Finding an Orthogonal Polynomial to x^2-1/2 on L2[0,1]

mandygirl22
Messages
4
Reaction score
0
Find a polynomial that is orthogonal to f(x)=x2-1/2 using L2[0,1].

I have looked all in the textbook and all over the internet and have found some hints if the interval is [-1,1], but still do not even know where to start here. I think I was gone the day our professor taught this because I do not know anything about it and the book does not make any sense out of it. Thanks for your help!
 
Physics news on Phys.org
Well, just DO it! The simplest kind of polynomial is linear. Integrate Ax+ B times [math]x^2- 1/2[/math] from 0 to 1 and choose A and B so the integral is 0.
 
*hits forehead* I knew there had to be some simple way of doing it that I was ignoring! Thanks!

(and the REALLY HARD solution ended up being f(x)=x) :smile:
 
Thread 'Derivation of equations of stress tensor transformation'
Hello ! I derived equations of stress tensor 2D transformation. Some details: I have plane ABCD in two cases (see top on the pic) and I know tensor components for case 1 only. Only plane ABCD rotate in two cases (top of the picture) but not coordinate system. Coordinate system rotates only on the bottom of picture. I want to obtain expression that connects tensor for case 1 and tensor for case 2. My attempt: Are these equations correct? Is there more easier expression for stress tensor...
Back
Top