Duhamel's Principle for Partial Differential Equations

[@FacultyofKhan]

To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/FacultyofKhan/. The first 200 of you will get 20% off Brilliant’s annual premium subscription.

[@arvindp551]

The sound level seems to be quite low on my laptop.

[@mohammedal-haddad2652]

Great lecture as all the lectures of this channel, but this time, the font size is rather small.

[@pjohnson81]

Forgive any ignorance, but is going through all of that for this simple PDE worth it, when you are still faced with an infinite sum to numerically solve? We still did not arrive at an answer that can be analyzed. From the Duhamel result, we still need to take the continuous integral of the infinite sum to in u_smp.. which isn’t it way more complicated than just conducting a finite difference or element method?

[@Wouter10123]

Usually with infinite sums like this, the terms decay very quickly (they have to, otherwise the sum would never converge). Often there's a 1/n! in there; in this case there isn't, but the exp(-n^2) still decays pretty darn quickly. Therefore it usually suffices to only compute the first few terms for a reasonable approximation.