(TXDo}HV/LQHDUHV+RPRJrQHDV
(TXDomR$X[LOLDU
&DVR5Dt]HV5HDLV'LVWLQWDV
\1 = H
£{I ( [)}= ) ( 6 )
{
Sol. Geral: \ = &1H + & 2 H
&DVR'XDV5Dt]HV5HDLV,JXDLV
1
\1 = H
P1 = α + Lβ
P2 = α − Lβ
α+ β
\ = &1H
+ & 2 Hα − β
3URSULHGDGHV
/LQHDULGDGH
£{I ( [)}= ) ( 6 ) e £{J ( [)}= * ( 6 )
£ −1 {&1 ) ( 6 ) + & 2 * ( 6 )}= &1 I ( [ ) + & 2 J ( [ )
&1 £ −1 {) ( 6 )}+ & 2 £ −1 {* ( 6 )}
Porém usando Euler:
β
H = cos β + LVHQβ
\ = Hα [&1 cos( β [ ) + & 2 VHQ( β [ )]
9DULDomRGH3DUkPHWURV
\ = \ + \
−
\ = H ∫
∫
∫H
( )
( )
£ −1 {) ( 6 )}= I ( [)
#
£ −1 {) ( V − α )}= Hα I ( [ )
( )
&RQYROXomR
£ −1 {) ( 6 )}= I ( [ )
I ( [ )G[
£
6ROXo}HVGH(TXDo}HV/LQHDUHVGH2UGHPQmR
KRPRJrQHDYLDYDULDomRGHSDUkPHWURV
+($9,6,'(
P(S) tem grau menor que Q(S)
U% ⇒ N = 1,2,3,....Q
→∞
 3( 6 ) 
3 (U% ) ( ) '
£ −1 
H
=∑
 4( 6 )  % =1 4 ′(U% )
, +
, +
, +
3(U1 )H 1
3(U2 )H 2
3(U* )H −1  3 ( 6 ) 
£ 
+
+ .... +
=
4′(U1 )
4′(U2 )
4′(U* )
 4(6 ) 
&
− £{I ( [ )}= ∫ I ( [)H G[
0
£{&1 I ( [) + & 2 J ( [)}= &1 £{I ( [)}+ &2 £{J ( [)}
= &1 ) ( 6 ) + & 2 * ( 6 )
8VDQGR/DSODFHSDUD&DOFXODU
7UDQVIRUPDGDGH/DSODFHGH'HULYDGDV
£{I ( [)}= ) ( 6 ) então
) ( 6 ) = £{I ( [)} então
£{\ ′}= 6 £{\}− \ (0)
£{\ ′′)}= 6 2 £{\}− 6\ (0) − \ ′(0)
£{\ ′′′}= 6 3 £{\}− 6 2 \ (0) − 6\ ′(0) − \ ′′(0)
{
}
−1
I (0) − 6
I *J
3) £ −1 {) ( 6 ).* ( 6 )}= I ( [ ) * J ( [ ) = J ( [ ) * I ( [ )
∫ I ( [)G[ = lim
∫ I ( [)G[
£ I ( ) ( [) = 6 ) (6 ) − 6
{) ( 6 ).* (6 )}= ∫ I (W ).J ( [ − W )GW =
2) £{I ( [ ) * J ( [ )}= ) ( 6 ).* ( 6 )
/LQHDULGDGH
$
3URSULHGDGHV
1) I ( [ ) * J ( [ ) = J ( [ ) * I ( [)
7UDQVIRUPDGDVGH/DSODFH
∞
−1
e £ −1 {* ( 6 )}= J ( [ )
0
\ ′′ + 3 ( [ ) \ ′ + 4 ( [ ) \ = I ( [ )
\ = X1 \1 + X 2 \ 2
Z
Z
\ = \ + \
X1′ = 1
X ′2 = 2
Z
Z
∞
ou
'HVORFDPHQWR
−
. I ( [ ) G[ + &1H ∫

− ∫ ( ) \ = &1H
)
}
"
£{I ( [)}= ) ( 6 )
I ( [ ) = £ −1 {) ( 6 )}
&DVR5Dt]HV&RPSOH[DV&RQMXJDGDV
G\
+ 3 ( [ ) \ = I ( [)
G[
(
− ( )

∫
∫
\=H
.∫ H

"
7UDQVIRUPDGD,QYHUVDGH/DSODFH
2
\ 2 = [H 2
Sol. Geral: \ = &1 H + & 2 [H
1
"
G
" ( ) ( 6 ))
£ [ I ( [ ) = (−1)
GV
2
!
0XOWLSOLFDomRSRU [ \2 = H
1
)RUPXOiULRGH0DWHPiWLFD$SOLFDGD
−2
I ′(0) − ..... − 6I
−
∫ H I ( [)G[ = ) (6 )
./
tomando limite quando V → 0
−2
(0) − I
−1
(0)
∞
∫ I ( [)G[ = ) (0)
0
'GKQ/G;@9