NOTES FOR CALC III SHAUMS OUTLINE

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NOTES FOR CALC IIISHAUMS OUTLINE

• CHAPTER 14 PART 3
• Finding the Laplace Transform for Basic Functions

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PART 1 REVIEW THEORY
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The Laplace Transform
Notice that the result is a function of s only
Notation
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DETOUR The Existence of The Laplace Transform
The Laplace Transform of a function exists if it
is of exponential order. That is if there is a
number a so that
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The Laplace Transform of a Sum
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The Laplace Transform of cf(t)
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The Laplace Transform of eat
(This is example 1 of finding a Laplace Transform)
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The Laplace Transform of eat
If s gt a
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The Laplace Transform of 1
In fact, if a 0
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EXAMPLE 4 Find L5x2 4
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EXAMPLE 4 Find L5x2 4
L5x2 4 L5x2 L4
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EXAMPLE 4 Find L5x2 4
L5x2 4 L5x2 L4
5Lx2 4L1
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EXAMPLE 4 Find L5x2 4
L5x2 4 L5x2 L4
5Lx2 4L1
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EXAMPLE 5 Find Lcos 5x
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EXAMPLE 5 Find Lcos 5t
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EXAMPLE 5 Find Lcos 5t
From the table of integrals
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EXAMPLE 5 Find Lcos 5t
From the table of integrals 99 of the inside
back cover of Stewart
The values at 8 are zero because each of the
functions are of exponential order.
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EXAMPLE 5 Find Lcos 5t
The values at 8 are zero because each of the
functions are of exponential order.
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EXAMPLE 5 Find Lcos 5t
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END CHAPTER 14 PART 3