Laplace transform

What the actual FRICK is the purpose of this fricking SHIT?
Did mathematicians one day just stuck their thumb up their buttholes and said "Hmmm *sucks dick-shaped pipe* elementary my dear Watson, let's make this as contrived as possible for no fricking reason whatsoever"?

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  1. 2 weeks ago
    Anonymous

    It allows you to transform integration and differentiation in the time domain into much simpler multiplication and division.

    • 2 weeks ago
      Anonymous

      You just googled that shit you wienersucker

      • 2 weeks ago
        Anonymous

        Just because you couldn't

  2. 2 weeks ago
    Anonymous

    >Laplace transform
    oh I hated that shit. lol

    • 2 weeks ago
      Anonymous

      Personally, after spending hours on variation of parameters problems and various other cancerous methods in ODE I was overjoyed when I saw the power of Laplace transforms.

      • 2 weeks ago
        Anonymous

        You can just learn how to factor differential operators.
        Then you can just solve things directly.

  3. 2 weeks ago
    Anonymous

    just another trick for solving diffy Qs what's the problem?

  4. 2 weeks ago
    Anonymous

    it just shows how much a decaying cosine the signal is. git gud.

  5. 2 weeks ago
    Anonymous

    I prefer f(st)*e^(-t).
    It transforms the exponential generating function of a sequence into the ordinary generating function of the sequence.

  6. 2 weeks ago
    Anonymous

    You learn this in the very first lecture of any decent signals and systems course. May God have mercy on your midwit soul if you get filtered by this.

    • 2 weeks ago
      Anonymous

      >You learn this in the very first lecture of any decent signals and systems course
      you learn to follow the recipe
      I do not think you learn what it actually means

      • 2 weeks ago
        Anonymous

        isn't it incredible how shitty the education system is?
        they teach you what the screwdriver is and not how to use it and when for what projects.

        • 2 weeks ago
          Anonymous

          no my point is you need a lot of maturing to actually get an idea what and why laplace/fourirer does without it just being handwaving

          saying
          >it solves equations
          >it transforms from time to frequency
          is just repeating some canned answer and does not feel satisfying

          • 2 weeks ago
            Anonymous

            NTA but I agree and disagree somewhat.

            When you say
            > no my point is you need a lot of maturing to actually get an idea what and why laplace/fourirer does without it just being handwaving
            You are definitely correct, but I also don't think it's necessarily required to teach the subject at its most serious level of depth to everyone all at once.

            Think about how you learned linear algebra. If you went to a somewhat normal university, your first exposure to linear algebra was probably in either a calculus class, or a computation/application oriented linear algebra course fairly early on in your education. You likely learned the basics of matrix algebra and operations, as well as the beginnings of eigenvector/eigenvalue analysis, determinants and traces, vector spaces and projections.

            This is not taught to a particularly rigorous or "complete" level of complexity, but it was good enough to teach you the linear algebra foundations you needed for other courses. Then, you may have taken an undergraduate level proof based linear algebra course, where the emphasis was instead looking at linear algebra as a transformation/mapping and the consequences of this view of the subject (product spaces, commutative rings, all of that jazz).

            Then, if you go to graduate school, you may have taken a graduate level linear algebra which looks at things at an even higher level of abstraction. You may have learned about layers of transformations, dual spaces, homologies etc.

            The point being, you never quite get a complete picture in any of these intermediary steps. Not only do you not get a complete picture, but it would be wildly inappropriate for your professors to introduce such nuances and rigor in your first exposures to the topic.

            The purpose of a signals and systems course is not to teach you Fourier analysis at a PhD level so you get the "most complete" level of analysis for the subject. The point is to give you a simple and intuitive understanding.

          • 2 weeks ago
            Anonymous

            I agree but it feels like the bar for intuition or ground-level knowledge is a few steps up from linear algebra when it comes to fourier/laplace/complex analysis at least for me

          • 2 weeks ago
            Anonymous

            I guess it depends on how you want to look at things.

            In some sense a characteristic equation is a characteristic equation. Does it really matter whether those characteristic roots correspond to eigenvalues vs. modal exponents for constant coefficient ODE's?

            In another sense, I don't think I really "got" the Laplace transform until I took a complex functions course and learned about Cauchy integration. I don't know if I would have "gotten" Cauchy integration if I wasn't already fairly comfortable with the Fourier and Laplace transforms from a "plug and chug" perspective. Hard to tell really.

  7. 2 weeks ago
    Anonymous

    its literally just for academic pseudointellectual mental masturbation and comparing metaphorical dick sizes of the mathematical part of the brain

    • 2 weeks ago
      Anonymous

      >t. non engineer

    • 2 weeks ago
      Anonymous

      you'll understand when you finish high school and start your engineering degree.

  8. 2 weeks ago
    Anonymous
  9. 2 weeks ago
    Anonymous

    Any function can be written as a linear combination of any other orthogonal basis vectors. It's like tilting your head at a girl to see up her skirt. The panties are there but a different perspective helped you see it. Sometimes you need a fourier perspective. Sometimes you need the Laplace perspective. That's all there is to it. Do you want to see the panties anon? Now, sure you can look at that hot piece of ass all you want while she has her tight wienertail dress on. But unless you get the right angle you're not going to see those panties.

    • 2 weeks ago
      Anonymous

      This. It's no different than identifying eigenvectors or working out canonical transforms or switching to some kind of center of momentum frame or comoving frame or non-inertial frame or any of the other million similar techniques:

      90% of solving mathematical and physics problems is figuring out the right 'angle' to look at the problem that makes the solution obvious.

