help- heat equation

1 .) i added several problems which i couldnt understand the approach for solving them.
i'm kinda confused, will glad if someone would guide me.

2.) in class weve talked about and calculated . n orders(0,1,2,3) of moments, how is it to do with the heat equations? and what is the importance?

thanks

chen
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 Quote by chenrim 1 .) i added several problems which i couldnt understand the approach for solving them. i'm kinda confused, will glad if someone would guide me. 2.) in class weve talked about and calculated . n orders(0,1,2,3) of moments, how is it to do with the heat equations? and what is the importance? thanks chen
For 1), I'd try the method of "Separation of variables". In other words, you make the ansatz (or assume) that a solution to the heat equation is of the form $u(x,t)=F(x)G(t)$. I suggest you to read about this method on the Internet.
2)I have no idea, never heard of such thing.