Transformada de lapalace

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  • Publicado : 24 de febrero de 2010
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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)...
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