MATH 1005 Lecture Notes - Lecture 1: Fourier Series

• School: Carleton University
• Department: Mathematics
• Course: MATH 1005
• Professor: Mark Blenkinsop

Document Summary

Fourier formulae: the full fourier series of f (x) is always de ned on the full period, [ l, l], such that f (x) = a0. L where a0 = an = bn = L f (x) dx f (x) cos( n x. ) dx: the half fourier series of f (x) are always de ned on the half period, [0, l], and require either an odd extension or even extension. Note the doubling of the integral, while only integrating over the half period: from 0 to l, not from l to l! (a) the fourier sine series (from the odd extension): f (x) = ) dx (b) the fourier cosine series (from the even extension): f (x) = a0. 0 f (x) dx f (x) cos( n x.