4. Laplace Transforms of the Unit Step Function
We saw some of the following properties in the Table of Laplace Transforms.
1. ![]()
2. ![]()
3. Time Displacement Theorem:
If
then
[You can see what the left hand side of this expression means in the section Products Involving Unit Step Functions.]
EXAMPLES
Sketch the following functions and obtain their Laplace transforms:
(a) 
Assume the constants a, b, and A are positive, with a < b.
(b) 
Assume the constants a and b are positive, with a < b.
(c) 
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