6.1 Laplace Transform

Definition

• We need to know what piecewise continuous is.

  • it’s a function that has a finite amount of breaks (sub functions like piecewise) and doesn’t have any where that explodes to infinity

• Laplace Transform

  • Suppose that $f(t)$ is a piecewise continuous function then the laplace transform is

    • $\mathcal{L}(f(t))={\int }_0^{\infty }{e}^{-st}f(t)dt$
      • What this definition doesn’t tell us is that the laplace transform is actually a new variable function of s