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WindowTitle->10. Formal Properties of the Inverse Laplace Transform: Part 1 | \
Laplace Transforms in Theory and Practice
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Cell["\<\
In this chapter, the formal properties of the inverse Laplace transform will \
be discussed. These properties are directly linked to analogous properties of \
the Laplace transform.\
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The following properties will be discussed in detail: linearity, scaling, \
first and second translation. It is noteworthy that these properties have \
significant applications and prove useful in determining inverses for various \
functions.\
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 " property is fundamental to the inverse Laplace transform. It asserts that \
the inverse Laplace transform of the sum of two functions equals the sum of \
the inverse Laplace transforms of those functions:"
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In fact, an even stronger statement holds when functions are multiplied by \
arbitrary constants:\
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In other words, one can \[OpenCurlyDoubleQuote]pull out\
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It should be obvious that linearity can be extended to sums involving more \
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The linearity property plays a central role in inverting functions that are \
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In the previous chapter, inverse Laplace transforms for certain functions \
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The following example illustrates an application of the linearity property.\
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Here, the Laplace transform\[CloseCurlyQuote]s first translation property has \
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The inverse Laplace transform has many properties with simple applications.\
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Here, the following inverse Laplace transforms have been used:\
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