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Laplace transform shift theorem
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Analysis
Integral transform
Laplace transform
Created
2026-09-24
Updated
2026-10-03
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For
a
≥
0
,
L
{
f
(
t
−
a
)
H
(
t
−
a
)}
(
s
)
=
e
−
a
s
L
{
f
}
(
s
)
.
Table of contents
Laplace transform time-shift rule
Laplace transform shift theorem
Heaviside step function
Laplace transform shift theorem
Laplace transform time-shift rule
0
0
0
Laplace transform shift theorem
The delayed unit step has
L
{
H
(
t
−
t
0
)}
(
s
)
=
s
e
−
s
t
0
,
Re
s
>
0.
(1)
Heaviside step function
(
H
)
0
2
0
Laplace transform shift theorem
The Heaviside
function
is zero before its switching
time
and one after it, allowing delayed
signals
to be written algebraically.
Ancestors
(6)
Laplace transform
Integral transform
Analysis
Area of mathematics
Mathematics
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Incoming links
(1)
Past exam of the mathematics course of the University of Cambridge
/
2007
/
ib
/
Paper 4
/
15F
/
i
/
Solution
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