Laplace transform of e^(3t)

Step by step

The question

Question: find the Laplace transform of e^(3t).

1 The idea

The Laplace transform turns a function of t into a function of s.

It is an integral, but we almost never work it out: we use a table made from it.

The table rows we need.

2 Use the table

Each part by its row: e^(3t) gives 1/(s − 3).

Careful!

e to the at gives s minus a.

Here a is 3, so it is s − 3.

3 Check

Let's check: read the table backwards.

1/(s − 3) comes from e^(3t): the question.

Right!

Let's look back.

First: the idea.

Then: use the table.

Last: check.