  10. 2 weeks ago
    Anonymous

    The Laplace transform is goated. It is probably the most useful linear transformation out there.

  11. 2 weeks ago
    Anonymous

    Representing a function as an infinitesimal sum of damping or amplifying oscillations. Much stronger that fourier's shit

  12. 2 weeks ago
    Anonymous

    For me, its the Fourier Transform

  13. 2 weeks ago
    Anonymous

    It's just a better behaved Fourier transform

    • 2 weeks ago
      Anonymous

      isn't the Fourier transform a generalization of the Laplace transform?

      • 2 weeks ago
        Anonymous

        The two sided Laplace transform is the same as the Fourier transform with [math] s = iomega [/math]
        The one sided Laplace transform is actually substantially different, because restricting the domain means that the initial conditions enter explicitly, and the integral can converge for exponentially decaying or growing solutions where the Fourier transform does not.
        In certain situations where there is exponential behavior that depends on the initial conditons, the Fourier problem of finding normal modes of the system can be ill posed, and will gove incorrect solutions when naively applying Fourier analysis, which means it must be treated as an initial value problem and solved via Laplace transforms. See the attachment for a physical example of where this difference matters.

  14. 2 weeks ago
    Anonymous

    For a Fourier transform you can see how it's composed by frequency. For Laplace, you get a combo of frequency and exponential decay functions

  15. 2 weeks ago
    Anonymous

    > as contrived as possible for no fricking reason whatsoever
    Ok dude have fun in the time domain trying to figure out if the thing you build will explode when subjected to oscillations.

    Meanwhile I’ll just take the laplace transform, find the roots of a simple polynomial & be done in 2 minutes

  16. 2 weeks ago
    Resolve

    It allows you to turn a differential equation into an algebraic one. It's an immensely useful tool.

  17. 2 weeks ago
    Anonymous

    Watch this playlist:
    https://m.youtube.com/playlist?list=PLldiDnQu2phvCb1QQhanJYm7A6xzEoC3F

    • 2 weeks ago
      Anonymous

      If you want the real answer, it is that it allows you to solve differential equations involving terms that are not technically functions, called tempered distributions. The most famous example is the delta distribution, and it pops up in control theory, where a short, but very intense, signal can be represented as such. It also satisfies nice identities with the convolution operation, which makes it a handy tool.
      See:

  18. 2 weeks ago
    Anonymous

    Idk bro I do ecology, hehe!

  19. 2 weeks ago
    Anonymous

    disregard everything said so far in this thread. a quick glance at wiki says how the laplace transform came to be. in fact euler and laplace came upon such methods in their studies of probabilities, it had nothing to do with muh time domain and muh fourier. engineers wrote that
    https://en.m.wikipedia.org/wiki/Moment-generating_function

    tldr; if you study probability you will encounter such methods in a more natural setting

    • 2 weeks ago
      Anonymous

      >engineers wrote that
      THOSE EVIL LYING BASTARDS!

    • 2 weeks ago
      Anonymous

      disregard everything said so far in this thread. a quick glance at wiki says how the fast Fourier transform came to be. in fact gauss came upon such methods in their studies of interpolating the motion of planets, it had nothing to do with muh signal processing and muh solving PDEs. engineers wrote that
      https://babel.hathitrust.org/cgi/pt?id=uc1.c2857678;view=1up;seq=279

      tldr; if you study orbital mechanics you will encounter such methods in a more natural setting

      • 2 weeks ago
        Anonymous

        >laughs in methmatics

  20. 2 weeks ago
    Anonymous

    >What the actual FRICK is the purpose of this fricking SHIT?
    Solve linear differential equations quickly and easily.

  21. 2 weeks ago
    Anonymous

    gives solutions to differential equations

  22. 2 weeks ago
    Anonymous

    F(t). S.t . T.dt. = -1

    ????

  23. 2 weeks ago
    Anonymous

    You know how you show your disdain for all these French bastards? You mispronounce their names. Not pronouncing a man's name properly is the ultimate slight. I give you LAP-LACE.

    • 2 weeks ago
      Anonymous

      >LAP-LACE
      Can someone vocaroo this? Not sure how this is supposed to be pronounced

      • 2 weeks ago
        Anonymous

        /ˈlæpleJs/

      • 2 weeks ago
        Anonymous

        La-plah-Ssss

  24. 2 weeks ago
    Anonymous

    making stuff easier for us moron engineers. thank you for your service, nerds.

  25. 2 weeks ago
    Anonymous

    >What the actual FRICK is the purpose of this fricking SHIT?
    Control theory.

  26. 2 weeks ago
    Anonymous

    It's like log in that it converts a difficult problem into a simple one

  27. 2 weeks ago
    Anonymous

    No one has answered my question yet what the frick

    • 2 weeks ago
      Anonymous

      It changes coordinates from time to frequency, there are you happy?
      Why this is useful is that it allows you to perform algebra with the boundary conditions of the given DE
      [math]mathcal{L}{f'(t)} = sF(s) -f(0)[/math]

  28. 2 weeks ago
    Anonymous

    it's very useful, you can solve differential equations with it really quickly.

  29. 2 weeks ago
    Anonymous

    People in this thread who explain it as a means of converting ODE into a linear equation are low IQ. Those who explain this as a way to represent a signal as a combination of exponentially growing and decaying oscillations are midwit.

    • 2 weeks ago
      Anonymous

      Thank you for your valuable contribution.

  30. 2 weeks ago
    Anonymous

    It's a tool for solving differential equations.
    What are you, an engineer?

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