Higher Engineering Mathematics, Sixth Edition
642 Higher Engineering Mathematics 2180 2120 260 290 230 30 60 90 120 150 180 360 y 5 y (^7) y 8 y^9 y 10 y 11 y 1 y 2 y 3 y 4 2 ...
A numerical method of harmonic analysis 643 Thus the Fourier series for currentiis given by: i= 8 .04 sinθ− 2 .00sin3θ− 0 .04 si ...
Chapter 71 The complex or exponential form of a Fourier series 71.1 Introduction The form used for the Fourier series in Chapter ...
The complex or exponential form of a Fourier series 645 Rearranging gives: f(x)=a 0 + ∑∞ n= 1 [( an−jbn 2 ) ej 2 πLnx + ( an+jbn ...
646 Higher Engineering Mathematics Problem 1. Determine the complex Fourier series for the function defined by: f(x)= ⎧ ⎨ ⎩ 0 , ...
The complex or exponential form of a Fourier series 647 Hence, the extended complex form of the Fourier series shown in equation ...
648 Higher Engineering Mathematics Hence,cn= ∫ 1 0 te−j^2 πnt=uv− ∫ vdu = [ t e−j^2 πnt −j 2 πn ] 1 0 − ∫ 1 0 e−j^2 πnt −j 2 πn ...
The complex or exponential form of a Fourier series 649 Now try the following exercise Exercise 236 Further problems on the comp ...
650 Higher Engineering Mathematics thef(x) axis. Thus equation (15) could have been used, giving: cn= 2 L ∫ L 2 0 f(x)cos ( 2 πn ...
The complex or exponential form of a Fourier series 651 From equation (11), the complex Fourier series is given by: f(x)= ∑∞ n=− ...
652 Higher Engineering Mathematics i.e. f(x)= 8 π ( sinx+ 1 3 sin 3x+ 1 5 sin 5x + 1 7 sin 7x+··· ) Hence, f(x)= ∑∞ n=−∞ −j 2 nπ ...
The complex or exponential form of a Fourier series 653 The complex coefficient is given by equation (12): cn= 1 L ∫ L 2 −L 2 f( ...
654 Higher Engineering Mathematics 21029 28 27 26 25 24 23 22 21 0 1 2 3 4 (^12345678910) n |cn| Figure 71.6 210 29 28 27 26 25 ...
The complex or exponential form of a Fourier series 655 From equation (21), ej(ωt+α)=cos(ωt+α)+jsin(ωt+α) and Vmej(ωt+α)=Vmcos(ω ...
656 Higher Engineering Mathematics 2 rad/s 2 rad/s Real axis Imaginary axis 024 Figure 71.10 negative direction) with an ang ...
The complex or exponential form of a Fourier series 657 Now try the following exercise Exercise 238 Further problems on phasors ...
Revision Test 19 This Revision Test covers the material contained in Chapters 66 to 71.The marks for each question are shown in ...
Essential formulae Number and Algebra Laws of indices: am×an=am+n am an =am−n (am)n=amn a m n=n √ am a−n= 1 an a^0 = 1 Quadratic ...
660 Higher Engineering Mathematics Arithmetic progression: Ifa=first term andd=common difference, then the arithmetic progressio ...
Essential formulae 661 Triangle formulae: With reference to Fig. FA2: Sine rule a sinA = b sinB = c sinC Cosine rule a^2 =b^2 +c ...
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