Determine the Fourier series of the following function
Determine the Fourier series of the following function f(x) = 1-1 0<x<2 3 - 2 <r<4
using the orthogonal Find the Fourier-Bessel series on (0, R] of the function f(x) set Ja (Az2x) (に1, 2, . . . ). using the orthogonal Find the Fourier-Bessel series on (0, R] of the function f(x) set Ja (Az2x) (に1, 2, . . . ).
Computing a fourier series : Compute the Fourier series for the function f(2)= {I 0 if – <r<0 1 if 0 <<< on the interval -1 <I<.
determine the fourier series if -2 Sto f(3) = { 1 + x2 if 0<<<2 f(x + 4) = f(x) - 5={17
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)...
Find the Fourier series of the following function, and calculate the sum of rn. n=1 f(x) = 12,2 if 0<r<\ if-1< 0 f(x + 2)-f(x)
Problem 3: Derive the Fourier series for the function f(x) = x + (1/2) for −1 < x < 1; plot the function and its Fourier series for −3 < x < 3
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks 3. Consider the function defined by...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of period Which of the following statement is true about the Fourier series of f? (A) The Fourier series of f has only cosine terms. (B) The Fourier series of f has neither sine nor cosine terms. (C) The Fourier series of f has both sine and cosine terms. (D) The Fourier series of f has only sine terms.
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)...