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In each of the following problems you are given a function on the interval - < x < . Sketch several periods of the corresponding periodic function of period 27. Expand the periodic function in a sine-cosine Fourier series: a. b. f(x) = -1, -<*1, x <n. 0, f(x) = 1, π Sketch each of the following functions on the interval (-1,1) and expand it in a sine-cosine series. f(x) = -{t 1, -<x<0, ㅠ 0<x< 2' <<n. -{ f(x)= 0 < x < 1. The functions f is given over one period. Sketch several periods and decide whether it is even or odd, then use (9.4) or (9.5) to expand it in an appropriate Fourier series. -1 < x < 0, -1, -< < 0, 0<x<n.

In each of the following problems you are given a function on the interval - < x < . Sketch several periods of the corresponding periodic function of period 27. Expand the periodic function in a sine-cosine Fourier series: a. b. f(x) = -1, -<*1, x <n. 0, f(x) = 1, π Sketch each of the following functions on the interval (-1,1) and expand it in a sine-cosine series. f(x) = -{t 1, -<x<0, ㅠ 0<x< 2' <<n. -{ f(x)= 0 < x < 1. The functions f is given over one period. Sketch several periods and decide whether it is even or odd, then use (9.4) or (9.5) to expand it in an appropriate Fourier series. -1 < x < 0, -1, -< < 0, 0<x<n.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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V. Find the exponential Fourier transform g(a) of the given function f(x) and write it as a Fourier integral (find g(a) in equation (12.2) and substitute your result into the first integral in equation (12.2)). [1, 0<x< 1 otherwise 0, Use the result to show that (12.2) f(x) = f(x) = g(a) = sin(a/2) α/2 -da = 2π g(a)e¹az da, f(x)e-iaz da.
Transcribed Image Text:V. Find the exponential Fourier transform g(a) of the given function f(x) and write it as a Fourier integral (find g(a) in equation (12.2) and substitute your result into the first integral in equation (12.2)). [1, 0<x< 1 otherwise 0, Use the result to show that (12.2) f(x) = f(x) = g(a) = sin(a/2) α/2 -da = 2π g(a)e¹az da, f(x)e-iaz da.
UMM AL-QURA UNIVERSITY College of Applied Science Department of Physics I. II. III. IV. b. f(x) = (9.4) Calculate the average values of the following functions on the given intervals: . f(x) = sin x on the interval (0,7) • g(x) = 1-e* on the interval (0,1) -x In each of the following problems you are given a function on the interval - < x < 7. Sketch several periods of the corresponding periodic function of period 27. Expand the periodic function in a sine-cosine Fourier series: a. (9.5) f(x)=1, HAHA 1, 0, -T<x<0, 0<x< f(x) = Mathematical Methods for Physics I Homework of chapter4 قسم الفيزياء 0, Sketch each of the following functions on the interval (-1,1) and expand it in a sine-cosine series. <x<H. <x<T. f(x) = -1. -HA&<0, 1, 0<x<n. If f(x) is odd, The functions f is given over one period. Sketch several periods and decide whether it is even or odd, then use (9.4) or (9.5) to expand it in an appropriate Fourier series. a {=} an=0. If f(x) is even, - 1<x<0, in 0 < x < 1. (71) b₁ = 0. Student's Name: nax f(x) sin da, ID:. an = f(x) cos 7 dx,
Transcribed Image Text:UMM AL-QURA UNIVERSITY College of Applied Science Department of Physics I. II. III. IV. b. f(x) = (9.4) Calculate the average values of the following functions on the given intervals: . f(x) = sin x on the interval (0,7) • g(x) = 1-e* on the interval (0,1) -x In each of the following problems you are given a function on the interval - < x < 7. Sketch several periods of the corresponding periodic function of period 27. Expand the periodic function in a sine-cosine Fourier series: a. (9.5) f(x)=1, HAHA 1, 0, -T<x<0, 0<x< f(x) = Mathematical Methods for Physics I Homework of chapter4 قسم الفيزياء 0, Sketch each of the following functions on the interval (-1,1) and expand it in a sine-cosine series. <x<H. <x<T. f(x) = -1. -HA&<0, 1, 0<x<n. If f(x) is odd, The functions f is given over one period. Sketch several periods and decide whether it is even or odd, then use (9.4) or (9.5) to expand it in an appropriate Fourier series. a {=} an=0. If f(x) is even, - 1<x<0, in 0 < x < 1. (71) b₁ = 0. Student's Name: nax f(x) sin da, ID:. an = f(x) cos 7 dx,
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