Uniform Convergence of Fourier Series

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SUMMARY

The discussion centers on determining the minimum number of terms (n) required for the average deviation of a Fourier Series to be less than 2%. The participants analyze the inequality derived from the Uniform Convergence of Fourier Series, specifically the expressions 2∏^2/M ≤ 0.02 and 2∏^2/M ≤ 2.0. The correct interpretation indicates that M must be at least 1000 to achieve a 2.0% error, confirming that M=1000 is the appropriate series for this requirement.

PREREQUISITES
  • Understanding of Fourier Series and their convergence properties
  • Familiarity with mathematical inequalities and error analysis
  • Knowledge of constants in mathematical contexts, specifically ∏
  • Basic skills in calculus and series summation
NEXT STEPS
  • Study the Uniform Convergence Theorem in detail
  • Explore error analysis techniques in Fourier Series
  • Learn about the implications of convergence rates in series
  • Investigate practical applications of Fourier Series in signal processing
USEFUL FOR

Mathematicians, engineering students, and anyone involved in signal processing or harmonic analysis will benefit from this discussion.

ZedCar
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Homework Statement


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


Homework Equations


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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Anyone happen to know?

I'm not sure if 0.02 should represent 2% or if 2 should?

Thank you
 

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