It follows that if f wodd a0 f 1 0 an f cos nx

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Unformatted text preview: he function f (t) = sin3 t is periodic of period 2π . Find its Fourier series. 3.1.3. The function f (t) = t, for −π < t < π , 0, for t = π , can be extended to be periodic of period 2π . Find the Fourier series of this extension. 3.1.4. The function f (t) = |t|, for t ∈ [−π, π ], can be extended to be periodic of period 2π . Find the Fourier series of this extension. 3.1.5. Find the Fourier series of the following function: f (t) = t2 , for −π ≤ t < π , f (t − 2kπ ), for −π + 2kπ ≤ t < π + 2kπ . 3.1.6. Establish the formulae (3.5) and (3.6), which were given in the text. 3 See, for example, Ruel Churchill and James Brown, Fourier series and boundary value problems , 4th edition, McGraw-Hill, New York, 1987 or Robert Seeley, An introduction to Fourier series and integrals , Benjamin, New York, 1966. 68 3.2 Inner products There is a convenient way of remembering the formulae for the Fourier coefficients that we derived in the preceding section. Let V be the set of...
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