Introduction to Fourier Integral

[overseastar]

I have a homework question asking to construct an orthonormal system from the three functions: 1, x, 3x^2 - 1, I know we can approach it using linear algebra method, but as this is a calculus course, I don't think that's what my prof wants us to use. Can anyone guide me through this? Thanks a bunch!

 

[cogito²]

I have a homework question asking to construct an orthonormal system from the three functions: 1, x, 3x^2 - 1, I know we can approach it using linear algebra method, but as this is a calculus course, I don't think that's what my prof wants us to use. Can anyone guide me through this? Thanks a bunch!

Well an "orthonormal set" is an object out of linear algebra so you're not going to be able to avoid using techniques out of linear algebra. You'll probably have to use the Gram-Schmidt process. But that depends specifically on the inner product you're using and since you didn't specify what that is, I can't really help you much more than this. (The inner product is probably defined in terms of an integral and that's where the calculus exercise would come in.)

 

[matt grime]

Why do people presume that just because 'this is a type X' course that they will never have to use something that they might not consider to be of 'type X'?

 

[overseastar]

Sorry, that was just a little assumption I made, matt grime.
i guess i should learn to start linking all my math concepts from the two types courses together.
The original question says that the 3 orthogonal functions are with respect to the weight function 1 on the interval [-1,1]

 

[matt grime]

The prerequisites you need to know are explained in the course material, and are evident in the syllabus, usually. Try to keep the discussion in the other thread to avoid duplicate answers.