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Unformatted text preview: The Laplace transform 1. The denition: L [ f ] = Z f ( t ) est dt. When in doubt, you can always compute something using this denition. 2. The inverse transform: L1 ( Y ) = y L ( y ) = Y . 3. Solving an ODE with constant coecients using Laplace transforms requires Knowing how to transform derivatives Knowing the two shift theorems: (1) L ( eat f ( t )) = F ( s + a ), and (2) L ( u a ( t ) f ( ta )) = eas F ( s ) . Using partial fractions. Knowing how to transform step functions. 4. The unit impulse function and the transfer function. (If we have class on Tuesday) 1...
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 Spring '08
 LERNER
 Differential Equations, Equations

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