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Uniform Convergence of Fourier Series

Smythe · 2011-10-23 21:36:26

Find the minimum number required (value of n) for the average deviation of the Fourier Series to fall below 2% Use the Uniform Convergence of Fourier Series. Where Sm is the partial sum of the Fourier Series. C is constant. Here C is ∏^2 So, 2∏^2/M ≤ 0.02 M≥10000 M=10000 series will give a 2.0% error. or 2∏^2/M ≤ 2.0…

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23-10-2011 10:36pm

#1

Smythe

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Join Date: March 2010

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Find the minimum number required (value of n) for the average deviation of the Fourier Series to fall below 2%

Use the Uniform Convergence of Fourier Series.

Where Sm is the partial sum of the Fourier Series.
C is constant. Here C is ∏^2

So,

2∏^2/M ≤ 0.02 M≥10000 M=10000 series will give a 2.0% error.

or

2∏^2/M ≤ 2.0 M≥1000 M=1000 series will give a 2.0% error

Which of these two attempts is correct?

Thank you!

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