The title basically says it all. For a mere three marks (out of 50) in our take home test, we've been asked to Laplace's Equation in spherical coordinates. As you can see from that post it's a mission. I basically gave up around half an hour ago. It seems that I made a mistake when I was inverting the Jacobian (2 pages of working), which is a slightly different way from the linked article, but that's how we've been asked to do it. Tomorrow I suppose I'll go through it and find my error, which will be tedious. I did get maple to do it for me, so I know what I should get, and I was pretty close, but it appears I messed up one column.
The frustrating part is that even when I've inverted the matrix, I still need to do the ridiculous substitutions you see near the bottom of that page. I won't do them all at once like that, I'll be a bit smarter, but still, it's going to be tedious.
The thing that's really annoying is not that this is particularly hard - it isn't, it's just tedious and a huge amount of work. I won't be surprised if this question goes to 4+ pages. And it's not the kind of work you have to do by hand any. That's why people developed computer algebra systems, why we rely on the work of people who have gone before us, so we don't have to sit there doing tedious calculations. However, I do understand the point, so I'll strive to do it well, plus I want a good mark in this paper, and the test is worth 20% so it is fairly important. Maths Away!
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