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

C
Engineering Mathematics - II - Vector Calculus - 2007
f .d r represents the work done in moving a particle of unit
along the Curve C from A to B.
mass
Surface Integral of a vector function
The
surface int egral
of
f
over a
surface
S
is
defined
as
S
f .n
dS
where
n
is the unit normal to the surface S and dS = dx dy
Physical Meaning:
The
surface int egral
of
f
gives
the
total normal
flux
through
a
surface.
Volume integral of a vector function
The
volume int egral
of f
over
a
volume V
is
defined
as
V
f dV
f1d V
i
f2
dV
j
d V
k
V V V
Integral Theorems
Green's Theorem (Statement only)
Let M(x,y) and N(x,y) be two functions defined in a region A in the xy plane with
a simple closed curve C as its boundary then
C
(M dx
Mdy)
N
x
A
M
dx dy
y
Strokes Theorem (Statement only)
Let S be an open surface bounded by a simple closed curve C for a field
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