Transformada de lapalace
Páginas: 5 (1161 palabras)
Publicado: 24 de febrero de 2010
TRANSFORMADAS DE LAPLACE POR DEFINICIÓN:
1) [pic]
L[pic]
2) [pic]
L[pic]
[pic]
3) [pic]
L[pic]
TRANSFORMADAS DE LAPLACE UTILIZANDO TEOREMAS:
1) [pic]
L[pic] L[pic]+ L[pic]= [pic]
2) [pic]
L[pic] L[pic]+ 6 L[pic]- 3 L [pic]= [pic]
3) [pic]
L[pic]= L[pic]+ 3 L[pic]+ 3 L[pic]+ L[pic]= [pic]
[pic]
4) [pic]
L[pic]= L[pic]+ 2 L[pic]+ L[pic]= [pic]5) [pic]
L[pic] L[pic]- 5 L[pic]+ 10 L[pic]- 10 L[pic]+ 5[pic]- L[pic]= [pic]
TRANSFORMADAS DE LAPLACE (1er. TEOREMA DE TRASLACIÓN):
1) [pic]
L[pic] L[pic]
2) [pic]
L[pic] L[pic]
TRANSFORMADAS INVERSAS:
1)L-1 [pic][pic]L-1[pic]= [pic]
2) L-1[pic] [pic]L-1[pic]= [pic]
3) L-1[pic] L-1[pic]+ L-1[pic]= [pic]
4) L-1[pic]= L-1 [pic]= [pic]L-1[pic] [pic]L-1[pic] [pic]L-1[pic]=
[pic]
5) L-1[pic]= L-1[pic]= L-1[pic]=
L-1[pic]+ [pic]L-1[pic]+ [pic]L-1[pic]+ [pic]L-1 [pic]= [pic]
6) L-1[pic]
7) L-1[pic]= L-1[pic] L-1[pic]= [pic]
8) L-1[pic] L-1[pic]= [pic]L-1[pic] [pic]
9) L-1[pic] [pic]L-1[pic] [pic]
10) L-1[pic] [pic]L-1[pic]
11) L-1[pic]= [pic]L-1[pic] L-1[pic]
12) L-1[pic]
[pic]
[pic], [pic]y [pic]L-1[pic]= [pic]L-1[pic] L-1[pic] L-1[pic]= [pic]
13) L-1[pic]
[pic]
L-1[pic]= [pic]L-1[pic] L-1[pic]= [pic]
14) L-1[pic]
[pic]
[pic], [pic], [pic]y [pic]
L-1[pic]= [pic]L-1[pic] L-1 [pic]
TRANSFORMADAS INVERSAS (1er. TEOREMA DE TRASLACIÓN):
1)L-1 [pic][pic]L-1[pic]
2) L-1[pic] L-1[pic] L-1[pic]
L-1[pic] L-1[pic]= [pic]
3) L-1[pic] L-1[pic] L-1[pic][pic]
L-1[pic][pic]
4) L-1[pic] L-1[pic] L-1 [pic]
L-1[pic] L-1[pic] L-1[pic] [pic]L-1[pic]
[pic]L-1[pic][pic] L-1[pic] L-1[pic]
[pic]
5) L-1[pic]
[pic]
[pic], [pic]y [pic]
L-1[pic]= L-1[pic] L-1[pic] L-1[pic] L-1[pic] L-1 [pic]=
[pic]
DERIVADA DE TRANSFORMADA:
1)L[pic]= [pic]L[pic]=[pic]
[pic]
2) L[pic] L[pic]
3) L[pic] L[pic]
[pic][pic]
4) L[pic]L[pic][pic][pic]
[pic]
5) L[pic] L [pic]
[pic][pic]
[pic][pic]
6) L[pic] L [pic]
[pic][pic]
[pic][pic]
[pic]
[pic]
TRANSFORMADAS DE LAPLACE (2do. TEOREMA DE TRASLACIÓN):
1)L[pic] L[pic]
2) L[pic] L[pic]
3) L[pic] L[pic] L[pic] L[pic]
[pic]L[pic] [pic]L[pic] [pic]
4) L[pic] L[pic]
5) L[pic] L[pic] L[pic]
6) L[pic] L[pic] L[pic]
[pic]L[pic] L[pic][pic]L[pic] L[pic]
7) L[pic] L[pic] L[pic]
L [pic][pic]L[pic] L[pic]
8) L[pic] L[pic]
TRANSFORMADAS INVERSAS (2do. TEOREMA DE TRASLACIÓN):
1)L-1[pic] L-1[pic] L-1 [pic]
