kindly solve Q3 kindly solve Q4 (25 Puan) f(x)={0 0 < x <4 Expand f(x) in Fourier series. 8 3. (25 Puan) f...
Let f(x) = x.a) Expand f(x) in a Fourier cosine series for 0 ≤ x ≤ π.b) Expand f{x) in a Fourier sine series for 0 ≤ x < π.c) Expand fix) in a Fourier cosine series for 0 ≤ x ≤ 1.d) Expand fix) in a Fourier sine series for 0 ≤ x < 1.
5. Expand the following functions as Fourier-Legendre series: (i) f(x)=x3 x >0 x < 0 1, (ii) f(x) = lo,
5. Expand the following functions as Fourier-Legendre series: (i) f(x)=x3 x >0 x
2, (a) Expand f(x) = 8, 0 < x < 3, into a cosine series of period 6. (b) Expand f(x) 8, 0<x3, into a sine series of period 6. (c) For each series, determine the value to which the series converges to when x (d) Graph the sine series in part (b) for 3 periods, over the interval [-9, 9] 42.
2, (a) Expand f(x) = 8, 0
Question 3 4 pts n. Q4. n 0 << A Fourier COSINE series is required for the function defined by f(x) = 0, (a) Write down the period T and the frequency wo of the extended function. (6) Calculate the coefficients a, = 5" f(x) cos(n wox) dx and simplify your answer. n <<n 3
find fourier series of
Question 3 Find Fourier series of f(x)= 0 if -55x<0 and f(x) = 1 if 0<x<5 which f(x) is defined on (-5,5).
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Expand the function, f(x) = x cosx in a Fourier series valid on the interval -1 <x<t. You must show the details of your work neatly.
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 < L, t>0} subject to the boundary conditions (0, t) (L, t) (x,0) f(x)
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 0} subject to the boundary conditions (0, t)...
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0 < x < 4 Using notation similar to Problem # 2 above, (a) Find the value of co. (b) Find the function g1(n, x). (c) Find the function g(n, x).
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x) = sin(x) on the interval [0, 1]. Hint: For the cosine series, it is easiest to use the complex exponential version of Fourier series. Question 5. Solve the following boundary value problem: Ut – 3Uzx = 0, u(0,t) = u(2,t) = 0, u(x,0) = –2? + 22 Question 6. Solve the following boundary value problem: Ut – Uxx = 0, Uz(-7,t) = uz (77,t)...
Problem 1. Expand f(x) em 1. Expand fo) (1.0 ,-π < x < 0 0, 0<X<T in a sine, cosine Fourier series. write out a few 0, 0<x<π in sine,cosine Fourier series Write out aferw terms of the series