What's everyone up to right now?

[Alex K]

Done torturig students with wind turbines...

[Alex K]

the mathematics of, that is

[Silver]

Drinking tomato juice for breakfast.

[Crossless2.0]

Recovering from arguing with Trumpsters online. Fucking Christ, I thought arguing with Evangelicals was pointless, but these people take 'stupid' and 'delusional' to a new level.

[Longhorn]

Done torturig students with wind turbines...

should we call someone?

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the mathematics of, that is

Oooh. Well that's still pretty brutal

[Kernel Sohcahtoa]

I'm working out how to derive the spherically symmetric solutions u(x1,...,xn) of Laplace's equation in n dimensional space.  In particular, the problem asks the reader to derive the equation for n=2 and n>2 (the book showed how to derive the equation for n=3, specifically for u(x,y,z)=f ( r ), where r= sqrt(x^2+y^2+z^2)).

So, what does it look like?

Here are my notes.  I'll post them in hide tags.  Also, I have a habit of taking detailed notes, so that if I pick up these notes months later, then I'll be able to get back into the groove of things without excessively scratching my head and wondering how I came to a particular result and/or results.



Introduction

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Pics 1-3: Deriving a spherically symmetric solution to Laplace's equation when n=2

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Pics 4&5: Intermission notes: Explanation/clarification of notes for deriving a solution for n>2

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Pics 6&7: Deriving a Spherically symmetric solution to Laplace's equation for n>2

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P.S. For anyone who's interested, here's a link to the actual album, which enlarges the photos a bit more; they are also clearer.

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Imgur

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[Alex K]

...

Amusing how the general solution seems to break when setting n=2, while your special solution shows that it's a log.

I got a teaser question for you (to which I know the answer bc. I encountered such problems in my work): can you nevertheless extract the seemingly special n=2 solution from your general solution using a (dirty and somewhat magical) trick?

[TheRealJoeFish]

You'll all be very proud of me - I am representing Satan in a lawsuit, sort of.

This guy sued one of my firm's clients, a mental hospital (which he was in), and, in addition to himself, named "The Body of Christ" as a Plaintiff. In addition to my client, he named "Satan" as a Defendant. Inasmuch as Satan doesn't seem inclined to appear in court, I may need to make arguments on his behalf.

There is a famous Pennsylvania case in which Satan was dismissed as a Defendant because, among other reasons, the Court wasn't sure how to serve legal papers upon him.

[Joods]

Halfway through canning 27 pounds of homemade pasta sauce.

[BrokenQuill92]

I baked mom a cheesecake for Mother's Day