In this lesson, the instructor explains how to use Laplace Transform to solve ODEs with discontinuous inputs. He introduces the unit step function and the unit box function, which handle jump discontinuities in functions very nicely. He then goes on to calculate the Laplace transform of the unit step function, which leads to a discussion of the inverse Laplace transform and the uniqueness of the solution. Finally, he derives a translation formula for the Laplace transform of a function, which is useful in solving differential equations.
Using Laplace Transform to Solve ODEs with Discontinuous Inputs -- Lecture 22. The last lecture using the Laplace Transform to solve ODEs.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms