Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Going over some revision. Not really sure what to do for the last bit of aii)

enter image description here

I know at $x = 0$, it will converge to $0$ and at $x = \frac{M}{2}$ it will converge to $1$, I'm not seeing how this relates to answering the last bit. Thanks!

share|improve this question
1  
How do you know it converges to $\frac{3}{2}$ at $x=0$? I think it shouldn't. –  Matt L. Apr 22 '13 at 15:29
    
Sorry, I meant it converges to zero, I was looking at a different question and getting muddled up! –  Mike Miller Apr 22 '13 at 15:36
    
OK, at discontinuities the Fourier series converges to the mean of the values to the left and to the right of the discontinuity, i.e. at $x=0$ it indeed converges to 0. –  Matt L. Apr 22 '13 at 16:06

1 Answer 1

It should converge everywhere $f$ is continuous to the value of $f$ here. This gives the result you need. As far as I can see, they're just emphasizing that it works in the middle but not at the endpoints. The "hence" seems misleading.

share|improve this answer
    
I can't see how just plugging $M=20$ in shows that works though. I feel I'm not understanding something fundamental here. –  Mike Miller Apr 22 '13 at 15:57
    
The choice of $M$ has nothing to do with anything; the only variable which matters is $x/M$. I think the question is very poorly phrased. The only thing there is to prove is that the Fourier series converges, which you can't deduce from its value at two points, as far as I can see –  Sharkos Apr 22 '13 at 16:07
    
So what would I do then? Quite confused now as to what I have to show. –  Mike Miller Apr 22 '13 at 16:14
    
Well, as I say, the question is very poorly worded. If you can assume the result that piecewise continuous functions like this have convergent Fourier series away from discontinuities (where you get the average of the two sides), then the result is trivial. Otherwise, it has nothing to do with the rest of the question, and it's bizarre. I guess I can't help with the interpretation. –  Sharkos Apr 22 '13 at 16:36
    
Well thanks anyway! –  Mike Miller Apr 22 '13 at 17:40

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.