# CHAPTER VI - 4 Laplace Transforms TOPIC 4 LAPLACE...

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1 4 Laplace Transforms TOPIC 4 LAPLACE TRANSFORMS 4.1 Definition of the Laplace transform 4.2 Properties of the Laplace transform - Linearity - First shift Theorem 4.3 Laplace transform of derivatives 4.4 Inverse Laplace transform 4.5 Using partial fractions to find the inverse Laplace transform 4.6 Solving linear constant coefficient differential equations using the Laplace transform 4.7 Sample problems related to engineering applications using Laplace transforms: 4.1 Definition of the Laplace transform L 0 ) ( ) ( )} ( { dt e t f s F t f st 0 s Example 1 Find the Laplace transform of 1 ) ( t f Solution Example 2 Find the Laplace transform of t . Solution

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2 4 Laplace Transforms Example 3 Find the Laplace transform of . at e Solution 4.2 Properties of the Laplace transform 4.2.1 Linearity L )} ( ) ( { t g t f L )} ( { t f L ) ( ) ( )} ( ( s G s F t g Example 4 Find the Laplace transform of (a) t e t 2 sin 6 7 3 3 (b) t t 3 cos 5 2 Solution (a) (b) 4.2.2 First shift theorem If L ), ( )} ( { s F t f then L ) ( )} ( { a s F t f e at Example 5
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• Spring '13
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