In this video I calculate the integral of 1/sqrt(x^2 + y^2) over the ring with inner radius a and outer radius b. It’s nothing fancy, but I think the result is pretty neat!
@@NoNTr1v1aL I love that still, it calls to mind the idea of 'the sand reckoner'; algebra is an accounting tool to 'rectify' the numbers and our errors in estimation. I can see how restore or reunite could translate to balance, if a situation is unfair you balance, rectify, or restore it to fairness. Oftentimes in algebra in a way you are 'reuniting' seemingly different information to come to a common idea. Thanks for the info! I've never studied a language that wasn't based in latin haha
I wonder if we should make an inequality notation for comparing the radii of polar numbers? Or at least the understanding that "this < assumes the left and right are absolute values". An interesting difference to normal comparators is that the identity x
What would the answer look like in the general case where the ring is centered at some arbitrary point and the same initial function is centered at some other point?
could you please do some examples where the circles aren't centered at the origin and when there isn't any nice symmetry that can be abused? lol thanks, great vid!
Um that's because this is kinda an easy problem which is *made* to be completely simplified in the end. Not saying it's not elegant, but it's far from conventional multivariable calc problems.
Hilbert Black, you are completely right, but what i meant is when you try solving some problems with single variable calculus ( if possible ) it gets pretty difficult when you try to solve single variable calc. problems with multivariable calc. it is usually easy
@@AndDiracisHisProphet True, but not exclusively, as in 'free body diagram' for any object. (B.t.w. Is german your mother tongue, or are you just good at languages?)
you pwned me on this one - from the title, I thought the answer about the average value of an annulus was the origin, since it was symmetric around the origin... grrr
6:16 What a beautiful simplicification
Anyone remembered ring of charge from classic E & M?
Your jokes are so great! I make jokes like that all the time (shoulda put a ring on it) lol. I love your personality and your style of teaching :D
very nice. Gives me confidence in multivariable calc :>
This was awesome! I love your videos, Gruss von Deutschland!
*aus Deutschland :-)
If you like Dr Peyam then you should integrate a ring with him
Haha I love your videos! Wish we had teachers like you here in our school in Austria:D
I had a feeling we'd get a Peyam video today! Yaay
commutative algebra kids will understand that double entendre title
Czeckie
Integral domain over a ring R or integral vector field over the ring of polynomials?
take your pick :) but I was thinking about integral element over a ring, which is a generalization of algebraic integer from algebraic number theory.
Wow, I was making a pun on rings, but I did not expect a pun on integrals, wow!!!
Love these calculus problems! :D
math chillax session, that's what i wanted to hear m8
Its so satisfying to see all of the terms cancel out haha its like some perfect algebraic balance!
Did u know? Algebra literally means balance!
^ I had no idea! :O
@@drpeyam wait I'm wrong. It actually means to reunite or restore. I don't remember where I heard balance lol.
@@NoNTr1v1aL I love that still, it calls to mind the idea of 'the sand reckoner'; algebra is an accounting tool to 'rectify' the numbers and our errors in estimation.
I can see how restore or reunite could translate to balance, if a situation is unfair you balance, rectify, or restore it to fairness.
Oftentimes in algebra in a way you are 'reuniting' seemingly different information to come to a common idea.
Thanks for the info! I've never studied a language that wasn't based in latin haha
@@plaustrarius yeah I think the idea of fairness did lead me to think of the word 'balance'.
I wonder if we should make an inequality notation for comparing the radii of polar numbers? Or at least the understanding that "this < assumes the left and right are absolute values". An interesting difference to normal comparators is that the identity x
See my video on comparing complex numbers :)
This man is so happy lol
Fantastic :)
That is amazing lol
Dr. peyam's please make video on convergence of sequence,series and function.I'm little bit confused what is exact means of this.
What would the answer look like in the general case where the ring is centered at some arbitrary point and the same initial function is centered at some other point?
1/sqrt(x^2 + y^2) is centred at (0,0). The ring, a^2
Patrick Salhany I know it gets more complicated, hence my question.
could you please do some examples where the circles aren't centered at the origin and when there isn't any nice symmetry that can be abused? lol thanks, great vid!
i am beginning to realize that, multivariable calculus is easier than normal calculus!
Um that's because this is kinda an easy problem which is *made* to be completely simplified in the end.
Not saying it's not elegant, but it's far from conventional multivariable calc problems.
Hilbert Black, you are completely right, but what i meant is when you try solving some problems with single variable calculus ( if possible ) it gets pretty difficult when you try to solve single variable calc. problems with multivariable calc. it is usually easy
Savage
But what if the ring is not centered around (0,0) ?
You would shift the ring until it’s centered at (0,0)
0:35 -boy- boi, in my first LA class in rthe beginning this confused me soooo hard. Also, what is a "Körper"? Something like a cone?
Körper? I think it’s the German word for Field!
yes. But it is also the german word for 3d geometric shapes.
@@AndDiracisHisProphet ... and also for body (zB in 'Zur Elektrodynamik bewegter Körper')
ja, aber Körper für body ist ja eher im biologischen sinne gesehen, während die Elektrodynamik bewegter Körper eher feste Objekte sind.
@@AndDiracisHisProphet True, but not exclusively, as in 'free body diagram' for any object. (B.t.w. Is german your mother tongue, or are you just good at languages?)
is a disk a filled circle?
@Patrick Salhany locus? i understood the rest, thanks
👌🏻👌🏻👌🏻👌🏻👌🏻
the guy seems high lol
you pwned me on this one - from the title, I thought the answer about the average value of an annulus was the origin, since it was symmetric around the origin... grrr
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I prefer 1/average r
I don't think integrating 1/r is very interesting tbh, maybe something harder?
sqrt(tan(r))
√(1+x³)