$7 FourierSeriesI. Introductionsin3t +sin5t +sin7t)(sint +U=一I53元u0.5-212-13-0
§7 Fourier Series sin7 ) 7 1 sin5 5 1 sin3 3 1 (sin 4 u t + t + t + t = I. Introduction
$7 Fourier SeriesI.Introductionsin3t +sin5t +sin 7t +--sin9t)(sint+.u=-93元5n5-2123-14sin3t +=sin5t +=sin7t +..)u(t) = -(sint +=s35元(一元<t<元,t±0)
§7 Fourier Series sin7 ) 7 1 sin5 5 1 sin3 3 1 (sin 4 ( ) + + + + u t = t t t t (− t ,t 0) sin9 ) 9 1 sin7 7 1 sin5 5 1 sin3 3 1 (sin 4 u t + t + t + t + t = I. Introduction
$7 Fourier SeriesI, Orthogonality of Trigonometric functions1.Trigonometric series80aoZ(a, cos nx + b, sin nx)2n=l2.Trigonometric functions1, cos x,sin x,cos 2x, sin 2x, ...cos nx, sinnx,
§7 Fourier Series II、Orthogonality of Trigonometric functions 1. Trigonometric series = + + 1 0 ( cos sin ) 2 n an nx bn nx a 2. Trigonometric functions 1,cos x,sin x,cos 2x,sin2x, cos nx,sinnx,
$7 FourierSeriesII, Orthogonality of Trigonometric functions3.OrthogonalityAcos nxdx = 0,sinnxdx = 0, (n =1,2,3,...)元一元0,m+n元sinmx sin nxdx :元，元m=n[0,m≠n元cos mx cos nxdx :一元[元,m=n元sin mx cos nxdx = 0.元
§7 Fourier Series II、Orthogonality of Trigonometric functions 3. Orthogonality cos = 0, − nxdx sin = 0, − nxdx (n = 1,2,3, ) − sinmx sinnxdx , , 0, cos cos = = − m n m n mx nxdx − sinmx cosnxdx , , 0, = = m n m n = 0