[pic]
2) L-1[pic] L-1[pic]= L-1[pic] L-1[pic]
L-1[pic] [pic]
[pic]
3) L-1[pic]= L-1[pic]
[pic]
L-1[pic]= L-1[pic] L-1[pic]
4) L-1[pic] L-1[pic]
[pic]
L-1[pic]= L-1[pic]
[pic]
TEOREMADE CONVOLUCIÓN:
1)L[pic]
[pic]
L[pic] L[pic] L[pic]
2) L-1[pic] L-1[pic] L-1[pic] [pic][pic][pic]
3) L-1[pic] L-1[pic] L-1 [pic]
[pic][pic]
4) L-1[pic] L-1[pic]L-1[pic]= [pic]
[pic]
5) L-1[pic] L-1[pic] L-1 [pic]
[pic][pic]
[pic][pic]
[pic][pic]
[pic][pic]
ECUACIONES DIFERENCIALES CON CONDICIONES INICIALES (TRANSFORMADA):
1) [pic][pic]
[pic]L[pic][pic]
[pic]
[pic]L-1 [pic]L-1 [pic]
2) [pic][pic]
[pic]L[pic]
[pic]
[pic]L-1 [pic]L-1 [pic]L-1 [pic]
3) [pic][pic], [pic]
[pic]L[pic]
[pic]
[pic]L-1 [pic]
4) [pic][pic], [pic]
[pic]L [pic]
[pic]
[pic]L-1 [pic]L-1 [pic]
[pic]
5) [pic][pic], [pic], [pic]
[pic]L[pic]
[pic]
[pic], [pic]y [pic]
[pic]L-1[pic] L-1[pic] L-1[pic]L-1[pic]L-1 [pic][pic]
6) [pic][pic], [pic], [pic], [pic]
[pic]
[pic]L-1[pic]
ECUACIONES INTEGRALES:
1) [pic]
L[pic]+ L[pic] L[pic]
[pic][pic][pic]L-1[pic]
2) [pic]
[pic]
[pic]
[pic]L-1[pic] L-1[pic]
3) [pic]
[pic]
[pic]
[pic]L-1[pic] L-1[pic] L-1[pic] L-1[pic] L1[pic]
ECUACIONES INTEGRODIFERENCIALES:
1) [pic][pic]
[pic]
[pic]L-1 [pic]
2)...
1) [pic]
L[pic]
2) [pic]
L[pic]
[pic]
3) [pic]
L[pic]
TRANSFORMADAS DE LAPLACE UTILIZANDO TEOREMAS:
1) [pic]
L[pic] L[pic]+ L[pic]= [pic]
2) [pic]
L[pic] L[pic]+ 6 L[pic]- 3 L [pic]= [pic]
3) [pic]
L[pic]= L[pic]+ 3 L[pic]+ 3 L[pic]+ L[pic]= [pic]
[pic]
4) [pic]
L[pic]= L[pic]+ 2 L[pic]+ L[pic]= [pic]5) [pic]
L[pic] L[pic]- 5 L[pic]+ 10 L[pic]- 10 L[pic]+ 5[pic]- L[pic]= [pic]
TRANSFORMADAS DE LAPLACE (1er. TEOREMA DE TRASLACIÓN):
1) [pic]
L[pic] L[pic]
2) [pic]
L[pic] L[pic]
TRANSFORMADAS INVERSAS:
1)L-1 [pic][pic]L-1[pic]= [pic]
2) L-1[pic] [pic]L-1[pic]= [pic]
3) L-1[pic] L-1[pic]+ L-1[pic]= [pic]
4) L-1[pic]= L-1 [pic]= [pic]L-1[pic] [pic]L-1[pic] [pic]L-1[pic]=
[pic]
5) L-1[pic]= L-1[pic]= L-1[pic]=
L-1[pic]+ [pic]L-1[pic]+ [pic]L-1[pic]+ [pic]L-1 [pic]= [pic]
6) L-1[pic]
7) L-1[pic]= L-1[pic] L-1[pic]= [pic]
8) L-1[pic] L-1[pic]= [pic]L-1[pic] [pic]
9) L-1[pic] [pic]L-1[pic] [pic]
10) L-1[pic] [pic]L-1[pic]
11) L-1[pic]= [pic]L-1[pic] L-1[pic]
12) L-1[pic]
[pic]
[pic], [pic]y [pic]L-1[pic]= [pic]L-1[pic] L-1[pic] L-1[pic]= [pic]
13) L-1[pic]
[pic]
L-1[pic]= [pic]L-1[pic] L-1[pic]= [pic]
14) L-1[pic]
[pic]
