Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
Scalar and Vector Fields
Scalar Valued Function
Let P(x,y,z) which is a scalar is called a scalar point function.
Note: A scalar point function is also called a scalar fixed . = (x,y,z)
Ex.: (x,y,z) = x 2 + y 2 + z 2
Vector Valued Function
Let P(x,y,z) be a point. A vector point function is a vector whose
components are real valued functions of x,y,z. A vector point function is called a
vector field F .
Ex:
f f (x, y, z) f1
i f2
j f3
k
F
xyz i
x
2
y j
yz k
Differential
operator
:
denotes
the
operation
i
x
y
j
k
z
i
x
does
not
represent
a
vector
if
only
defines
the
differential
operator
Gradient of a Scalar Field
Let(x, y, z) be a scalar field, then i k i
x z x
is called the gradient of denoted by .
The
following
are
some
results
obtained
by
the
definition
of
.
1. ( )
,
is a scalar cons tan t.
2. ( )
,
and are scalar fields.
3. ( )
,
and are scalar cons tan ts
4.()
5.
2
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