Potential Flow and Method of Images with

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  • Опубліковано 1 жов 2024

КОМЕНТАРІ • 285

  • @TomRocksMaths
    @TomRocksMaths  3 роки тому +55

    Grant also taught me something - check out the 'Power Tower' video here: ua-cam.com/video/dnZ3xlif9VA/v-deo.html

    • @leif1075
      @leif1075 3 роки тому

      What does z represent at 6:15..you didnt say

    • @jaredjones6570
      @jaredjones6570 3 роки тому

      @@leif1075 z is a complex-valued number - z = x+iy. Think of this as the "coordinate" of the complex plane.

  • @PapaFlammy69
    @PapaFlammy69 3 роки тому +217

    :v

  • @danielkron2513
    @danielkron2513 3 роки тому +226

    Ah, yes, two sexiest mathematicians in one video

    • @LeoStaley
      @LeoStaley 3 роки тому +14

      Grant is so attractive he is the only man who could seduce me.

    • @davidgjam7600
      @davidgjam7600 3 роки тому +16

      I'm glad this is the first comment, cause I wanted them to kiss from the moment I looked at the thumbnail

    • @joshuajoshua46
      @joshuajoshua46 3 роки тому +9

      BONK

    • @Arbmosal
      @Arbmosal 3 роки тому +1

      you must be unaware of Ed Frenkel :D

    • @klutchboi3266
      @klutchboi3266 3 роки тому

      @@davidgjam7600 👀

  • @Nick08352
    @Nick08352 3 роки тому +148

    im taking a break from learning maths with a maths Video, weird isn´t it ^^

    • @dee8163
      @dee8163 3 роки тому +21

      somehow the college experience is just about getting distracted from doing maths by another different kind of maths

    • @zetsubou1108
      @zetsubou1108 3 роки тому +5

      yeah i m watching this video instead of practising for my circuit theory test.

    • @Hi_Brien
      @Hi_Brien 3 роки тому +1

      I have a class in 4 minutes

    • @okhan5087
      @okhan5087 5 місяців тому

      Same!

  • @franteryda4730
    @franteryda4730 3 роки тому +86

    Just in time for my fluid dynamics exam! Haven't seen the video yet but man, this collab is epic

    • @sudheerthunga2155
      @sudheerthunga2155 3 роки тому +1

      Hehe ikr!!

    • @Eyes_On_America
      @Eyes_On_America 3 роки тому +1

      Good luck :D

    • @franteryda4730
      @franteryda4730 3 роки тому +1

      @@aiyopasta lots of maths, not so easy but super interesting!

    • @tapuwachitiga2547
      @tapuwachitiga2547 3 роки тому +2

      I had my exam like 4 weeks ago... We had a question on method of images and it was AWFUL, i just think this video was suggested to mock me

    • @Stream_Function
      @Stream_Function 3 роки тому

      @@aiyopasta depends on your lecturer
      In general it should be easy

  • @IrshaadAdatia
    @IrshaadAdatia 3 роки тому +75

    Oh goodness.... Math bursting at the seems, all we need now is an onlyfans. Hahahahaha.... Kidding not kidding.
    Fluid flow, for sure.

    • @lloydgush
      @lloydgush 3 роки тому +4

      Tom is a good example why there isn't a nobel for math.
      I hope you got the joke.

    • @pappaflammyboi5799
      @pappaflammyboi5799 3 роки тому

      Is the word "seems" intentionally misspelled?

    • @20031bibi
      @20031bibi 3 роки тому

      @@lloydgush not me explain pls lol

    • @lloydgush
      @lloydgush 3 роки тому +2

      @@20031bibi The joke is that nobel didn't made a nobel for math because a mathematician was fucking his wife.
      Tom is heavily flirting with a married man.
      Therefore, a joke.
      But he flirts with everyone, after this christimas season I'd say he had an only fans, but who am I kidding, this is youtube, everyone has an onlyfans.

    • @20031bibi
      @20031bibi 3 роки тому +1

      @@lloydgush LMAOOOOOO

  • @alexwolffe7805
    @alexwolffe7805 3 роки тому +29

    Maths, fluid dynamics, Tom and Grant. Simply amazing.

  • @EpicMathTime
    @EpicMathTime 3 роки тому +18

    Is Grant really huge or is Tom really small? Or am I just bad at understanding camera angles?

    • @LeoStaley
      @LeoStaley 3 роки тому

      Grant is large.

