4. Laplace Transforms of the Unit Step Function

We saw some of the following properties in the Table of Laplace Transforms.

1. MATH

2. MATH

3. Time Displacement Theorem:

If MATH then

MATH

[You can see what the left hand side of this expression means in the section Products Involving Unit Step Functions.]

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EXAMPLES

Sketch the following functions and obtain their Laplace transforms:

(a) MATH

Assume the constants a, b, and A are positive, with a < b.

(b) MATH

Assume the constants a and b are positive, with a < b.

(c) MATH

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