LaplaceTable.pdf - Laplace Transform Table f(t ←→ 1 1 ←→ 2 tn ←→ 3 eat ←→ 4 tn eat ←→ 5 cos bt ←→ 6 sin bt ←→ 7 eat cos bt

# LaplaceTable.pdf - Laplace Transform Table f(t ←→ 1 1...

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Laplace Transform Table f ( t ) ←→ F ( s ) = L { f ( t ) } ( s ) 1. 1 ←→ 1 s 2. t n ←→ n ! s n +1 3. e at ←→ 1 s - a 4. t n e at ←→ n ! ( s - a ) n +1 5. cos bt ←→ s s 2 + b 2 6. sin bt ←→ b s 2 + b 2 7. e at cos bt ←→ s - a ( s - a ) 2 + b 2 8. e at sin bt ←→ b ( s - a ) 2 + b 2 Laplace Transform Principles Notation: F ( s ) = L{ f ( t ) } Linearity L { af ( t ) + bg ( t ) } = a L { f } + b L { g } Input Derivative Principles L { f 0 ( t ) } ( s ) = s L { f ( t ) } - f (0) L { f 00 ( t ) } ( s ) = s 2 L { f ( t ) } - #### You've reached the end of your free preview.

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Unformatted text preview: sf (0)-f (0) First Translation Principle L { e at f ( t ) } = F ( s-a ) Transform Derivative Principle L {-tf ( t ) } ( s ) = d ds F ( s ) The Dilation Principle L { f ( bt ) } ( s ) = 1 b F ( s/b ) ....
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