Complex Fourier Series

Comments · 66

• TH

  @thomasdehaeze3422 · 6 years ago (edited)

  Minor comment about the integral : if j=k, then the exponential in the integral is equal to one, therefore the integral is equal to 2pi. Then we don't have to deal with limits.

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• ER

  @erickappel4120 · 2 years ago

  Steve Bruton explains so well. He deserves a statue!!!

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• BO

  @BoyozBey · 5 years ago (edited)

  well, your impact on society after taking the decision of sharing videos about your knowledge is an important asset. Thank you very much for your brief and clear explanation of Fourier analysis. I have watched all videos from this playlist and founded decent as an electronics engineer from Turkey. Thank you again, Mr. Brunton

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• FN

  @fnegnilr · 6 years ago

  I like how you are using geometric figures to keep us grounded in the explanations.

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• ZA

  @zacharythatcher7328 · 6 years ago

  This has been really helpful for my understanding of quantum mechanics. Professors always pretend to intuit that the easiest solutions to the hamiltonian are the complex periodic basis functions. Then when they say that they form a complete and orthogonal set of basis functions for all solutions I have a really hard time believing it. Breaking down that the Fourier series was invented as an eigenfunction/Hilbert space solution to PDEs on purpose really helps me digest that the basis is complete by grounding me in the fact that it is just a Fourier representation of any potential answer. Seeing you go through the proofs that quantum courses always go through, but in a more general sense for complex Fourier representations, really helps me understand that these aren’t magical properties of quantum mechanics that someone came up with by analyzing schrodinger’s equation, but rather intuitive properties of the mathematical tools that we are using to understand quantum phenomena.

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• CH

  @christophs1801 · 6 years ago

  I like this video series a lot. Very energetic and enthousiastic style of presenting! One thing i want to mention is that this only proves the orthogonality part, it does not show that the psi-functions form a basis.

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• CL

  @Clegg471 · 1 month ago

  Im 15 and This is soooooooo useful for my high science project, Its a weird feeling change from (x,y,z) to an infinite dimension vector spaces, but Its fun, Its really fun

• IS

  @ISKportal · 4 years ago

  Is it me or y'all find This playlist super exciting.

• EL

  @ElMalikHydaspes · 2 years ago

  first time, really seeing a geometrical basis (no pun intended) explanation of Fourier series ... really well done and clear!

• LI

  @lioneloddo · 4 years ago (edited)

  Thanks to this video, I realize that the concept of &quot;orthogonality&quot; is one of the most beautiful concept of physics !<br>I see one corner in the room where I&apos;m located and it&apos;s the same thing as the vibration of my guitar that I can see below the corner !<br>It&apos;s incredible that, thanks to the maths, we can proove that there is a relationship, a link, an harmony between these 2 things : A room and a guitar.<br>And this is the orthogonality !

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• MA

  @MathFinGuy · 2 years ago

  Very clear explanation ! that any function f(x) can be represented as projections on an infinite basis , given by e^(ikx)

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• CH

  @ch3432 · 5 years ago

  Explanation and derivation of the concepts are so clear! Thanks for uploading the course :)

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