Complex Analysis: what is a contour integral?

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  • เผยแพร่เมื่อ 23 ม.ค. 2025

ความคิดเห็น • 40

  • @ryankelly9772
    @ryankelly9772 ปีที่แล้ว +43

    common Maths505 W

  • @danielakovatch
    @danielakovatch หลายเดือนก่อน +1

    watching this as a review for finals and it feels really good to be able to be like “ah i know that already!!” thank you for the wonderful overview!

  • @Waffle_6
    @Waffle_6 17 วันที่ผ่านมา

    yo i love all your vids, been watching them nearly daily now forever. please make more educational content like this! i would love to see a complex or harmonic analysis series

  • @TI5040
    @TI5040 ปีที่แล้ว +15

    Video was pretty good. To get a clear intuition on what exactly an integral in complex analysis mean I recommend the book "Visual complex analysis" by Tristan Needham combined with vector calculus chapter in "Feynman lectures in physics".

  • @quanle1539
    @quanle1539 7 หลายเดือนก่อน +1

    Hi there! I just wanted to say that your video on complex analysis is fantastic. I'm starting to learn it again on my own, and your video has been a tremendous help. Great work, and thank you so much!

  • @ShujaWaras-nn4fw
    @ShujaWaras-nn4fw 9 วันที่ผ่านมา

    Thank you so much for explaining so well and easily

  • @AB-nu5we
    @AB-nu5we ปีที่แล้ว +4

    Didn't I watch this on your other site, focusing on Complex Analysis. I keep going crazy. Not that watching it again is a bad thing as doing so builds strong bones and teeth.

  • @快來快
    @快來快 ปีที่แล้ว +2

    Although my math is bad,I still watch most of your videos idk I probably enjoy watching someone solving hard problems

  • @ikarienator
    @ikarienator ปีที่แล้ว +2

    That's a very nice introduction! Can you cover the branch cut next time? I think I have never really understood it.

    • @maths_505
      @maths_505  ปีที่แล้ว +3

      I've made videos on branch cuts for all the important functions. Check out the complex analysis lectures playlist. The discussion of branch cuts starts with the the complex exponential from Euler's formula.

  • @maxvangulik1988
    @maxvangulik1988 ปีที่แล้ว +2

    does parametrasiation mater?

    • @maths_505
      @maths_505  ปีที่แล้ว +4

      No it doesn't and my spellings are horibal

  • @youknowwhatlol6628
    @youknowwhatlol6628 11 หลายเดือนก่อน +1

    thanks for the video!
    i didn't understand your proof (since i am a beginner in advanced calculus and analysis)...i don't know these sums are and most importantly - WHY we have this inequality....intuitively, for me, it doesn't make sense. Could you guys (or the admin) please enlighten me on this? Thanks so much, in advance :)

    • @KusacUK
      @KusacUK 11 หลายเดือนก่อน

      For the inequality, imagine summing the values 1, -2, 3. If you take the absolute value of each element, then do the summation, it has to be greater than the absolute value of the overall sum - because the absolute value of -2 would be +2.
      The inequality in general is less than or equals (or >= depending on which way round you write it) because the number of negative items in your set of values might be zero (so the sums would be equal).

    • @KusacUK
      @KusacUK 11 หลายเดือนก่อน

      As for the Riemann sums - that’s really just the definition of integration, written in summation notation. Dividing the area under the curve into rectangles of width delta x, then taking the limit as the number of rectangles approaches infinity (and delta x therefore approaching 0).

  • @spiderjerusalem4009
    @spiderjerusalem4009 ปีที่แล้ว +1

    Did you use shakarchi's complex analysis 🤔

    • @maths_505
      @maths_505  ปีที่แล้ว

      Who?

    • @maths_505
      @maths_505  ปีที่แล้ว +2

      I use lang, dettman and gamelin for complex analysis

  • @tifn4g190
    @tifn4g190 ปีที่แล้ว +1

    I have a question about double intégrals: when you have a double intégral from 0 to Infinity, and the integrand is f(x,y) dx dy. My question is when can you inverse dx and dy (like what are the conditions on f ?)

    • @maths_505
      @maths_505  ปีที่แล้ว +2

      Continuity of the function.

    • @tifn4g190
      @tifn4g190 ปีที่แล้ว +2

      @@maths_505 there isn't any condition on the convergence of the integral?

    • @maths_505
      @maths_505  ปีที่แล้ว

      @tifn4g190 isn't that plainly obvious????? Convergence is always key.

  • @giacomocervelli1945
    @giacomocervelli1945 ปีที่แล้ว

    Why did you upload this here and not on the second channel? (Just out of curiosity)

    • @maths_505
      @maths_505  ปีที่แล้ว +1

      Experimental purposes

  • @notsodope834
    @notsodope834 6 หลายเดือนก่อน

    Ok but 1/z dz integral is not ln(z) here😢

  • @mtl.wraith9981
    @mtl.wraith9981 ปีที่แล้ว +1

    could you do a line integral next? i see them for one formula in my physics class but they were not explained at all

  • @anupamamehra6068
    @anupamamehra6068 ปีที่แล้ว

    hi thanks for this... by the way are you a bachelor in mathematics or physics?

    • @maths_505
      @maths_505  ปีที่แล้ว +1

      Majored in math Nd took lots of physics courses.

  • @AlBoulley
    @AlBoulley ปีที่แล้ว

    DOES PARAMETERIZATION MATTER

    • @maths_505
      @maths_505  ปีที่แล้ว

      NO IT DOES NOT

    • @maths_505
      @maths_505  ปีที่แล้ว

      My spellings are pretty horibal

  • @pandavroomvroom
    @pandavroomvroom ปีที่แล้ว

    pretty cool

  • @apologizemin9457
    @apologizemin9457 ปีที่แล้ว +1

    :'0 WOW

  • @worldnotworld
    @worldnotworld 5 หลายเดือนก่อน

    OK Cool

  • @축복이-x6u
    @축복이-x6u ปีที่แล้ว

    asnwer= dz isit hmm