MATH 264 Study Guide - Quiz Guide: Fourier Series, List Of Trigonometric Identities, Scilab

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 264
• Professor: Sancho

Document Summary

This assignment will not be marked: let. Add the two versions of the trigonometric identity in the hint together: cos(a + b) = cos(a) cos(b) sin(a) sin(b) cos(a b) = cos(a) cos(b) + sin(a) sin(u) = cos(a + b) + cos(a b) = 2 cos(a) cos(b). 1 (cid:19) + cos(cid:18) (m n) x (cid:19) + (m n) . = 0. (cid:19)(cid:21) dx sin(cid:18) (m n) x (cid:19)(cid:21) : take l = and apply the formulae for the fourier coe cients: a0 = (n 1) an = N2(cid:20) sin(nx) nx cos(nx)(cid:21)0 f (x) sin(nx)dx. 0 if n = 1, 3, 5, . if n = 2, 4, 6, . ( 1)n n + 1. (2n + 1)2 cos((2n + 1)x) + ( 1)n n + 1. Xn=1 sin(nx): seperation of variables yields solutions of the form u(x, t) = b + ax. + (g cos x + h sin x)e 2 t steady state.