Yeah, but most (the vast majority) of the literature uses time as the independent variable. I was looking for examples that do not.
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?
A Laplace transform is a mathematical operation that transforms a function from the time domain to the frequency domain. It is often used in engineering and physics to analyze systems with time-dependent inputs and outputs.
In a Laplace transform, the independent variable is typically time. However, it is possible to perform a Laplace transform on a function with other independent variables, such as space or temperature.
A Laplace transform is similar to a Fourier transform, but it also takes into account the decay of a function over time. This makes it more useful for analyzing systems that have transient behavior, such as electrical circuits or mechanical systems.
A Laplace transform is calculated by integrating the function multiplied by an exponential function e^(-st), where s is a complex number. The result is a new function in the frequency domain, with s representing the frequency variable.
Laplace transforms have many applications in engineering, physics, and mathematics. They are commonly used to solve differential equations, analyze system dynamics, and study the stability of systems. They are also used in signal processing, control theory, and circuit analysis.