Laplace transform of function with independent variables OTHER than time

Click For Summary
The discussion focuses on the application of the Laplace transform beyond time as the independent variable. Participants clarify that while the Laplace transform is typically associated with time-dependent signals, it can be applied to other variables by simply renaming the independent variable. There is a specific interest in real-world engineering problems, such as heat transfer along a beam, where the independent variable could be length instead of time. The conversation highlights the challenge of finding literature on this topic, as most resources emphasize time-based applications. Overall, the participants acknowledge the versatility of the Laplace transform in various contexts.
TooFastTim
Messages
12
Reaction score
0
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
 
Physics news on Phys.org
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.
 
Yeah, but most (the vast majority) of the literature uses time as the independent variable. I was looking for examples that do not.
 
P.S. bit of a bugger Googling "laplace transform -time" :)
 
Yeah, but most (the vast majority) of the literature uses time as the independent variable. I was looking for examples that do not.

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.
 
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?
 
Redbelly98 said:
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?

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.
 

Similar threads

Undergrad Solving a differential equation using Laplace transform
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad PDEs: Laplace's Equation over a Parallelogram
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad On Laplace transform of derivative
  • · Replies 17 ·
Replies
17
Views
3K
Laplace transform vs phasor analysis in circuit analysis
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Laplace Transform of Sign() or sgn() functions
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad On a bijective Laplace transform
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Solution of delayed forcing function
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Transforming a PDE with Laplace method
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Inverse Laplace transform of a piecewise defined function
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad How did the author transform the original equation into the Legendre equation?
  • · Replies 4 ·
Replies
4
Views
2K