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Exercise 102

Avg difficulty 2.5

Let f(t)=tfor   −λ<t≤λ   (for some λ>0)f(t) = t \qquad \text{for } \; {-\lambda} < t \leq \lambda \; \text{ (for some } \lambda > 0 \text{)} extended periodically.

  1. Compute the Fourier series for f(t)f(t).
  2. Write out the series explicitly up to the 3rd3^{\text{rd}} harmonic.

Lebl, Notes on Diffy Qs, §4.3 More on the Fourier series, exercise 102

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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.