Laplace of every function does not exist in general. So the question arises when does Laplace of a given function exist? What condition one should put on the function so that definitely the Laplace will exist. We will see that if a function is piecewise continuous and it is of exponential order then Laplace of such a function always exists. We will see a short and nice proof of this theorem. We will also see that converse of this theorem is not true. That means if a Laplace of given function exists then the function needs not satisfy both or either of the above 2 conditions. Thus existence theorem of Laplace talks about the sufficient condition for Laplace to exist and not a necessary condition. ======================================= Links for previous lectures: =================== Counter example to Existence Theorem: 1/root(t) https://www.youtube.com/watch?v=IYnREgjNQO4 ====================================== What are Laplace transforms: https://www.youtube.com/watch?v=Xd_vZzm0AqQ ===================================== Examples on Laplace Transforms: https://www.youtube.com/watch?v=pnSBNpSN030 ====================================== Exponential growth : Concept and Examples: https://www.youtube.com/watch?v=FgqiP4eQ7lo ====================================== First Shifting Theorem: https://www.youtube.com/watch?v=XvHg53VAILM