 Welcome back MechanicalEI. Did you know that partial differential equations can be used to describe a variety of phenomenon such as heat, fluid dynamics, sound, etc. This makes us wonder, what are partial differential equations? Before we jump in, check the previous part of this series to learn about what Passwell's identities are. Now, a differential equation involving partial derivatives of one or more dependent variables with more than one independent variable is called a partial differential equation. The order of the highest derivative term in the equation is called the order of the PDE. Above equations are all of the second order. It is also a common practice to use subscript notation in writing partial differential equations. For example, the Laplace equation in 3-dimension space, dow squared u upon dow x squared plus dow squared u upon dow y squared plus dow squared u upon dow z squared equals to 0, can be written as uxx plus uyy plus uzz equals to 0. First method to find a solution for PDEs is the Bender-Schmidt explicit method. Consider a general equation of the form, dow u upon dow t equals to alpha squared into dow squared u upon dow x squared. The explicit formula is given by the following equation, where lambda equals to k upon ah squared. The explicit formula is only valid for values of 0 less than lambda less than or equal to 1 by 2. If lambda is 1 by 2, then the explicit formula is reduced to ui comma j plus 1 equals to 1 by 2 into ui plus 1 comma j plus lambda into ui minus 1 comma j. This formula is called Bender-Schmidt formula. The values of i and j are then filled in a table to present the solution. Hence, we first saw what partial differential equations are and then went on to see how numerical solutions of PDE are obtained using Bender-Schmidt explicit method. 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 Crank Nicholson method is.