    • @fburton8
      @fburton8 3 роки тому +3

      Why, man, he doth bestride the mathematical world. Like a Colossus.

  • @ashoulle8953
    @ashoulle8953 3 роки тому +23

    i heard "sauce" when Tom says "source" and honestly that didn't asked myself any question before finding out it wasn't sauce

    • @asklar
      @asklar 3 роки тому +4

      These equations can describe sauce flow too... For the right choice of sauce (incompressible, inviscid, irrotational sauce)

  • @gandalftolkien2879
    @gandalftolkien2879 3 роки тому +15

    Maybe you guys haven't seen it or it has been a while, but I would check out Feynman's Lectures on Physics. In volume 2 there is a neat section on the method of images for electrostatic potentials!

  • @ManojKumar-cj7oj
    @ManojKumar-cj7oj 3 роки тому +11

    I was looking for a video on method of images of electrostatics but ended up watching this amazing fluid video ❤️

  • @mith873
    @mith873 3 роки тому +19

    i see tom i see 3b1b i click

  • @sebastianmorales9787
    @sebastianmorales9787 3 роки тому +24

    Next: Laminar flows with Dustin, the epic fluid collab, and it doesnt get any better than that

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +12

      I'm down

    • @leif1075
      @leif1075 3 роки тому

      @@TomRocksMaths Are those walls supposed to be solid walls or walls of stationary fluid or something?

    • @tylercrowley2559
      @tylercrowley2559 3 роки тому

      @@leif1075 those would be work with any walls along which the potential flow is 0 so perfectly stationary fluid walls with infinite mass would definitely work and solid walls would as well. Not sure about other stationary fluids with finite mass

  • @amaarquadri
    @amaarquadri 3 роки тому +22

    Definitely one of the coolest ideas in fluids! One of my favorites is if you have a source at (1, 0) and 2 walls leaving from the origin at slopes of +30 degrees and -30 degrees, then you can replace it with 6 sources at the 6 roots of unity (hexagonal symmetry).

    • @marcocecchi9853
      @marcocecchi9853 10 місяців тому +2

      Your comment made me start thinking. Have you realized you can generalize this method? If you have a similar setup but with an angle of 2pi/2k between upper wall and x axis you can construct a solution with k charges on the vertixes of a poligon with k edges.
      And if k goes to infinity? I think in some sense it converges to the infinite channel example

    • @arnosuess9020
      @arnosuess9020 10 місяців тому

      reading this comment felt really good @@marcocecchi9853

  • @MrWhiteVzla
    @MrWhiteVzla 3 роки тому +11

    I didn't know Tom had his own channel! I just saw the drag equation video on the Numberphile channel and the recommended video was this one. Thank you algorithm!

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +7

      It's good to know it does its job sometimes :)

  • @InvisibleThinker
    @InvisibleThinker 3 роки тому +29

    This is what happened when mathematicians go with the flow!

  • @maurice22ravel
    @maurice22ravel 3 роки тому +9

    Next video: "Grant and I are a couple now! #MathLove"

  • @baoboumusic
    @baoboumusic 3 роки тому +8

    Are you kidding me? I just found your channel and you have a collab with Grant? Christmas came really early this year :)

  • @wingpandora6381
    @wingpandora6381 3 роки тому +17

    Also a question how do people even think of this abstract idea it feels magical

    • @muhammadsaid4654
      @muhammadsaid4654 3 роки тому

      Kutta, blasius, zhoukovsy etc they were all extremely gifted

    • @muhammadqaisarali
      @muhammadqaisarali 3 роки тому +3

      Its today's computer,, internet and technology, which paralyzed our mind and creativity. we are so much dependent on computers that we even don't try to imagine things, we search youtube for animations etc, which feels super easy to grab the things but in long term our brain gets lazy.
      the time when there were no computer machines, all computations were supposed to be done in the brain, as a matter of fact, the more you use the brain the more it gets trained and powerful. and then curiosity will be developed for nature, and the ultimate result will be discoveries and inventions.

  • @luckyw4ss4bi
    @luckyw4ss4bi 3 роки тому +11

    Greatest math video ever created. I am in awe at how amazing this journey how perfect the format is.

  • @googleit1370
    @googleit1370 3 роки тому +6

    The method of images is so amazing that it deserves a background music of its own: "Mirror on the wall, here we are again...."

