Electronics and Communication Engineering
Define scalar and vector point functions?
Discussion started by Geetha , on 479 days ago
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Scalar Point Function:
A scalar point function is a function that assigns a real number (i.e. a scalar) to each point of some region of space. If to each point (x, y, z) of a region R in space there is assigned a real number u = Φ(x, y, z), then Φ is called a scalar point function.
Examples. 1. The temperature distribution within some body at a particular point in time. 2. The density distribution within some fluid at a particular point in time.
Syn. scalar function of position
Scalar field. A scalar point function defined over some region is called a scalar field. A scalar field which is independent of time is called a stationary or steady-state scalar field.
A scalar field that varies with time would have the representation
u = Φ(x, y, z, t)
Vector Point Function:
A vector point function is a function that assigns a vector to each point of some region of space. If to each point (x, y, z) of a region R in space there is assigned a vector F = F(x, y, z), then F is called a vector point function. Such a function would have a representation
F = f1(x, y, z) i + f2(x, y, z) j + f3(x, y, z) k
or equivalently,
Syn. vector function of position
A scalar point function is a function that assigns a real number (i.e. a scalar) to each point of some region of space. If to each point (x, y, z) of a region R in space there is assigned a real number u = Φ(x, y, z), then Φ is called a scalar point function.
Examples. 1. The temperature distribution within some body at a particular point in time. 2. The density distribution within some fluid at a particular point in time.
Syn. scalar function of position
Scalar field. A scalar point function defined over some region is called a scalar field. A scalar field which is independent of time is called a stationary or steady-state scalar field.
A scalar field that varies with time would have the representation
u = Φ(x, y, z, t)
Vector Point Function:
A vector point function is a function that assigns a vector to each point of some region of space. If to each point (x, y, z) of a region R in space there is assigned a vector F = F(x, y, z), then F is called a vector point function. Such a function would have a representation
F = f1(x, y, z) i + f2(x, y, z) j + f3(x, y, z) k
or equivalently,
Syn. vector function of position