# Laplace transform of function with independent variables OTHER than time

1. May 25, 2010

### TooFastTim

Hi all

Conventionally we used to seeing the Laplace transform applied to problems that use time as the independent variable, can anybody point me at some examples that do not use time as the independent variable?

Thanks

Tim

2. May 25, 2010

### HallsofIvy

I'm not sure what you mean. A Laplace transform is a MATHEMATICAL operator. It doesn't matter whether you interpret the variable as time or any other physical quantity.

3. May 25, 2010

### TooFastTim

Yeah, but most (the vast majority) of the literature uses time as the independent variable. I was looking for examples that do not.

4. May 25, 2010

### TooFastTim

P.S. bit of a bugger Googling "laplace transform -time" :)

5. May 25, 2010

### Cyosis

Sure grab your examples in which t is the independent variable. Now rename t with any other letter you like, although I recommend against calling it s, which would be confusing. Now you have plenty of examples where the independent variable is not time.

6. May 26, 2010

### Redbelly98

Staff Emeritus
I think the OP is looking at this from an applied standpoint. As used in electrical engineering or control systems engineering, the Laplace Transform is always(?) applied to time-dependent signals.

What real-world (i.e. engineering) problems employ Laplace Transforms where time is not the dependent variable?

7. May 26, 2010

### TooFastTim

Correct, I was thinking of an application analogous to the original application of the fourier seies which was (I'm open to correction here) heat transfer along a beam, so the independent variable in that case would have been length along the beam. I'm sure somebody has used the Laplace transform for applications other than time dependent ones.

Actually you guys have already been a help. Thanks.