  • @ZakNabi
    @ZakNabi 3 роки тому +5

    Early gang

  • @likithstochastic
    @likithstochastic 3 роки тому +4

    This was nice! Fluid dynamics is very similar to electric field theory we did in physics. The source is like a positive charge, sink being a negative charge and the velocity vectors are like electric field vectors. We do use potentials in electrostatics but I don't remember using complex potentials. In that way electrostatics might be a bit simpler.
    The mirror method is elegant indeed! Visualizing images of source in mirrors and doing the calculations. In electrostatics the wall is in fact a conducting surface. The infinite channel example was particularly enlightening.

  • @MA-nx3xj
    @MA-nx3xj 3 роки тому +2

    As Richard Feynman put it - the flow of "dry water"...

  • @MatesMike
    @MatesMike 3 роки тому +2

    Epic colab!

  • @EmilyMGin
    @EmilyMGin 3 роки тому +6

    Yay! More Grant and Tom collabs!

  • @Ghost____Rider
    @Ghost____Rider 2 роки тому +1

    Where was this video when I was doing fluid mechanics last year 😭

  • @momolover3606
    @momolover3606 3 роки тому +9

    HENCE PROVED TOM ROCKED

  • @Celthiccness
    @Celthiccness 3 роки тому +3

    Now I'm remembering fluid dynamics... Oh no... the screams. The terrible screams.

  • @richcole157
    @richcole157 11 місяців тому +1

    What about a wall with two holes in it and does it generalize to n dimensions.

  • @BobBeatski71
    @BobBeatski71 9 місяців тому +1

    Ahhh, that's what PotentialFOAM does.

  • @wingpandora6381
    @wingpandora6381 3 роки тому +5

    Youre a really good teacher wow

  • @ManojKumar-cj7oj
    @ManojKumar-cj7oj 3 роки тому +2

    I was looking for a video on method of images of electrostatics but ended up watching this amazing fluid video ❤️

  • @mharbol
    @mharbol 3 роки тому +2

    Thoroughly enjoy these collaborations with Grant. I think the visuals with barriers and reflections would make a great 3Blue1Brown video (like a followup to the Maxwell's equations video).

  • @christianorlandosilvaforer3451
    @christianorlandosilvaforer3451 2 роки тому +1

    i never saw this aproach in fluids, since i just knew it from EM topic ... epic greetings from colombia

  • @VibratorDefibrilator
    @VibratorDefibrilator 3 роки тому +2

    When I saw the first example with the source and the wall - 12:41 - I thought about an additional step: to imagine every point of the wall as a kind of source itself, but a linear one in particular direction alpha, depending of its position relative to the source of the flow. But, wait a minute!... this is the definition of the mirror, and as we already know, we can imagine the second source behind the wall, placed at its special spot as it was shown in the video. (By the way, the method of mirror images is also used in the field of electrodynamics, which is my speciality - so, you see, I was taught to think in this manner.)
    How clever it is! What mathematical wonders are hidden in Fluid Dynamics... I can only guess!
    Ah, and the last example was also very elegant! What am I talking about - all they are!
    These things must be popularised and the host of this channel is doing great, I admire his efforts... as with the same favour for mathematics that 3Blue1Brown is doing with his magnificent visualisations... big fan!

  • @aero33888
    @aero33888 3 роки тому +4

    Not just maths but also chemistry!! ❤️

  • @theverner
    @theverner Рік тому +1

    I needed this for electrodynamics

  • @Michael-il8ls
    @Michael-il8ls 2 роки тому +1

    why complex values? why not x y?

  • @firusclad
    @firusclad 3 роки тому +2

    Great video! The method of images is very useful when dealing with phenomena that can be treated as linear, e.g. in (linear) acoustics.

  • @nickwisely2581
    @nickwisely2581 3 роки тому +3

    "It's like you're looking at the mirror and then you give him a high five. Of course, it will stop there"
    That's a very good analogy for a method of images.

  • @johnboard407
    @johnboard407 3 роки тому +2

    Eye candy, brain candy. Also happpy 2021 to the both of you!

  • @Upsallauniversity123
    @Upsallauniversity123 3 роки тому +2

    Please makes videos on streamline, streakline, pathline and stream functions etc 🙏 please 🙏.

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому

      Added to the video idea list - thanks!

  • @Aquadolphin314
    @Aquadolphin314 3 роки тому +2

    Thanks for the great video! Really interesting and well-explained 😊
    I just have one question that's been bothering me since the beginning of the video: why do you take the potential to correspond to u *minus* iv, and not u+iv?
    Is there some physical or mathematical logic behing this choice?

