Python Assignment on Jupyter Notebook.

Analysis of formulas derived from Taylor Series

The primary goal of the task is to have you write Python/NumPy/Matplotlib code for computing finite difference approximations for the first derivative of a specified function, and to plot these approximations along with the analytical first derivative. Your tasks will be to

Write the code for the specified function, its derivative, and its string LaTeX format (so that you can put this in the plot title)

Write code for functions to compute the forward, backward and centered finite difference approximations of the first derivative. I have provided you with code for the forward difference, fda_fwd(), so you simply need to emulate this for the correct backward and centered finite difference approximations.

Plot the three approximations as well as the true first derivative curves. Again, I have gotten you started by plotting the forward difference curve and the true first derivative curve. You should enhance the plot by adding your name and the stepsize to it, as I have illustrated in the following graphic

Once you have this working with the function that I have given you, you should prepare your deliverables by

Using a new function, , create plots for values of and .

In a Markdown section underneath the code, explain in GREAT DETAIL how the Python functions are working. I want you to convince me that you understand all the details of exactly what kinds of values and structures are being passed into the functions, what kinds of values and structures are being used locally within the functions, and what kinds of values and structures are being returned from the functions. Likewise, you should explain in detail the plotting functions being used. The point of this step is to insure that you fully understand the foundations of NumPy and Matplotlib and how they are being used in this code. This step is very important. Dont take it lightly. Ive given you a lot of code without making you figure it out for yourself, so you should take the time to fully understand and explain it

fptrue fda fwd fptrue -fda fwd - fda bwd _ fda ctr _ fda bwd fdactr