 Welcome back MechanicalEI, did you know that unlike ordinary differential equations which deal with one-dimensional dynamic systems, partial differential equations can solve multi-dimensional dynamic systems? This makes us wonder, what are applications of partial differential equations? Before we jump in, check out the previous part of this series to learn about what Crank Nicholson method is. Now consider the transverse vibrations in an elastic membrane. The membrane subjected to a transverse load perpendicular to the plane of the frame of magnitude Q of x,y, where x,y is a system of Cartesian coordinates in the plane of the unloaded membrane. We are interested in calculating the transverse deflection at w of x,y corresponding to an equilibrium configuration. The transverse vibrations of a tensed membrane are given by solving the PDE equation, wxx plus wyy equals to minus Q upon t plus rho h upon t into wtt, here h is the thickness of the membrane. One another application of PDE was a heat flow equation, which is given by w of x,t upon dow t equals to delta u of x,t, where delta operator equals to summation of dow squared upon dow x squared i from i equals 1 to 3. The heat flow equation was based on Newton's law of cooling. Hence, we saw applications of PDE first in transverse vibrations of an elastic membrane and then in the heat flow equation. 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 two and three-dimensional Laplace equations are.