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

Engineering Mathematics - II - Vector Calculus - 2007
Directional derivative: . a is called the directional derivative in
the direction of a .
Divergence of a vector field :If f f1
i f2
j f3
k
is
a vector
field
then
div
f .
f
f
1
x
f
2
y
f3
z
f1
x
Solenoidal:
f
is
solenoida.l of
div f
0
Laplacian of a scalar field: Let be a scalar field then
2
2
x
2
2
y
2
2
z
2
Curl
of
a
vector
field: Let
f
be
a
vector
field
then
curl
of
f
Curl
f
f
i j k
x
y
z
f1 f2
f3
f
3 f
2
i
y z
Irrational: f
is
irrational if
Curl
f 0
Introduction
In this chapter the basic concepts of Differential Calculus of scalar functions are
extended to vector functions.
Here we study vector differentiation, gradient, divergence, curl, solenoidal and
irrational fields.
Also we study about vector integration and verification of the integral theorems.
Vector Function of a Scalar Variable
Let f f1
i f2
j f3
k where f1, f2
and f3
are
functions
of
a
var iable
t
is called a vector function.
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