### Fourier-Legendre Expansion of F(θ) = 1 - cos 2θ

Number 18. Please don't do the CAS nor the plot. Please see the attached file for the fully formatted problems.

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Number 18. Please don't do the CAS nor the plot. Please see the attached file for the fully formatted problems.

1.(a) Evaluate the Fourier coefficients ao, an, bn and the exponential coefficient Dn for the waveform shown below; do not use MATLAB or a calculator for integrations. (b) Plot 2 or 3 cycles of the Fourier series using MATLAB and verify whether the plot matches the given waveform. (c) Find C0 and Cn from the answer to part (a)

Can someone please solve this heat equations with details on how to arrive at the solution.? Solve the heat equation: u_t = 3*u_xx with the following I.C/B.C: u(0,t) = u(L,t) = 0 u(x,0)=L*[1-cos(2*Pi*x/L)]

Write the cosine and sine Fourier Series. Determine the sum of each. { 4x 0≤x≤2 f(x) ={ -3 2<x<4 { 1 4≤x≤7 Please see the attached file for the fully formatted problems.

Find Fourier series for f(x) = {-4 for x greater than/= -pi, and x less than/= 0 { 4 for x greater than/= 0, and less than/= pi

Find the first four terms of the Fourier series expansion of the function f(x) = (1 - (x^2/pi^2))per on the interval (-pi, pi). Make a graph of f(x) with the two Fourier series expansions. Show three periods of f(x).

Please see attachment.

See attachment. Please use the Fourier transform tables rather than a direct computation. Cheers.

Find the nth Fourier coefficient (in terms of the an's) of the signal y(t) defined by: y(t) = x(t+1) + x(1-t), for all t in <R>. Please see attachment for more readable form of question.

For of the periodic functions , I need to find the value to which the Fourier series converges at x= 0 , Pi/2 , - Pi/2 , Pi , -Pi , 2Pi , - 2Pi Using Dirichlet's theorem --- (See attached files for full problem description)

Please help ... what is the Fourier series expansion of f(t). It is a multiple answer question. (See attached file for full problem description)

The problem is from Fourier Cosine and Sine Transforms, and Passage from Fourier Integral to Laplace Transform: Solve using a cosine or sine transform. u'' - 9u =50e^-3x (0<x<infinty) u'(0) = 0, u(infinity)bounded

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. Fourier Cosine and Sine Transforms, and Passage from Fourier Integral to Laplace Transform: Given the rectangular pulse.. Please see attached.

Evaluate the following using Appendix D (Fourier Tranform Table). You may need to use more than one entry. Cite, by number, any entrie that you use. a)F{4x^2e^(-3|x|)} c) F{cos 3x/(x^2 + 2)} Please see the attached file for the fully formatted problems.

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. 3. Expand... in terms of the eigenfunctions of the Sturm-Liouville problem. Please see attached.

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. Expand the function f(x) = {x^4, 0 <= x < 2 {0, 2 <= x <= pi in terms of the eigenfunctions of the given eigenvalue problem. Use computer software, such as the Maple int command, to evaluate the expan

4. Use the results of Exercise 3 to recast each of the following differential equations in the Sturm-Liouville form (1a). Identify p(x), q(x), and w(x). (a) xy" + 5y' + lambda xy = 0 (b) y" + 2y' + xy + lambda x^2y = 0 (c) y" + y' + lambda y = 0 (d) y" - y' + lambda xy = 0 (e) x^2y" + xy' + lambda x^2y = 0 (f) y" + (cot

1. Identify p(x), q(x), w(x) alpha, beta, gamma, delta, solve for the eigenvalues and eigenfunctions, and work out the eigenfunction expansion of the given function f. If the characteristic equation is too difficult to solve analytically, state that and proceed with the rest of the problem as though the lambda_n's were known.

The problems are from Fourier Series, Fourier Integral, and Fourier Transform. Please show each step of your solution. Obtain a computer plot of the partial sums of the Fourier series (19) of the periodic function shown in the attached figure, for (a) n =2 (b) n = 5 (c) n = 10 (d) n = 20 (e) n = 30 (f) n = 50 Ple

Work out the Fourier series of f, given over one period as follows. At which values of x does the series fail to converge to f(x)? To what values does it converge at those points? (h) |cos x| for all x (k) x on 0<x<1, 1<x<2

Find the Fourier transfrom of the following function: f(t) = te^(-2t), for t > 0

Find the complex Fourier series coefficients for the function x(t) depicted in the below figure Please see

Here, we have to find f(t) from the given value of Cn. I am not able to arrive at f(t)={3/[5-4cos(pit+pi/20)} despite many attempts. Please show me how to arrive at the final expected f(t) value.

Proof regarding a Fourier Transform for L1R. Show 1/2pi ∫-1 -->1 (1 -|y|)e^(iyx) dy = 1/2pi [(sin x/2)/(x/2)]^2 Please see the attached file.

In the interval (-pi, pi), δn(x) = (n/x^1/2) e ^(-n^2 x^2) a) Expand δn(x) as a Fourier Cosine Series. b) Show that your Fourier Series agrees with a Fourier expansion of δn(x) in the limit as n--> infinity. Please see the attached file for the fully formatted problems.

A signal function f(t) of period 2 pi is given by: (See attached file) As required by my question I have drawn the above signal in the interval -4pi < t < 4pi which I beleive to be a sawtooth signal. I also need to find if f(t) is odd, even or neither, hence state which coefficients, if any, are zero. If there

A function h(x) is positive or zero for all values of x. Assume h(x) is even. If the Fourier transformation of h(x) is H(u) show that... (See attachment for full question)

The answer is provided - please provide step by step work and explaination and solution. 4. Find the Fourier series of the periodic function attached...

Use the Fourier series of the function f(x) and the properties of Fourier series to obtain the Fourier series of... (aee attachment for full question)

Yinon, If you do not wish to work on the Laplace diffusion problem anymore, I would like to see the solution you have formulated thus far and will pay you some credits even though it is not entirely correct. Please leave me a note. Thank you!