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +1

      We very briefly touched on this in the video, but the idea is so that when you calculate the derivative of the potential as dw/dz the velocities match up with the real and imaginary parts. If we instead define dw/dz as u + iv then the vertical velocity would be the negative of the imaginary part of the derivative.

  • @aftermath__7060
    @aftermath__7060 2 роки тому +1

    could you explain how did you differentiate and apply the limits at 21:08

    • @TomRocksMaths
      @TomRocksMaths  2 роки тому

      ln(f(x)) differentiates to f’(x) / f(x) and then I rationalise the denominator by multiplying the top and bottom by the complex conjugate

  • @johnchessant3012
    @johnchessant3012 3 роки тому +3

    I love how Grant just knows the answer was some cotangent thing. You prove it with Parseval's identity, correct? Or is there a more fun way?

    • @johnchessant3012
      @johnchessant3012 3 роки тому +1

      On second thought, I realized that you can do it with a contour integral, which is a bit less tedious.

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +1

      I was thinking contour integrals...

  • @morphx666
    @morphx666 3 роки тому +1

    Queue some amazing fluids visualizations @ 3Blue1Brown in 3... 2...

  • @flirkami
    @flirkami 3 роки тому +1

    Could someone explain the differentiation and simplificatiom step? I don't even really know what he has written down there ..

    • @felicote
      @felicote 3 роки тому

      You start of with the derivative being the sun from -inf to inf of 1/(z - 2nai) since the derivative of ln is 1/z. Then multiply top and bottom of each term of the summation by its complex conjugate. You get sum from -inf to inf of (z - 2nai)/(z^2 + 4n^2a^). Then extract the n = 0 term and group each of the rest with its corresponding negative term. You get 1/z + sum from n=1 to inf of (z - 2nai + z + 2nai)/(z^2 + 4a^2n^2). Cancelling out the 2nai terms and adding the z's and factoring them out of the sum you get the desired result. (Tom got it slightly wrong, the sum should start at 1 instead of 0. You could also include 0 in the sum but that would then negate the 1/z term we pulled out earlier).

  • @thunder852za
    @thunder852za 3 роки тому +2

    The thing that strikes me - is the simplicity with which it all has to be approached. If nothing else this shows how to make maths accessible; or that even some of the best minds in math, still when introduced to a new topic, take it from the most basic forms and build on that. Sublime!

  • @abhinanda2967
    @abhinanda2967 3 роки тому +2

    I needed a quick revision on this topic for my PhD Quals and there you are Grant. Awesome collab Tom xD.
    Also, the series should start from n=1,inf after taking the derivative. Sorry it had to be done :)

  • @BobBeatski71
    @BobBeatski71 3 роки тому +1

    I understand the concept, but the math leaves me in the dust !

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +1

      This is 2nd year maths undergraduate level so don't feel bad!

  • @jmdr48
    @jmdr48 3 роки тому +3

    Could not asked for a better new year gift. I am working with these for past 2 years and it still amazes me how beautiful the math is.

  • @pourushsood
    @pourushsood Рік тому

    Won't we see multiple reflections even in the case of corners? When the boundaries are aligned at 90 degrees? Why did we consider only a single reflection there?

  • @benwinstanleymusic
    @benwinstanleymusic Рік тому +1

    Thank you Tom and Grant! Just in time for my Fluids exam

  • @scottychen2397
    @scottychen2397 Місяць тому

    Which magically yields the same results as the method of conformal maps : there is nothing trivial , nor obvious about that coincidence ,
    Which has to do with the existence of smooth complex maps ….
    An analytical discipline . Which has a non trivial relationship with the discipline of iteration.

  • @MarkusDarkess
    @MarkusDarkess 3 роки тому

    A 2D paper. Can manipulate into a mobious strip by a 3D being. To double the distance a 2d character would experience with out mass increase. A 4D. Is time. A memory is 5D. Men in black 3. 5D being can see through time and space. =memory. What is 1D. Senses. The brain dychpers patterns. The movie about black women being the computer for NASA.
    Burned diseased bodies after the blubonic plague. Causes a chemical reaction to rise to the air. The disease transferred to the air. Ferngully.
    A pure body should be burned. And diseased body should be buried. Slower particles because not heat. And slower reaction to the environment. A town poisoned the aquifer by burying bodies in one location. Because rain in Spain goes to the drains. The water collected built up decomposing bodies and sunk to the town's drinking water.
    Someone poisoned the watering hole. And no one admits it. Who poisoned it and everyone has proof with videos. But have a town with a graveyard over an aquifer then thay is the source.
    Native americans almost died out from blankets. Warm water is used to build cultures. Cold water is best to prevent bacteria breeding.
    Only boiling water eliminates bacteria. No one should be washing their hands in boilingwater. .

