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:
“The man who is admired for the ingenuity of his larceny is almost always rediscovering some earlier form of fraud. The basic forms are all known, have all been practicised. The manners of capitalism improve. The morals may not.”
—John Kenneth Galbraith (b. 1908)
“The cart before the horse is neither beautiful nor useful. Before we can adorn our houses with beautiful objects the walls must be stripped, and our lives must be stripped, and beautiful housekeeping and beautiful living laid for a foundation.”
—Henry David Thoreau (18171862)