Visualization of partial differential equation solutions

PDEs occur in various engineering disciplines. In developing visualization strategies, we considered only problems involving a spatially independent variable x (or in cylindrical coordinates, r) and the temporal variable t, which is also an independent variable. Given that the solutions are functions of two variables - x (or r) and t - the solution's character is difficult for engineering students and practitioners to understand. We've explored several visualization strategies, employing extensive graphics to appeal to the graphical learners among us. Here we present parts of the solutions to three typical engineering problems selected from the 20 we've addressed.