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this post was submitted on 25 May 2024
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From an engineering perspective, functional analysis is the main mathematical framework behind (1) and (2) in my previous comment. Although they didn't teach functional analysis for real in any of my coursework, I kinda picked up that it was going to be an important topic for what I want to do when I kept seeing textbooks for it cited in PDE and "signals and systems" books. I've been learning it on my own since I finished Calc III like four years ago.
Such an incredibly interesting and deep topic IMO.