6.1 Laplace Transform

Definition

• We need to know what piecewise continous is.

  • its a function that has a finite amount of breaks (sub functions like picewise) and doesnt have any where that explodes to infinity

• Laplace Transform

  • Suppose that $f(t)$ is a piecewise continous function then the laplace transforrm is

    • $\mathcal{L}(f(t))={\int }_0^{\infty }{e}^{-st}f(t)dt$
      • What this definition doesnt tell us is that the laplace transform is actually a new varible function of s