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Review of Fourier Series

Part 4: Summary

  1. How must the form of the approximating polynomials and the formulas for the Fourier coefficients be changed in going from a 2 pi-periodic function to a 2L-periodic function?
  2. For which functions of period 2L are the Fourier approximations composed entirely of sine terms? entirely of cosine terms?
  3. How is it possible to approximate a function on [0, L] by a trigonometric polynomial containing only sine terms? only cosine terms?
  4. When does the half-range sine approximation to a continuous function f on [0, L] converge to f at 0?
  5. When does the half-range sine approximation to a continuous function f on [0, L] converge to f at L?
 

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