If we make use of eulers formula we can write the

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 10. 76 3.3.4. Find the Fourier sine series of the following function defined on the interval [0, 1]: f (t) = 5t(1 − t). 3.3.5.(For students with access to Mathematica) Find numerical approximations to the first ten coefficients of the Fourier sine series for the function f (t) = t + t2 − 2t3 , defined for t in the interval [0, 1], by running the following Mathematica program f[n ] := 2 NIntegrate[(t + t∧2 - 2 t∧3) Sin[n Pi t], {t,0,1}]; b = Table[f[n], {n,1,10}] 3.4 Complex version of Fourier series* We have seen that if f : R → R is a well-behaved function which is periodic of period 2π , f can be expanded in a Fourier series f (t) = a0 + a1 cos t + a2 cos(2t) + . . . 2 +b1 sin t + b2 sin(2t) + . . . . We say that this is the real form of the Fourier series. It is often convenient to recast this Fourier series in complex form by means of the Euler formula, which states that eiθ = cos θ + i sin θ. It follows from this formula that eiθ + e−iθ = 2 cos θ, e−iθ + e−iθ = 2i sin θ, or eiθ + e−iθ eiθ + e−iθ , sin...
View Full Document

This document was uploaded on 01/12/2014.

Ask a homework question - tutors are online