  • @vwcanter
    @vwcanter Рік тому

    It's not clear why Tom says there is no divergence in the field with a source. There would obviously be a divergence, wouldn't there? Isn't that what a source is?
    I also don't understand the complex factor z that is added to the expression for w. It appears to already have a magnitude and a direction everywhere, without z. And it just appears out of nowhere. Why is there a z in there?

  • @adayah2933
    @adayah2933 3 місяці тому

    The series at the end actually doesn't converge. But since a potential is only defined up to a constant, we can subtract from each term an appropriate constant just so that it converges. This way we can use the Weierstrass product formula for sin(z) and get the same result.

  • @GrungeMaster92
    @GrungeMaster92 3 роки тому

    My IQ just jumped 3 points.
    THANKS OBAMA

  • @vetrubio13
    @vetrubio13 3 роки тому +2

    Finally I got the images method! 👏🏼👏🏼👏🏼

  • @atrumluminarium
    @atrumluminarium 3 роки тому +3

    That was so beautiful ❤️
    I miss fluid dynamics

  • @rat_king-
    @rat_king- Рік тому

    Hold on.... doesnt this assume that the source is positionally static. as in, not migrating in space due to its changes upon the flow field...
    What occurs for a migratory source?

  • @luorisluo3634
    @luorisluo3634 3 роки тому +2

    i am doing a fluid mechanics master degree and this really brainstorming, thanks so much for sharing.

  • @zubin8010
    @zubin8010 3 роки тому +2

    18:14 Grant is thinking: "did you see that throw? nailed it!" but, unluckily, Tom is focused on the graph :(

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +2

      Haha I think I said a quiet 'nice' before immediately getting back to the maths...

    • @zubin8010
      @zubin8010 3 роки тому

      @@TomRocksMaths Nice! I had missed that

  • @kristianwichmann9996
    @kristianwichmann9996 3 роки тому +1

    I'm getting flashbacks from electrostatics class.

  • @ShaunJW1
    @ShaunJW1 3 роки тому +2

    Both of you are assisting me with my physics maths degree, final year student ❤️

  • @WhenThoughtsConnect
    @WhenThoughtsConnect 3 роки тому

    idk but change of variables always throw's me off for some reason

  • @cheasify
    @cheasify 3 роки тому +1

    Cool just like electrostatics.

  • @guyfromkerala3577
    @guyfromkerala3577 3 роки тому +3

    Physics students learn this in Griffith em.

  • @rat_king-
    @rat_king- 3 роки тому

    Still sad to find out Grant is Married, Happy for him but still sad.

  • @ws_zilch
    @ws_zilch 3 роки тому +9

    14:39 plot twist 🔥😂

  • @lloydgush
    @lloydgush 3 роки тому +1

    Well, tom shows us the reason why we don't have a nobel for math...
    lol!

  • @domc3743
    @domc3743 3 роки тому +3

    brilliant content as usual, thank you

  • @schurch1569
    @schurch1569 3 роки тому +3

    I dont understand a word but eh... fun :)

  • @mudkip_btw
    @mudkip_btw 3 роки тому +2

    Never seen the source in a channel before. Thanks Tom great video!

    • @mudkip_btw
      @mudkip_btw 3 роки тому +1

      I now see why you chose potential flow and the method of images to show to Grant, you had a brilliant example :D

  • @mattywlion5174
    @mattywlion5174 4 місяці тому

    MAAAAN CAN YOU SOLVE THE VORTEX IN THE WAKE OF A CILINDER PLEAAASE

  • @cold3lectric
    @cold3lectric 2 роки тому

    see also: stagflation glow 🤷🚬
    thanks:)

  • @luisbreva6122
    @luisbreva6122 3 роки тому +9

    Just in time for my EM exam lol thank u

  • @prdoyle
    @prdoyle 3 роки тому +1

    Wow, amazing. That's one of those concepts you never forget once you've seen it.

  • @onlineshoppingsuggestor830
    @onlineshoppingsuggestor830 3 роки тому

    I did mathematics well until no alphabets came .

