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Original post by Zacken
It's a bit late here, so maybe not four paragraphs, but basically what Laplace transforms do is, you feed it some sort of differential equation or system of differential equations in a variable tt and it transforms these into some other space where the variable you work with is ss, you then solve this in the ss-plane so to speak, because it's much easier to solve things in the ss-plane (sometimes) and then you convert it back to the tt-plane. So it's sorta like integration substitutions in the sense, you substitute something (laplace transform), the integration is easy (solving the problem in terms of s), you integrate it in the new variable (s plane) and then transform it back to the t-plane (back-sub) where the brackets are used for the analogous action.

A good way of explaining this in a "analogy" way is:



But I'm afraid that the above only tends to make sense once you've studied a teensy bit about Laplace transform and know how to do the mechanics behind them, the above then explains in a certain fashion why the mechanics works the way it does and what motivates it.

If you're interested in this sorta stuff, there is an excellent introductory lecture here which has garnered international acclaim. :-)


Ah, so a bit like the modular and elliptic curves thingy, thanks fam, will get started on the videos when I'm free


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Original post by drandy76
Ah, so a bit like the modular and elliptic curves thingy, thanks fam, will get started on the videos when I'm free


I'm afraid I know very little about the modular/elliptic bleh stuff, but it does ring a bell, so I think you're right. :lol:

Cheers fam
Original post by Zacken
I'm afraid I know very little about the modular/elliptic bleh stuff, but it does ring a bell, so I think you're right. :lol:

Cheers fam


Lol I vaguely remember it from reading fermats last theorem, something about each modular equation has an elliptic form, would love to read into it but sadly I've got exams and Game of thrones keeping me busy


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Original post by drandy76
Lol I vaguely remember it from reading fermats last theorem, something about each modular equation has an elliptic form, would love to read into it but sadly I've got exams and Game of thrones keeping me busy


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Preach
Original post by Zacken

If you're interested in this sorta stuff, there is an excellent introductory lecture here which has garnered international acclaim. :-)


MIT OCW is really good, isn't it? Do you often watch the lectures on there? I used to watch it, done the whole single-variable, a bit of multi variable calculus and some of Walter Lewin's wonderful lectures on Physics. I am definitely going to get back to watching them after exam time. So much exciting math to do after exams!



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Original post by Insight314
MIT OCW is really good, isn't it? Do you often watch the lectures on there? I used to watch it, done the whole single-variable, a bit of multi variable calculus and some of Walter Lewin's wonderful lectures on Physics. I am definitely going to get back to watching them after exam time. So much exciting math to do after exams!


I watched one or two but quickly grew agitated and moved on to other things, it's an excellent resource though and I do plan on getting used to it (I find it hard to sit down and focus for an hour on a lecture) and learn some stuff after exams.
Original post by Zacken
I watched one or two but quickly grew agitated and moved on to other things, it's an excellent resource though and I do plan on getting used to it (I find it hard to sit down and focus for an hour on a lecture) and learn some stuff after exams.


I used to watch the lectures during breakfast, lunch, dinner - when I can't do math and eat at the same time. Started during the summer and stopped a bit before the interview period, I think I stopped watching them because each lecture is about one hour and my schedule didn't allow it.


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Original post by Insight314
I used to watch the lectures during breakfast, lunch, dinner - when I can't do math and eat at the same time. Started during the summer and stopped a bit before the interview period, I think I stopped watching them because each lecture is about one hour and my schedule didn't allow it.


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Just realised I have a playlist saved on linear algebra by them, some 40 hours or so to get through, summer will be crathy


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Original post by drandy76
Lol I vaguely remember it from reading fermats last theorem, something about each modular equation has an elliptic form, would love to read into it but sadly I've got exams and Game of thrones keeping me busy


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C'mon, at least get them the right way round XD
@IrrationalRoot @Insight314 can u give me a hint for the first part of Q4 2010 S3 ?

what exactly does f1(y)f^-1 (y) mean ?
(edited 7 years ago)
Original post by Duke Glacia
@IrrationalRoot @Insight314 can u give me a hint for the first part of Q4 2010 S3 ?

what exactly does f1(y)f^-1 (y) mean ?


Are you sure you referenced the right question? I don't see any f1(y)f^{-1}(y).
Original post by IrrationalRoot
C'mon, at least get them the right way round XD


I'm finished on this platform, only thing left for me to do is drop out and get started on a hair and beauty course at my local college


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Original post by EricPiphany
Are you sure you referenced the right question? I don't see any f1(y)f^{-1}(y).


soz 2011 sIII
Original post by Glavien
In the step solutions for question 7 of 1,2011, how do they get from the second to last line to the last line of part (i)? It's when they are showing the value of kT for large alpha.


Use directly their hint at the start of lnx= whatever and it leads straight to the answer. You don't need to justify your approximations of lnx since they said use this fact at the start, all you need to do is see if conditions of 1/alpha and x match up.


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Original post by Duke Glacia
soz 2011 sIII


yy is a dummy variable, if that helps. f1f^{-1} is the inverse as you know it.
Original post by Duke Glacia
soz 2011 sIII


STEP III 2011 timed mock is in a few days. Sorry m8.


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Original post by Duke Glacia
soz 2011 sIII


Hint, if you still need one, it's hard to find a hint that won't give the idea away.

Spoiler

Original post by EricPiphany
Hint, if you still need one, it's hard to find a hint that won't give the idea away.

Spoiler


Spoiler

Original post by EricPiphany
Hint, if you still need one, it's hard to find a hint that won't give the idea away.

Spoiler


Thnx !
For q 2 STEP II 2009, for the last part I used the 2nd 3rd and 4th turning points instead 1st 2nd 3rd hence my area calculated is almost the same, but the log term is different. How many marks would I lose for this?

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