Im Back (I think)

26 Jul 2016

For the past 5 months I've been taking a break from electronics and revisiting my roots in mathematics. In particular, Ive been studying differential equations starting from my undergrad level to as much information as I can find. I know computers can solve many of these DEs, but Ive been learning how to solve each type by hand.

I've known DEs for 15 years, but never really went in depth like I wanted. The numerical methods in particular are of great interest.

Interestingly, MIT now puts many classes online. So any of us can attend MIT as if sitting in the classroom.

One thing to note, just watching the videos doesnt do much, you MUST also do the homeworks they provide to prove you know the material.

Of course a good test of understanding is to try to interpret the theory of relativity, which is a set of DEs.

I still need to do my review for my Pi3. it didnt work at first but I got it up and running, will know that out next week!

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dubbie over 4 years ago

Are you going to give us some interesting examples? (with workings out obviously)

Dubbie
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Andrew J over 4 years ago in reply to dubbie

Here we go Dubbie. Not exactly a differential equation but this is the Standard Model Lagrangian which describes the dynamics of every particle and their interaction. I solved it for W only to find that, as we all knew in our hearts, money will never grow on trees. Shame.

Also not differential bu I find the following quite interesting:
1-1+1-1+1-1+1...infinity = 0. or 1. or 1/2. Take your pick
1+2+3+4+...infinity = -1/12. Because 1-1+1-1+1-1+1.... can equal 1/2

(Ramanujan Summation)
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Fred27 over 4 years ago in reply to Andrew J

Andrew J wrote:
this is the Standard Model Lagrangian which describes the dynamics of every particle and their interaction.
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Andrew J over 4 years ago in reply to Fred27

I caught up with this series a few weeks back. It was pretty good, enjoyed it, although the ending was a little far fetched!!
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dubbie over 4 years ago in reply to Andrew J

Andrew,

I found the first one a bit long for my old brain but I liked the later ones. My favourite equation at the moment is

0 x (infinity) = any number you feel like entering

I went of a weeks course many many years ago now to learn a computer language called Z I think it was. We used it to prove

1 + 1 = 2

Dubbie
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jc2048 over 4 years ago in reply to Andrew J

Rearranging the operators a little

+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1+1+1+1+1...

So now 'infinity' = any integer between 0 and 42, but we don't know which one.

Curiously, the arrangement of the operators specifies what 'infinity' isn't rather than what it is.
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Andrew J over 4 years ago in reply to dubbie

Was Z a notation for proving the logic of a computer program rather than a language in its own right? I might be thinking of something else.
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Andrew J over 4 years ago in reply to dubbie

Was Z a notation for proving the logic of a computer program rather than a language in its own right? I might be thinking of something else.
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dubbie over 4 years ago in reply to Andrew J

Andrew,

I think it was something like that. It was called Z because it was supposed to be the last computer language you would ever need. It was definitely on a computer and it executed, so as much as I can remember, it was a language, but who knows, it was so long ago. I think the idea was to be able to prove that a programme was correct instead of having to test it.

Dubbie
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