  • @gaeb-hd4lf
    @gaeb-hd4lf 3 роки тому +2

    Channel is growing my man, awesome!

  • @kartikkalia01
    @kartikkalia01 3 роки тому +1

    Cool nerdy stuff

  • @jayjayf9699
    @jayjayf9699 3 роки тому

    Why are complex numbers involved in potential flow? You could of used cartesian coordinates?

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +1

      It's a neater way to write out the potential and allows us to use lots of nice results from complex analysis such as conformal mapping.

  • @scott_the_engineer
    @scott_the_engineer 3 роки тому +1

    Amazing video. How would you calculate the flow with a curved surface instead of a flat plane?

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +2

      Ah, now that requires a completely different theory... this only works for 2D flows.

  • @mariadelourdesaniessanchez1473

    for me every day
    my color is pink
    when I remember

  • @koketsomohale8596
    @koketsomohale8596 3 роки тому +2

    This is the best video on the internet

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +1

      A bold claim, but I'm not complaining - thank you

  • @Erin-ks4jp
    @Erin-ks4jp 3 роки тому +1

    Are the conditions of incompressibility and irrotation equivalent to a meromorphic potential? - it looks like they should be.

    • @ws_zilch
      @ws_zilch 3 роки тому

      U speaking the gods language hooman..

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому

      There is a lot of crossover with Complex Analysis which is where the 'complex potentials' idea comes from

  • @NEONHYPERTURTLE
    @NEONHYPERTURTLE 3 роки тому

    Im a little confused, why are we able to just add another potential flow when using the method of images? won't that equation be different than the 1 source case (This is for the infinite plane case)

    • @TomRocksMaths
      @TomRocksMaths  2 роки тому

      adding in the other sources acts to create the 'wall'. the flow pattern is in fact the same for two symmetrical sources and one with a wall - and you can verify this with experiments

  • @Cannongabang
    @Cannongabang 3 роки тому +1

    then conformal mapping appears and renders everything more useful

  • @zach4505
    @zach4505 Рік тому

    Electron energy levels for the hydrogen atom? Is that Tom's Tattoo on his right arm? If so, that's an awesome concept

    • @TomRocksMaths
      @TomRocksMaths  Рік тому

      great idea - but my tattoo represents the Basel problem

  • @lordloneshadow7572
    @lordloneshadow7572 3 роки тому

    There's a cut at 0:38 because Grant snapped and said "I am not scientifically illiterate Tom!"

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому +1

      ... this is some kind of niche superpower

  • @phenixorbitall3917
    @phenixorbitall3917 2 роки тому +1

    Great :)

  • @adrianhimmelreich3911
    @adrianhimmelreich3911 2 роки тому

    Is there a book that explains the computation steps of the last problem a bit more in depth? Tried to do the computations on my own but failed :D

    • @TomRocksMaths
      @TomRocksMaths  Рік тому

      I recommend 'Elementary Fluid Dynamics' by David Acheson

  • @balajisriram6363
    @balajisriram6363 3 роки тому +1

    Love eeeeeeeeeeeeeetttttttttt!!!!

  • @SayanSamanta123
    @SayanSamanta123 3 роки тому

    Lol, we do this in materials kinetics all the time. Same exact concept really. Momentum or particles.

  • @Medellinish
    @Medellinish 3 роки тому +1

    I studied physics and then went on with a not related degree. This video reminded me of when I used this mirror method for potentials in electrodynamics where there is e.g. some point charge (Punktladung in German) in a plane.
    In such moments I dont know if I feel sad to have "abondend" the world of physics/maths and their methods.

    • @sebf9847
      @sebf9847 3 роки тому +2

      Reminded me of the same thing

    • @TomRocksMaths
      @TomRocksMaths  3 роки тому

      The same method is indeed used in electrostatics - well remembered :)

  • @maxm1947
    @maxm1947 3 роки тому

    Mathematically, the point perpendicular to the mirror (15:00) is fine, but physically what would happen to the atoms and building up of the energy around that point?

  • @maxm1947
    @maxm1947 3 роки тому

    Mathematically, the point perpendicular to the mirror (15:00) is fine, but physically what would happen to the atoms and building up of the energy around that point?

  • @4sety
    @4sety 3 роки тому +1

    Sounds like Tom is... super StOkEd to do this

  • @mariadelourdesaniessanchez1473

    Yes
    every day is the Boys