Laplace's Equation and Poisson's Equation

Comments · 49

• _R

  @_RTheBruce · 1 year ago (edited)

  <a href="https://www.youtube.com/watch?v=nmvs0vrBT18&amp;t=930">15:30</a> &quot;Then you get poisson&apos;s equation. It&apos;s a little fishy if you ask me.&quot; 😂 good casual joke

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• MU

  @Mutual_Information · 4 years ago (edited)

  “Naiver Stokes.. those are the PDEs for momentum conservation in a fluid.” - that is such an excellent and simple way of explaining something I, as of only a few minutes ago, could not explain.

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• LG

  @lgl_137noname6 · 4 years ago

  Please consider publishing the associates notes to this series as a single repository for quick access and review.<br>Thank for your consideration.

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• CH

  @ChristinaSolomonRichardson · 2 years ago

  I am an applied math grad student in my final semester. I do feel like I have so much to learn and I still have no idea where all of this will take me . I feel like there are a lot more questions in my universe than there are answers. However, when it comes to you, Dr. Brunton, I don&apos;t have any questions. I come back to your instruction time and time again. You have helped me so much see the engineering and data science applications of the mathematics that I have studied. I love that-- what can I do with this?! You always answer that question for me. I appreciate you and the time you take to be &quot;so excited&quot; and how much you &quot;love&quot; literally everything about every single subject you teach! Thank you for your contributions to science and to academics and most selfishly to my journey!

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• VA

  @vazkuzhd1321 · 2 years ago

  GG to everybody taking PDE class

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• DO

  @douglasstrother6584 · 1 year ago

  &quot;Partial Differential Equations in Physics&quot; by Arnold Sommerfeld is based on his lectures on Theoretical Physics. &nbsp;It, like other volumes in the series, illustrates the thought-processes of a truly great mind; &nbsp;he was one of the strong bridges between Classical and Quantum Mechanics.

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• CU

  @curtpiazza1688 · 2 years ago

  Great! &nbsp;Love the phrase &quot;mathematical architecture&quot;! &nbsp;<br>Poisson sounds &quot;fishy&quot; ! &nbsp;Great. twist on French words! 😂

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• DO

  @douglasstrother6584 · 1 year ago

  Detailed discussions of Laplace&apos;s and Poisson&apos;s Equations, and the construction of Green&apos;s Functions can be found in Chs. 7 &amp; 8 of &quot;Modern Electrodynamics&quot; by Andrew Zangwill. &nbsp;It&apos;s on the level of Jackson&apos;s &quot;Classical Electrodynamics&quot;, with fewer sharp edges.

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• PT

  @PTE · 11 months ago

  Poisson&apos;s equation &amp; Laplace equation are useful in electrostatics to find electric potential ❤

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• EL

  @elyepes19 · 2 years ago

  My ¢5 contribution to this amazing video: You need temporal Initial conditions (IC) and spatial boundary conditions (BC) because, &nbsp;without them, in linear algebra parlance, the system of linear equations that describe the PDE system would be incomplete. In other words, if you express the PDE as a matrix equation <br><br> Ay = b, <br><br>without IC and BC, &nbsp;your matrix A (the one that relates x and t) &nbsp;would not be square, and the solution u(x,t) couldn&apos;t be unique

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• YA

  @YassFuentes · 4 years ago

  Beautiful equations ❤️ thanks for the video :)

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• MA

  @mathunt1130 · 4 years ago

  The Laplace equation also comes into play where you have a flow of global constant vorticity or vorticity which is purely a function of depth.

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