TRANSFORMADA DE LAPLACE.

...

[pic 161]

[pic 162]

[pic 163]

- Hallar la transformada de la derivada para hallar [pic 164]

[pic 165]

[pic 166][pic 167][pic 168]

[pic 169]

[pic 170]

[pic 171]

[pic 172]

[pic 173]

- Hallar la transformada de la derivada para hallar [pic 174]

[pic 175][pic 176][pic 177]

[pic 178]

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[pic 181]

TRANSFORMADA DE LA INTEGRAL

[pic 182]

- Demostrar [pic 183]

[pic 184]

[pic 185]

[pic 186]

[pic 187]

[pic 188]

[pic 189]

[pic 190]

[pic 191]

[pic 192]

- Hallar f(t), usando la transformada de la integral:

- [pic 193]

[pic 194]

[pic 195]

[pic 196]

[pic 197]

[pic 198]

[pic 199]

[pic 200]

- [pic 201]

[pic 202]

[pic 203]

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[pic 206]

[pic 207]

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- [pic 209]

[pic 210]

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APLICACIONES (ECUACIONES DIFERENCIALES)

- Resolver: [pic 216]

[pic 217]

[pic 218]

[pic 219]

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[pic 222]

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- [pic 225]

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DERIVADA DE LA TRANSFORMADA

[pic 237]

Donde: [pic 238]

Para [pic 239]

[pic 240]

F(s)= [pic 241]

[pic 242]

[pic 243]

Para [pic 244]

[pic 245]

[pic 246]

[pic 247]

Ejemplos

- [pic 248]

[pic 249]

[pic 250]

[pic 251]

[pic 252]

[pic 253]

- [pic 254]

[pic 255]

[pic 256]

[pic 257]

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[pic 259]

INTEGRAL DE LA TRANSFORMADA

[pic 260]

- Demostración

[pic 261]

[pic 262]

[pic 263]

[pic 264]

Ejemplos:

- Hallar:[pic 265]

[pic 266]

[pic 267]

; [pic 268][pic 269]

[pic 270]

- Hallar:[pic 271]

[pic 272]

[pic 273]

[pic 274]

[pic 275]

[pic 276]

[pic 277]

- Hallar:[pic 278]

[pic 279]