I have just started learning about the Laplace transform, and our professor said that it transforms a function on the time domain to a function on the frequency domain.
The definition we had is the following
$$\mathcal{L} \{ f(t) \}=F(s)= \int_{0}^\infty f(t)e^{-st}dt$$ where $s$ is a real number.
I understand how $s=\sigma+i\omega$ could represent complex frequency, where $\omega$ is the angular frequency and $\sigma$ represents exponential decay or growth.
But if we limit $s$ to be only a real variable, then what does it mean for the Laplace operator to transform a function from time domain to frequency domain?