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 5 years ago

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

Dubbie
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Andrew J over 5 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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dubbie over 5 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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jc2048 over 5 years ago in reply to Andrew J

42 was a nod to a radio programme, from years ago, scripted by someone called Adams.

I misunderstood your post and thought you were saying 'infinity =' rather than '(the sum to) infinity ='. My fault for reading Dubbie's post straight after yours and merging the two ideas in my head.
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Andrew J over 5 years ago in reply to jc2048

It read like you were being serious and my maths being what it is....
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jc2048 over 5 years ago in reply to Andrew J

I'm useless at maths, so don't take too much notice of what I say, but I think there might be a serious point there. Addition and subtraction are commutative, so in an infinite series it's valid to rearrange the operators. It shouldn't make any difference to the final sum, yet I've just increased the possibilities from either 0 or 1 to any integer between 0 and 42. Although not very rigorous, isn't that a proof by absurdity that you're doing something wrong [trying to take the limit of a series that doesn't converge]?
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Andrew J over 5 years ago in reply to jc2048

Well, yes, that's the Ramanajan Summation. Or rather Cesàro Summations which don't converge. But it's still amusing even when you know that there is some mathematical trickery going on.
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Andrew J over 5 years ago in reply to jc2048

Well, yes, that's the Ramanajan Summation. Or rather Cesàro Summations which don't converge. But it's still amusing even when you know that there is some mathematical trickery going on.
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