fields and scalar fields except that they change sign under an orientation-reversing map: for example, the curl of a vector field is a pseudovector field, and if one reflects a vector field, the curl points in the opposite direction. This distinction is clarified and elaborated in geometric algebra, as described below.
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