[pic], [pic], [pic]y [pic]
L-1[pic]= [pic]L-1[pic] L-1 [pic]
TRANSFORMADAS INVERSAS (1er. TEOREMA DE TRASLACIÓN):
1)L-1 [pic][pic]L-1[pic]
2) L-1[pic] L-1[pic] L-1[pic]
L-1[pic] L-1[pic]= [pic]
3) L-1[pic] L-1[pic] L-1[pic][pic]
L-1[pic][pic]
4) L-1[pic] L-1[pic] L-1 [pic]
L-1[pic] L-1[pic] L-1[pic] [pic]L-1[pic]
[pic]L-1[pic][pic] L-1[pic] L-1[pic]
[pic]
5) L-1[pic]
[pic]
[pic], [pic]y [pic]
L-1[pic]= L-1[pic] L-1[pic] L-1[pic] L-1[pic] L-1 [pic]=
[pic]
DERIVADA DE TRANSFORMADA:
1)L[pic]= [pic]L[pic]=[pic]
[pic]
2) L[pic] L[pic]
3) L[pic] L[pic]
[pic][pic]
4) L[pic]L[pic][pic][pic]
[pic]
5) L[pic] L [pic]
[pic][pic]
[pic][pic]
6) L[pic] L [pic]
[pic][pic]
[pic][pic]
[pic]
[pic]
TRANSFORMADAS DE LAPLACE (2do. TEOREMA DE TRASLACIÓN):
1)L[pic] L[pic]
2) L[pic] L[pic]
3) L[pic] L[pic] L[pic] L[pic]
[pic]L[pic] [pic]L[pic] [pic]
4) L[pic] L[pic]
5) L[pic] L[pic] L[pic]
6) L[pic] L[pic] L[pic]
[pic]L[pic] L[pic][pic]L[pic] L[pic]
7) L[pic] L[pic] L[pic]
L [pic][pic]L[pic] L[pic]
8) L[pic] L[pic]
TRANSFORMADAS INVERSAS (2do. TEOREMA DE TRASLACIÓN):
1)L-1[pic] L-1[pic] L-1 [pic]
[pic]
2) L-1[pic] L-1[pic]= L-1[pic] L-1[pic]
L-1[pic] [pic]
[pic]
3) L-1[pic]= L-1[pic]
[pic]
L-1[pic]= L-1[pic] L-1[pic]
4) L-1[pic] L-1[pic]
[pic]
L-1[pic]= L-1[pic]
[pic]
TEOREMADE CONVOLUCIÓN:
1)L[pic]
[pic]
L[pic] L[pic] L[pic]
2) L-1[pic] L-1[pic] L-1[pic] [pic][pic][pic]
3) L-1[pic] L-1[pic] L-1 [pic]
[pic][pic]
4) L-1[pic] L-1[pic]L-1[pic]= [pic]
[pic]
5) L-1[pic] L-1[pic] L-1 [pic]
[pic][pic]
[pic][pic]
[pic][pic]
[pic][pic]
ECUACIONES DIFERENCIALES CON CONDICIONES INICIALES (TRANSFORMADA):
1) [pic][pic]
[pic]L[pic][pic]
[pic]
[pic]L-1 [pic]L-1 [pic]
2) [pic][pic]
[pic]L[pic]
[pic]
[pic]L-1 [pic]L-1 [pic]L-1 [pic]
3) [pic][pic], [pic]
[pic]L[pic]
[pic]
[pic]L-1 [pic]
4) [pic][pic], [pic]
[pic]L [pic]
[pic]
[pic]L-1 [pic]L-1 [pic]
[pic]
5) [pic][pic], [pic], [pic]
[pic]L[pic]
[pic]
[pic], [pic]y [pic]
[pic]L-1[pic] L-1[pic] L-1[pic]L-1[pic]L-1 [pic][pic]
6) [pic][pic], [pic], [pic], [pic]
[pic]
[pic]L-1[pic]
ECUACIONES INTEGRALES:
1) [pic]
L[pic]+ L[pic] L[pic]
[pic][pic][pic]L-1[pic]
2) [pic]
[pic]
[pic]
[pic]L-1[pic] L-1[pic]
3) [pic]
[pic]
[pic]
[pic]L-1[pic] L-1[pic] L-1[pic] L-1[pic] L1[pic]
ECUACIONES INTEGRODIFERENCIALES:
1) [pic][pic]
[pic]
[pic]L-1 [pic]
2)...
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