find the Fourier series represen- tation of the given function over the indicated fundamental interval and use a computer to plot the indicated partial sum Sn(x) over the fundamental interval. f(x) = { 0, sinx, 0≤x≤л. Plot Sε(x).

Please solve the following by hand and without the use of AI. I am working to understand the step by step procedure of solving this problem so pleaase give a detailed step by step procedure, explaining each part as you go. Thank you!

Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0- 0.8- 0.6- 0.4- 0.2 0.0- -0.2- -0.4- -0.6 T T T 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep.

vibrations, please help

Please show steps

answer please

HW7_4 We wish to find the result of sin(x - 2) dx 1.6 However, this function is difficult to integrate. Hence, instead of calculating ¹6 sin(ex − 2) dx we will estimate its value by computing the integral of the interpolating polynomial fitted through the following data points which are the actual values of f(x) = sin(e* — 2). This is a much easier task as polynomials are easy to integrate and it provides a good estimate if the two functions are look close to each other when plotted (areas under the curves are also similar) X 0 y 0.4 0.8 1.2 -0.8415 -0.4866 | 0.2236 0.9687 1.6 0.1874 Accordingly, carry out the following tasks (all plots are to be produced on the same figure): a) Plot the above data points using discrete point plotting. b) Plot the function f(x) = sin(e* — 2). c) Use polyfit to do polynomial interpolation for the above data. Plot the interpolating polynomial, using polyval. d) At this point, run your code to produce the plotting results. Do f(x) and the interpolating…

Use MATLAB

The integrals arise when finding the Fourier series expansion of eax over the interval -L< x < L. Use the result cosnл = (-1)" for integral values of n to establish the stated result. eax sin nxdx = (−1) n+1 (eaл. Lea e -ал for integral (a² + n²) values of n.

A9