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You will be writing three different Python programs, and you will upload a single zip file named Homework4.zip. Name the three programs prob1.py, prob2.py and prob3.py In this assignment, you must use variables, loops, if statements, your own function definitions and function calls to write the required functions. For now, you may not use any of the powerful functions available in python modules, with a few exceptions: You may import functions from the math copy. matplotlib.plot and numpy. You may NOT use numpy.linalg.lstsq0 or numpy.linalg.det 1) Write a program that demonstrates the Fourier Series method as defined on the MAE 3013 equation sheet. You must write and call at least the following 3 functions: def FourierCoeffs(func. L. nterms) # which calculates and returns the Fourier a's and b's # the a's and b's are each numpy arrays of length terms # func is the name of the function. L is the half-period. # this function must call scipy integrate.quado def PlotFourier(a. 6. L. xmin, xmax npoints=5000) # which plots the Fourier Series def main(): def Sharkfin(x): if x