Uploaded by Nirbhay Aher

Partial Differential Equations

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Function
n
Andy
when
a
value
for
n and
o
z
flu
two
of
function
every pair of
a
Specific
valuer
of
y
y
as
where
the
z
be
can
height of
Region
If
and
there
the
of
that
set R
o
has
z
considered
the surface
o
independent variables
is
any
set
a
bet R
two points
R
can
be
the
Anc
Pitz
of points fu y
p
and
joined
in
lies
Pz
such
the
Open Region
does not
include
points of its boundary
the
region
If
the
all
Closed region
Includes
all the points
0
of its boundary
Neighbourhood
The set
of points
has
centre
within
Aib
as
which
radius 850
circle
the
and
This is said to be neighbourhood of
Carb in the circular region
R
o
z
flu y
u
t
a
I
t
82
b
y
fume of
than
more
variables
2
Limit e
flu
y
If limith
tends to
is
limit
us
as
independent of
followed by
Etna
as
Cuny
flu
y
nsa
l
a
the
g
y
path
b
b
o
limit
l
en terms
of
circular
neighbourhood
Junction flay defined in region R
lends to limitll
as
usa
yo b
if
and
only if
corresponding to
another
tre
Ca
for every point
0
E
ne
tre
ell E
y
a 2
in
g
there
enists
such that
s
member
I fan
O c
a
b
for
82
2
R
Continuity
flag
is
agha
continuous
8619
at
exists and
Continuous in that region
Function is continuous at
that
carb
all
if
a
flab
points of
g
Discontinuous at that Pt
Function not continuous
not
but
Usually
at
point
a
always
ntima
finis
ageing
In
functions of
If
lim
una
flu
glim finna fenny
variable
one
y
l
and
yo b
alina glary
m
then
ye b
lim
g
lim
flay
feng
guy
flury
gCn y
YT's
lim
TIE
ltm
Iggy
a
l
m
elm
If flu
at
y
aib
and gCais
then
are
provided that
are continuous
also continuous at Carb
gluey
0 in
Partial Derivatives
Ey En
O Representation of P D
of 2 WA N
Dnf
Ey
Representation of PD
of
a
wut
y
Dy f
I Eu
Ya
Y
Ig
Ii
d
tu lucy
sign
or
or
or
If
fy
my
fun
Ig
or
fan
sign
or
fry
fu
In
an
ordinary
cases
Jj
jj
95.1
Us t
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at
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on
it
fCntCA
by
yo tant
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t
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ay
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ur tan
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y3
y
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p
fgf
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age
g
f'cut
fl
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uta
f lurch
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lurch
d Cn d
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to
cu
a
In
a
et
flat
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fi lurch
of
e
c
f
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C
utca
t
flint et
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2
the
it
f
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t
t
d
uct
u
u
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d
not
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et
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d in A
If
Curly
Egs
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if thy
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if
0
n
redo
ya
reino
since r
0,0
May
Polar coordinates
rise
at
o.o
o
of my
since
Cuny
1
0,0
and
I since
s
lim
Mcg
Eg2
cool
M
Co o
flu g
2
0
luppose that
Cury
lim
fu D
ay
you
oo
f
o
ayy
all
for
I n
if
if
O
o.o
Cuny
o.o
0,0
Cury
10,0 along
nen
flu
yen
tn
I
that
Suppose
lim
nay
y
za
Egg
fl
oo
a
9
a
0,07 along
notion In
un
y
n
I
U
f Cuny
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3ns
By
JJ
342
3h
fun
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E
Eg
2
fay
fyn
o
Cury
yo buy
E
Jj
Ey
Geometrical Representation of Partial Derivati
the
order
of
first
Graphically
a
surface
the
ferric
2
flu
y
represents
fuel a b
denotes the tangent of the angle
in which
which the tangent to the curve
to
the ZX plane
the plane y b
cuts the surface
P a b fla b
If
ego
b
ya
the
point
with
makes
h anis
a
fg
2abz
aeant
flan by
acanthyfican by
of
By
at
earth f Can by
z
pore
parallel
beauty flantby
beamby flan by
b Ent
U
re
firs
natya
me
Inst T
fufu
fie
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