Transcription of Trigonometric Fourier Series
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3 Trigonometric Fourier Series Ordinary language is totally unsuited for expressing what physics really asserts,since the words of everyday life are not sufficiently abstract. Only mathematics andmathematical logic can say as little as the physicist means to say. Bertrand Russell(1872-1970) to Fourier SeriesWe will now turn to the studyof Trigonometric Series . You have seenthat functions have Series representations as expansions in powers ofx, orx a, in the form of Maclaurin and Taylor Series . Recall that the Taylorseries expansion is given byf(x) = n=0cn(x a)n,where the expansion coefficients are determined ascn=f(n)(a)n!
Trigonometric Fourier Series “Ordinary language is totally unsuited for expressing what physics really asserts, ... (3.1) is a sum of sine and cosine functions with the same frequency and different amplitudes. If we can find a and b, then we can easily determine A and f: A = p a2 +b2, tanf = b a. We are now in a position to state our goal.
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