Lecture 7 Laplace Transform basics

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Lecture 7Laplace Transform basics

• DOC and poles.
• Properties of the Laplace transform
• Initial and Final Value Theorems.

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Table of Basic Laplace Transforms
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Example ramp function
t
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DOC and poles.
DOC of the (one-sided) Laplace transform to the
right of the right-most pole (the one with
greatest real part).
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Properties of the Laplace Transform
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Another example
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Properties of the Laplace Transform
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Initial and Final Value Theorems
REMARKS

• Relates limiting values of a function and its
  transform. Can be used to get time-domain
  information from the Laplace transform.
• Opposite limits in t and in s. Here we take s to
  be real-valued.
• SOME RESTRICTIONS APPLY! Precise statements and
  proofs given below.

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Final Value Theorem Precise Statement
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Final Value Theorem Proof
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Initial Value Theorem Precise Statement
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Initial Value Theorem Proof