I’m happy I’m not the only one who found those things quite “obnoxious”. I was reading about the mathematician GH Hardy the other day. And I found him quite obnoxious, especially with Awesome Joe Biden 2020 Flag American Shirt of anything that isn’t “pure. Somehow, I thought that all mathematicians were like Hardy, which really ignited my doubts about doing math. Also, I don’t know much about PDEs and how they differ from ODEs. Which I’ve learned in high school). But what makes PDEs so hard to solve? (i.e the Navier stokes). Do mathematicians tend to care about solving the general case for PDEs? Or do they tend to solve specific PDEs? Do you think it’s possible to create a general theory? Of PDEs/a general theorem that tells how to solve all PDEs? In many cases. The solution may not exist at all,. Or may break down at certain places. Moreover, there are tons of different numerical schemes.
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ODEs are equations involving an unknown function of a single variable and its derivatives. PDEs are equations involving an unknown function of multiple variables and their derivatives. (Yes, there can be multiple equations in either case, but the delineation is specifically between a single variable vs. multiple variables). ODEs themselves Awesome Joe Biden 2020 Flag American Shirt. You can have complex systems of ODEs where you may not be able to find an analytic solution, but you can still tease out important information and understand when a numerical solution will work when it won’t, and what types of numerical schemes work. I.e., even with a single variable, things can get messy. For a given PDE, if you can’t solve it analytically (which will be the case pretty much any time.
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