Tugas 4

MATA KULIAH:

“KALKULUS LANJUT”

DOSEN PENGAMPUH

Prof.Dr.P. Siagian, M.Pd

NAMA: HERI RISDIANTONIM : 8106172005

PENDIDIKAN MATEMATIKAPASCA SARJANA

UNIVERSITAS NEGERI MEDAN2010

1 . L -1 (s−5

s2+6 s+5 ) =…………..Jawabs−5

s2+6 s+5 =

s−5( s+1)( s+5 )

s−5( s+1)( s+5 ) =

As+1

+ Bs+5

s−5= A( s+5 )+B (s+1)s−5=As+5 A+Bs+BA+B=15 A+B=−5−4 A=6

A=−32

A=−32→ A+B=1

B=1−(−32

)

B= 52

L -1 (

s−5s2+6 s+5 ) = L -1

(−32s+1+

52

s+5 )

=L -1(−32s+1 )

+ L -1( 52s+5 )

=52e−5 t−3

3e3 t

2 . L -1 (s2+2 s−4s4+2 s3+s2 ) =…………..

Jawab

s2+2 s−4s4+2 s3+s2 =

s2+2 s−4s2( s2+2 s+1 )

s2+2 s−4s4+2 s3+s2 =

As+Bs2

+ Cs+D(s+1)2

s2+2 s−4 = ( As+B )( s2+2 s+1 )+(Cs+D )( s2)

s2+2 s−4 =As3+2 As2+As+Bs2+2Bs+B+Cs3+Ds2

A+C=02 A+B+D=1A+2 B=2B=−4A=10C=−10D=−12

L -1 (

s2+2 s−4s4+2 s3+s2 ) = L -1 (

10 s−4s2

+−10 s−12

(s+1)2 )

=L -1(10 ss2

)- L -1

( 4s2

) - L -1(10 s( s+1 )2) - L -1(12( s+1 )2)

=L -1(10s

)- L -1

( 4s2

) - L -1(10 s+10( s+1 )2 ) - L -1(12−10(s+1)2 )

=L -1(10s

)- L -1

( 4s2

) - 10 L -1( s+1

( s+1 )2) - L -1( 2( s+1 )2)

=10−4 t−10 e−t−2te−t