Transforms of Derivatives

# Transforms of Derivatives - = Differential Equations Second...

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Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna – Mathematics Department, MIT 172 Lesson 34 Transforms of Derivatives Specific Objectives: At the end of the lesson, the students are expected to: Find the Laplace transforms of the derivatives of functions Let f(t) be a continuous function for t ≥ 0 , then, L )} ( { ) ( t F n = )] 0 ( ... ) 0 ( ' ' ) 0 ( ' ) 0 ( [ )} ( { ) 1 ( 3 2 1 + + + + n n n n n f f s f s f s t f L s = = 1 0 1 ) 0 ( )} ( { n k k n n f s t f L s Ex. 1. Find )} ( ' ' ' { 2 t e f L t e t f 2 ) ( = 1 ) 0 ( = f t e t f 2 2 ) ( ' = 2 2 ) 0 ( ' ) 0 ( 2 = = e f t e t f 2 4 ) ( ' = 4 ) 0 ( ' ' = f Thus, )] 0 ( ' ) 0 ( ' ) 0 ( [ } { )} ( ' ' ' { 2 2 3 2 f sf f s e L s e f L t t + + = ] 4 ) 2 ( ) 1 ( [ ] 2 1 [ 2 3 + + = s s s s 4 2 2 2 3 = s s s s Ex. 2. Find )} (sin ' ' { 2 t f L t t f 2 sin ) ( = 0 ) 0 ( = f t t t t f 2 sin cos sin 2 ) ( ' = = 0 ) 0 ( ' = f Thus, ) 0 ( ' ) 0 ( } {sin ) (sin ' ' { 2 2 2 f sf t L s t f L = 0 ) 0 ( )} 2 cos 1 ( 2 1 { 2 = s t L s } 2 cos 1 { 2 2 t L s

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Unformatted text preview: = Differential Equations Second Quarter SY 0506 ____________________________________________________________________________________________________________ Silva, Alviso and Llacuna – Mathematics Department, MIT 173 [ ] } 2 {cos } 1 { 2 2 t L L s − =       + − = 4 1 2 2 2 s s s s 4 2 2 + = s s Seatwork: Perform the indicated operations: 1. )} sin ( ' ' { wt t f L 2. )} (cos ' ' ' { wt f L Homework: Perform the indicated operations: 1. )} (sin ' ' ' { wt f L 2. )} cos ( ' ' { wt t f L...
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## This note was uploaded on 01/17/2012 for the course MATH 24 taught by Professor Dantesilva during the Spring '11 term at Mapúa Institute of Technology.

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Transforms of Derivatives - = Differential Equations Second...

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