Due Date Is Over
Due Date: 13-09-2024
Half Range Series and Harmonic Analysis
1. Find the Half range cosine series for f(x)=x in (0,Ï€) .
2. Find the half range cosine series for f(x)=x(Ï€-x) in (0,Ï€)
3. Find the Half range cosine series of f(x)=(Ï€-x)2, 0<x<Ï€. Hence find the sum of series
4. Find the half range cosine series expansion of (x-1)2 in 0<x<1.
5. Obtain the Fourier cosine series expansion of f(x) =x in 0<x<4. Hence deduce the value of
a.
6. Find the Fourier series of y=f(x) up to third harmonic which is defined by the following data in (0,2Ï€)
x 0 π/3 2π/3 π 4 π/3 5 π/3 2 π
f(x) 1 1.4 1.9 1.7 1.5 1.2 1
7. Find the Fourier cosine series up to third harmonic to represent the function given by the following data:
x 0 1 2 3 4 5
y 9 18 24 28 26 20
8. Determine the first two harmonics of Fourier series for the following data.
x 0 T/6 T/3 T/2 2T/3 5T/6 T
f(x) 1.98 1.30 1.05 1.30 -0.88 -0.25 1.98
