Complex Analysis 3 | Complex Derivative and Examples

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  • Опубліковано 23 гру 2024

КОМЕНТАРІ • 54

  • @brightsideofmaths
    @brightsideofmaths  2 роки тому +3

    Please do the quiz to check if you have understood the topic in this video: tbsom.de/s/ca

  • @NewDeal1917
    @NewDeal1917 2 роки тому +10

    00:00 Intro
    00:34 The [geometric] intuition for complex derivative
    4:11 Producing the formal definition
    5:19 Example 1. A linear polynomial in C
    7:34 Example 2. A conjugate function

  • @LuukeFX
    @LuukeFX 7 місяців тому +1

    Just discovered your videos now as I have to refresh my memory on this topic. Wish this existed during my study! Super clear explanation, thanks for sharing this for free!

    • @brightsideofmaths
      @brightsideofmaths  7 місяців тому +1

      Glad it was helpful! :) It is for free but only because nice people support me :)

  • @BariScienceLab
    @BariScienceLab Рік тому

    My brain is completely fried and I love it. Thank you for this series!

  • @PunmasterSTP
    @PunmasterSTP 2 роки тому +4

    Complex derivative and examples? More like "Completely dynamite and expansive!" Thanks for helping to shatter our old ways of thinking and broadening our horizons.

  • @jaimelima2420
    @jaimelima2420 2 роки тому +5

    Cool! BTW, another way to show how crazy this limit in the second example gets is to put the limit in the polar format using our old boy Euler's formula. The function that measures distance in the metric space returns a real number, and this is good because we want ordering. However, the price to pay, and the phantom that will haunt us forever on this, is that the phase(argument) information collapses and is lost, and strange things the average normal human mind has trouble accept at first start to happen.

  • @Hold_it
    @Hold_it 2 роки тому +3

    Nice to see the next video so soon.
    I really appreciate it.

  • @reptilewithsadhumaneyes
    @reptilewithsadhumaneyes 2 роки тому +2

    Great video as always, excited for the series

  • @alejrandom6592
    @alejrandom6592 Рік тому +2

    3:54 shouldn't there be an error term for f(z)?

  • @darthtleilaxu4021
    @darthtleilaxu4021 2 роки тому +1

    Haa ! Je viens justement de finir mon thé ☕.
    Bonne pause en perspective. 👌

  • @samuellongo9530
    @samuellongo9530 15 днів тому

    I have a question about the linear approximation for f(z). I agree that the Delta function can (or does) exist, but it doesn't look right that it is equal to the differential limit. The limit imposes an infinitesimal difference between z and z0, while the linear approximation accepts any z, for a given z0. So my question is: where am I getting it wrong?

  • @codeo6246
    @codeo6246 2 роки тому +2

    Incredible videos!!! Thank you so much!

  • @blind_vigilante.murdock4972
    @blind_vigilante.murdock4972 4 місяці тому

    wouldn t the last example give the same results in a function that mirrors dots in cartesian plane because none of the process included some unique complex property or anything?? i rlly need an answer

    • @brightsideofmaths
      @brightsideofmaths  4 місяці тому +2

      Any function f: C → C is also also a function f: ℝ²→ℝ²

  • @geoglyphproject
    @geoglyphproject 9 місяців тому

    I love this playlist thanks for sharing

    • @brightsideofmaths
      @brightsideofmaths  9 місяців тому

      I'm glad you like it :) And thanks for the support!

  • @Linkarlo_ti_ta_thes
    @Linkarlo_ti_ta_thes 2 роки тому +1

    Love it :) Thank you!

  • @AJ-et3vf
    @AJ-et3vf 2 роки тому

    Awesome video! Thank you!

  • @khalidmohammadjama
    @khalidmohammadjama 2 роки тому +1

    nice work 👍

  • @kitstudent4446
    @kitstudent4446 2 роки тому +4

    really interesting, will you be covering modular forms?

  • @20a3c5f9
    @20a3c5f9 Рік тому

    Why is this form linear aproximation before z is fixed to z0? Delta is just hiding nonlinearity until it is evaluated, this nomenclature confuses me.

    • @brightsideofmaths
      @brightsideofmaths  Рік тому +1

      That's the whole thing for "linear approximation". Delta is not hiding anything. It's just the non-linear part you would omit for the linear approximation.

  • @YoumingZhao-nt9yn
    @YoumingZhao-nt9yn Рік тому

    I guess there is a typo in the representation of the linear approximation of complex functions. In the end of the formula, it is supposed to be z_0 instead of z?

    • @brightsideofmaths
      @brightsideofmaths  Рік тому

      I don't see a typo. Can you give a timestamp?

    • @sirlewis3975
      @sirlewis3975 9 місяців тому

      @@brightsideofmaths 3:19 delta(z) should be delta(z_o)?

    • @brightsideofmaths
      @brightsideofmaths  9 місяців тому

      @@sirlewis3975 No, it should be Delta(z).

  • @kaursingh637
    @kaursingh637 7 місяців тому

    SIR - WHETHER CONTOUR IS DOMAIN OF FUNCTION ? THANK U SIR

  • @ekisvioleolivaradamos6701
    @ekisvioleolivaradamos6701 2 роки тому +1

    Amazing 🤩🤩🤩

  • @Canda-fh4xc
    @Canda-fh4xc 2 роки тому +2

    We will really appreciate it 🙏 🙌
    if you can teach us
    Geometric Analysis

  • @juancarlosperez911
    @juancarlosperez911 2 роки тому

    if delta is defined so f(z)=f(z0)+(z-z0)*Delta(z), then why isn't Delta (z)= (f(z)-f(z0))/(z-z0) instead of the limit of that expression? I mean the derivative as the slope would still work if it is defined as the limit of delta and not delta itself. f(z)=f(z0)+(z-z0)*f'(z) is not correct in general.

    • @brightsideofmaths
      @brightsideofmaths  2 роки тому

      The limit comes in because Delta should be continuous at z_0.

  • @itexsoo
    @itexsoo Рік тому

    9:27 is it f(z)=z!.

    • @brightsideofmaths
      @brightsideofmaths  Рік тому

      What is the question?

    • @KM-om1hm
      @KM-om1hm Рік тому

      Complex factorial?

    • @brightsideofmaths
      @brightsideofmaths  Рік тому +1

      @@KM-om1hm Yeah, this could be defined, see Gamma function? :)

    • @KM-om1hm
      @KM-om1hm Рік тому

      @@brightsideofmaths okay let's check it out, thank you

    • @brightsideofmaths
      @brightsideofmaths  Рік тому

      @@KM-om1hm Yeah, I have a nice video about it: tbsom.de/s/aoms

  • @StratosFair
    @StratosFair 2 роки тому

    I'm sorry but I simply can not accept the fact that taking the complex conjugate is not a differentiable map. I will need at least one week to wrap my head around that ridiculous sounding fact

    • @brightsideofmaths
      @brightsideofmaths  2 роки тому +1

      The next videos can help you: "complex differentiable" is just a very strong notion.

    • @AkamiChannel
      @AkamiChannel Рік тому

      It makes sense to me bc the complex conjugate is a very jarring thing. It reflects things about the real axis. That's not a very smooth operation. It causes the input to suddenly jump in another direction.

  • @ADCtEADCtE
    @ADCtEADCtE 5 місяців тому

    This is BULLSHIT. No one has shown a complex number on a complex axis.

  • @baramillseo5610
    @baramillseo5610 2 роки тому +2

    Great video as always, excited for the series