 Welcome back Mechanical AI. Did you know that direct delta functions are suited to functions that exert a large force over a small time frame, like a hammer striking an object or a shot in an electrical system? This makes us wonder, what is direct delta function? Before we jump in, check out the previous part of the series to learn about what Heaviside Unit Step function is. Now, in the above examples, we saw that the large force or voltage could be exerted on the system over a very short time frame. The direct delta function is used to deal with these kinds of forcing functions, simply because Heaviside Unit functions cannot handle these kinds of large functions. Direct delta function can be seen as the first derivative of Heaviside Unit functions as speed is for distance. An important property of direct delta function is del of t minus a equals 0, where t is not equal to a. At t equals a, direct function is sometimes thought to of as having infinite value. So, Laplace transform of del of t minus a is given by integral of e power minus st into del of t minus adt from 0 to infinity equal to e power minus as, provided a is greater than 0. Periodic functions as the name suggests are those functions which repeat after time t. That means a function f of t is said to be a periodic function, if f of t plus capital t is equal to f of t and t for all t greater than equal to 0. The Laplace transform of f of t is given by integral of f of t e power minus st dt from 0 to capital t upon 1 minus e power minus s into capital t. Hence, we first saw what direct delta function is and then went on to see what periodic functions and their Laplace transforms are. So, like, subscribe and comment with your feedback to help us make better videos. Thanks for watching. Also, thanks a lot for those constructive comments. You helped the channel grow. So, here are the top Mechanical EIs of our last videos. In the next episode of Mechanical EI, find out what inverse Laplace transforms are.