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Exercise 106

Avg difficulty 2.5

Let f(t)={0if   −2<t≤0,2if   −0<t≤2,f(t) = \begin{cases} 0 & \text{if } \; {-2} < t \leq 0, \\ 2 & \text{if } \; \phantom{-}0 < t \leq 2, \end{cases} extended periodically. Suppose F(t)F(t) is the function given by the Fourier series of ff. Without computing the Fourier series evaluate

  1. F(0)F(0)
  2. F(−1)F(-1)
  3. F(1)F(1)
  4. F(−2)F(-2)
  5. F(4)F(4)
  6. F(−9)F(-9)

Lebl, Notes on Diffy Qs, §4.3 More on the Fourier series, exercise 106

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.