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.
Read more about this topic: Vector Calculus
Famous quotes containing the words basic and/or objects:
“Southerners, whose ancestors a hundred years ago knew the horrors of a homeland devastated by war, are particularly determined that war shall never come to us again. All Americans understand the basic lessons of history: that we need to be resolute and able to protect ourselves, to prevent threats and domination by others.”
—Jimmy Carter (James Earl Carter, Jr.)
“I was afraid that by observing objects with my eyes and trying to comprehend them with each of my other senses I might blind my soul altogether.”
—Socrates (469–399 B.C.)