MHB Find Fourier Sin Series for f(x)=1, 0 < x < c

[Joystar77]

3. Fourier sin series for f(x) = 1, 0 < x < pi is given by 1 = 4/n E 1/ (2n-1) times sin (2n-1) x, (0 < x < n).

Using this, find the Fourier sinc series for f(x)= 1, on 0 < x < c where c > 0. Then find the Fourier series for g(x), x > 0 where g(x) = 1, 0 < x < c, -1, c < x < 2c, g (x + 2c) = g(x), g (nc) = 0, n = 1, 2, 3, ...

Finally, sketch the graph of g(x), x > 0. Be sure to justify convergence is the F series to g(x) at every x > 0.

 

[Joystar77]

Sorry, I forgot to mention in the original thread of this posting that I am totally lost and confused with this problem. I don't understand it and am not sure exactly how to work out this problem or where to start at. Can someone please help me step-by-step with this problem?

 

[Joystar77]

I thought maybe it might help to at least use some mathematical symbols in this problem than none at all. Here is the problem again as follows and I hope that its easier to read:

Fourier sin series for f (x) = 1, 0 < x < Pie, is given by

1 = 4 / n $$$$ 1/ (2n-1), sin (2n-1)x, (0 < x < Pie)

Using this, find the Fourier sin series for f (x) = 1 on 0 < x < Pie, where c > 0. Then find
Fourier sin series for f (x) = 1, 0 < x < Pie, is given by

1 = 4 / n $$$$ 1/ (2n-1), sin (2n-1)x, (0 < x < Pie), where c > 0. Then find the Fourier series for g (x), x > 0, where g (x) =

1, 0 < x < c

-1 c < x < 2c , g (x + 2c) = g (x),

g (nc) = 0, n = 1, 2, 3, …

Finally, sketch the graph of g (x), x >0

Be sure to justify convergence is the F series to g (x) at every x > 0.

 

[Dustinsfl]

\(\text{pie}\neq \pi\)

 

[Joystar77]

Please explain this on what your trying to say! I thought that since I wasn't able to find the mathematical symbol under Microsoft Word, then I would spell it out. Isn't the word spelled correctly for math when using the following:

Pie (∏)?

What is the difference between pie and pi in math?

\(\text{pie}\neq \pi\)

 

[Dustinsfl]

Please explain this on what your trying to say! I thought that since I wasn't able to find the mathematical symbol under Microsoft Word, then I would spell it out. Isn't the word spelled correctly for math when using the following:

Pie (∏)?

What is the difference between pie and pi in math?

Pie you eat and pi is an irrational number.

To achieve \(\pi\) type
Latex Code:

\(\pi\)

Also in the notes section you will find a whole pdf on Fourier Series.

http://mathhelpboards.com/math-notes-49/fourier-series-integral-transform-notes-2860.html

 

[Joystar77]

Thanks for answering my question (s) and letting me know this information. What I typed was questions that my instructor gave me so the wording of the questions he is asking me to do is an error on his part. I will correct that for next time. Thank you again!

Pie you eat and pi is an irrational number.

To achieve \(\pi\) type
Latex Code:

\(\pi\)

Also in the notes section you will find a whole pdf on Fourier Series.

http://mathhelpboards.com/math-notes-49/fourier-series-integral-transform-notes-2860.html