I finished a partial differential equations course last semester and I feel like I got through by just memorizing the algorithms to solving each PDE in different scenarios. how could I interpret the solution to this IBVP?
I still remember how to solve these, by making our solution "guess". the solution is
is this solution supposed to represent how heat is distributed across plate and how it evolves with time? and that since it's a negative exponential sine wave, it's very strong at the center and gets very cool as we go towards the edges of the plate? and how as we expand the summation, we see which terms make greater contributions to the heat distribution?
am i looking at this right? if so, how would this solution help me solve real world problems? does this tell me where the best place is to add insulation on a plate or something?
thank you for reading.