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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 &lt; t &lt; 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 &lt; π , f (t − 2kπ ), for −π + 2kπ ≤ t &lt; 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...
View Full Document

Ask a homework question - tutors are online