# Defining Laplace transforms and their complex values

chief10
How to define Laplace transforms and their complex values?

## Homework Statement

the tutorial question asks to compute the Laplace transform of cos(3t) without using linearity theorem

it then asks where the laplace transform is defined in terms of complex values

## Homework Equations

L(f(t))=s/s^2+a^2

## The Attempt at a Solution

now it's been a while since I did Laplace but what I get just from looking at the standard Laplace table is s/[(s^2)+9] obviously, is there something else I'm missing here in terms of linearity or?

I must also confess that i don't recall complex values relating to Laplace other than the fact that 's' is complex in the sense that it gives a+bi for instance. It's not defined just for {R} is it?

any pointers you could give me on this would be just great guys and girls! thanks a lot.

-chief10

Last edited:

## Answers and Replies

chief10
no idea's anyone? :)

chief10
no matter I worked it out

just have to use the integral definition of a Laplace Transform and work out for what values of s does it exist in a limit. Take a limit from 0 to b for instance.

chief10

## Homework Statement

the tutorial question asks to compute the Laplace transform of cos(3t) without using linearity theorem

it then asks where the laplace transform is defined in terms of complex values

## Homework Equations

L(f(t))=s/s^2+a^2

## The Attempt at a Solution

now it's been a while since I did Laplace but what I get just from looking at the standard Laplace table is s/[(s^2)+9] obviously, is there something else I'm missing here in terms of linearity or?

I must also confess that i don't recall complex values relating to Laplace other than the fact that 's' is complex in the sense that it gives a+bi for instance. It's not defined just for {R} is it?

any pointers you could give me on this would be just great guys and girls! thanks a lot.

-chief10

SOLVED

I worked this out. Just have to use the integral definition of a Laplace Transform and work out for what values of s does it exist in a limit. Take a limit from 0 to b for instance and solve the integral and sub in the nodes. To double check your answer, quickly solve the f(t) using your standard laplace table, make sure your integral solved answer is the same and works with your applied limits.

For anyone that's interested :)