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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
Differential Operators 10-11
= + +
= =
f
x
n
x y z x
nx r nx r
n
n
n
2
2
2 2 2
1
2
1
2
2
2
( )
( ) .
Similarly,
=
=
=
+
+
=
f f
f
f f f
y
ny r
z
nz r
i
x
j
y
k
z
n
n n2 2
and
grad
(
xxi y j zk r nr r
n n
+ + =
) .
2 2
Example 10.5 Show that
grad ( )a r a =
Solution:
a r a x a y a z
a r i
x
a r
i
x
a x a y a z
a
= + +
=
=
+ +
( )
=
1 2 3
1 2 3
grad ( ) ( )
11 2 3
i a j a k
a
+ +
= .
10.3 DIVERGENCE AND CURL OF A VECTOR POINT FUNCTION
If f be a differentiable vector point function, then the divergence of f written as div f f= ∇⋅( ) is
defined as:
div f i
f
x
j
f
y
k
f
z
i
x
j
y
k
z
=
+
+
=
+
+
⋅⋅
= ∇⋅
= ∇⋅ =
f
f
f f i
f
x
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Publisher Resources

ISBN: 9789353948221