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:
“I fly in dreams, I know it is my privilege, I do not recall a single situation in dreams when I was unable to fly. To execute every sort of curve and angle with a light impulse, a flying mathematicsthat is so distinct a happiness that it has permanently suffused my basic sense of happiness.”
—Friedrich Nietzsche (18441900)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worryingas a reflex response to demandnever puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. Worrying and Its Discontents, in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)