Lectuie 3
Monlao3
2Fe
RIURBAI 1OoN
Aequlay Pertrbaion pro
blem
for which
the per turbe d
REGULAR
ne
noh-2ero
S
m
a
l
as
S a m e
the
alue ofEis problem for
quelitaive.
unpertur bated problem
far E
ExAMPL
-(46)x+S-2¬)x
+ E ) + ( 5-26 )
-2+¬2:
-PE
.
- 2 +e2
using
Putbog
in
.EV,+ex+.)-(1+¬)(+¬ M, tEM t )
5-26)(x,+¬ M,+e*t . ) -2+E =o
.-(6)
y
+2v,M,+2tvgM2t
.-24¬
)-HS M,+ 5¬ V,SEx- 26* * *
367, Yt 36,X,t3tV,
-9M,"-eX-
2
.
,-EV-8¬v,x
M,+5%,+ SE V, 5EM, -2 K,
2x-.. .-2+¬o
Collecbng
the coefficicv
3%X
o
Po wer
3x,X- +Sv,-2 x, O
e
Selutio
of
Zeroth ovder
-1( N,-)'o
S
3
-
2
and
o
-3M.+2
-o
-Y, +2 =Fo
-2
v(M) -1(M, -2)o
2
12,
Stubion of fist oder:
X, L3x,-31,4S
hen
2.
=2
2 3 E +6 E )
hen 1 1, then ca,
will ive
this indicates that the assuma
epension
n
Cor Yect ths
t
determne he expan gon
toke
5
2
Now b4Sn
V
N
2
2
+(5-2)(+¬Ytt ) - 2+
2
14
2
3 Y,2 3EX+3EE2 33fx
2Et
2
T
-2.t
O
2
-BE
NA
1
+ 3E,+ 3A+3e vxl-Y-8%,
2vt
-
-
E
2
+S At S
-
2
-2
2
2-2e -/2 t¬E
Here
2
dominot inq tcim
2
their
1
2
Sin
n (S
36
-
3
)
us in
in
Pouers Should
be
EXMPLE:
,
Let +
S1
M.+¬,
+¬ x,+ *
-(2)
in
Ev, t
e,
)+ (M.+ ¬x, +¬M,)-
Y.)ex,
+3(e)v,) +3(¬,)a,
2v,-E
E
Collechog Power et efKient
3M
22
V
f¬
x 1 J =o
o
1
u)
epcalrel
Ybot
Yepratd Yot
Sol4hon
ofo(e')
,_1
3Mt 2
when :
-1
3
M
hen
o
2
-I+6 oCe) (A)
o
2
--~n
using
in (1
2
2
)
)'-o
2
3
SE,',
ere
t
+¬M, 26,
=O-
2V
2
uSinn
(y-t)
1 - (
= e(11)+ (o}(E)
te4oCe)
A
AiTeRNAlIvE
Consido
ihe
he
the
Smollterm repreendh
difference b/w
the
Leading tevm ,
the Sluon
O
A
Sub hty bing th
The
in
dominoiog leem a
oC')
E,
and
sin
in o
. . +(M,E
Mt
(Y,E
E+3E
O
2
t
3¬
,
42
E 72.
e
oe')
oC)
Eo(e)Solve:- ( - D ( - ) ( x - 3 )
tE
-O