$1.(35$ Points$)$ The map and data below represent an extraction well at steady state. The extraction well is overprinted on a hydraulic gradient where groundwater would be flowing from the northeast corner to the southwest. For this problem you do not have an analytical solution for this problem. Calculate the gradient and magnitude of the gradient using the centered finite difference method. For this problem it is important to show your work for at least three locations. For the remainder of them you can use Excel or Python to fill out the tables below. Don't forget about boundary conditions. To fill out the tables below you can use Excel or Python. Keep $5$ decimals for all of your answers.