Use of Laplace Transform to solve linear differential equations.

Description
How can Laplace Transform fail to exist, is explained in this video tutorial. How Laplace Transform are used to solve linear differential equations with constant coefficient, is also discussed. The delta function is defined. The region of convergence of the delta signal is the entire complex plane. The use of Laplace transform in solving initial value problems are shown. Laplace transform is a good way to find unit impulse responses.Unit impulse response is equal to the weight function. Inverse transform is discussed.
Prof. Arthur Mattuck, Maths, 18.03.Differential Equations, Spring 2010: 19: Derivative Formulas: Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed November 9, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc