Programmed tutorial: Inverse Laplace Transform Example 1a

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Find the inverse Laplace transform of
Inverse Laplace transform problem with linear denominators

How do we go about finding entries in the Table of Laplace Transforms?

For each term, we compare its denominator with those in the table.

For the

term, which entry in the table matches the denominator?

#1.

Does the numerator match?

No.

How can we fix it?

We can factor the 3.

Rewrite this term with that factoring.

It becomes

Find the inverse Laplace transform for this term.

We get ℒ

For the

, which entry in the table matches the denominator?

#2.

Does the numerator match?

Yes.

What will be the algebraic sign of the exponent in the inverse Laplace transform?

Positive.

Find the inverse Laplace transform for this term.

We get ℒ

For the

term, which entry in the table matches the denominator?

#2.

Does the numerator match?

No.

How can we fix it?

We can factor the -7.

Rewrite this term with that factoring.

It becomes

What will be the algebraic sign of the exponent in the inverse Laplace transform?

Positive.

Find the inverse Laplace transform for this term.

We get ℒ

We have found the inverse Laplace transform of each term of the original problem. How do we find the solution to that problem?

We add the result we got for each term.

Do that.

ℒ

The end. If you found this helpful and would recommend that I create more pages like this one, please let me know: Email to John Taylor