- #1
pinkflahippo
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I'm working on a P.D.E. homework problem and the one part of it my professor gave us a function and wants us to set it equal to a given series and find the variable. Specifically, find f(sub n) in
x-x^{2}=\sum (from n=1 to \infty) f(sub n) sin(n\pix)
I'm not sure exactly how to do this. I tried writing out the series, then taking the derivative of both sides and setting x=0 (then repeat process) and trying to find a pattern, but I ended up getting an unequal statement. My attempt there was hoping that something would zero out and I could see how the f is changing from f(sub 0) to f(sub 1) to f(sub 2)... I guess my question is where my logic is wrong and how I should begin the problem instead. Thanks in advance!
x-x^{2}=\sum (from n=1 to \infty) f(sub n) sin(n\pix)
I'm not sure exactly how to do this. I tried writing out the series, then taking the derivative of both sides and setting x=0 (then repeat process) and trying to find a pattern, but I ended up getting an unequal statement. My attempt there was hoping that something would zero out and I could see how the f is changing from f(sub 0) to f(sub 1) to f(sub 2)... I guess my question is where my logic is wrong and how I should begin the problem instead. Thanks in advance!
