Diseren tial 19ector Operators
ko introduee n9ee tor caleudes:
We Cre
going part.
ld' is imporfant tor th is
leid
tet fie Ras eadues
term qunity LRat
kerm ield, re fers ko quntity is veetor
Jhe regjon. 14 the
a t all
oin t o a 5seetorfield '. otlerise
its dis tribution AS deseribed as
Saea sealar field
it is
sealar Siedd.
Ghradient, V :- Let (x,9, 2) ÀS thematicaly defned
" field , ma
9radient of Sealar
JRe
as,
grad
f+
k;IVis del /nablap
e
point, i s
Scaloy
tunetion at any
any
Gradient as
O geetor quantiy.
, Interpreka tion od Gradient :
2 Physica l surdace very elose to each otker
Let their be two
of the surfaces and +d
JRe JuncHion
Æke lensel surfaces o
On
points P ond R positien
two be
respeetively. Let
and
elative : kg ng
+d¢ p and R respectinsely
eetors
then PR= d.
arbitary origin,
(y,2) an d
co-ordinate ot Pa and R
1f respeetisely Ehen
+dx, y+dy,z +da)
(x
+j dy + 2 k dz
di dx
and R
sealar tunetion at P
the alues
As orite
we mouy
are
and d¢+
+
22
(2
, consider khat poin t R iies
partieulan
Level Surtoee , then
Ahe
level surfaee .
rmal
nor to the
is
normal rom point P
along
|f d is distanee
then
to
dn = PQ =
.n
<s
So,
component of vd
Derigative : Jhe direetioncal dervative
the
Diree tlonal is
dineetion of A ¢ and is
gien by.
Ln
dineetion ot
ko introduee n9ee tor caleudes:
We Cre
going part.
ld' is imporfant tor th is
leid
tet fie Ras eadues
term qunity LRat
kerm ield, re fers ko quntity is veetor
Jhe regjon. 14 the
a t all
oin t o a 5seetorfield '. otlerise
its dis tribution AS deseribed as
Saea sealar field
it is
sealar Siedd.
Ghradient, V :- Let (x,9, 2) ÀS thematicaly defned
" field , ma
9radient of Sealar
JRe
as,
grad
f+
k;IVis del /nablap
e
point, i s
Scaloy
tunetion at any
any
Gradient as
O geetor quantiy.
, Interpreka tion od Gradient :
2 Physica l surdace very elose to each otker
Let their be two
of the surfaces and +d
JRe JuncHion
Æke lensel surfaces o
On
points P ond R positien
two be
respeetively. Let
and
elative : kg ng
+d¢ p and R respectinsely
eetors
then PR= d.
arbitary origin,
(y,2) an d
co-ordinate ot Pa and R
1f respeetisely Ehen
+dx, y+dy,z +da)
(x
+j dy + 2 k dz
di dx
and R
sealar tunetion at P
the alues
As orite
we mouy
are
and d¢+
+
22
(2
, consider khat poin t R iies
partieulan
Level Surtoee , then
Ahe
level surfaee .
rmal
nor to the
is
normal rom point P
along
|f d is distanee
then
to
dn = PQ =
.n
<s
So,
component of vd
Derigative : Jhe direetioncal dervative
the
Diree tlonal is
dineetion of A ¢ and is
gien by.
Ln
dineetion ot
