Differential Equations, Lecture 5.2: Properties & applications of the Laplace transform

Differential Equations, Lecture 5.2: Properties & Applications of the Laplace transform

In this lecture, we learn about two key properties of Laplace transforms: (i) they are linear, and (ii) they "turn derivatives into multiplication." We also see some formulas about how to quickly compute the Laplace transform of a function times an exponential or a polynomial. Next, we solve a differential equation using Laplace transforms, which requires the notion of an inverse Laplace transform. This can involve familiar techniques such as partial fraction decomposition, or completing the square. Finally, we observe the similarities between solving ODEs "the old way" vs. with Laplace transforms, and write the general solution as the sum of the "state-free solution" and the "input-free solution."

[Peter_]

You are saving my life at the moment here, man.
I study a course called "Linear Analysis" here in Sweden right now and that course is heavily focused on stuff like Fourier Series, Fourier Transforms and Laplace Transforms..