the first few steps this program produces plot of the vertical position with timeas seen in figure as you noticethe code lines from the ball py program in have not changed muchbut the height is now computed and plotted for thousand points in timelet us take look at the differences between the new program and our previous program from the topthe first difference we notice are the lines from numpy import from matplotlib pyplot import you see the word import hereso you understand that numpy must be libraryor module in python terminology this library contains lot of very useful functionality for mathematical computingwhile the matplotlib pyplot module contains functionality for plotting curves the above import statement constitutes quick way of populating your program with all necessary functionality for mathematical computing and plotting howeverwe actually make use of only few functions in the present programlinspaceplotxlabeland ylabel many computer scientists will therefore argue that we should explicitly import what we need and not everything (the star *)from numpy import linspace from matplotlib pyplot import plotxlabelylabel others will claim that we should do slightly different import and prefix library functions by the library nameimport numpy as np import matplotlib pyplot as plt np linspace( plt plot(typlt xlabel(' ( )'plt ylabel(' ( )'we will use all three techniquesand since all of them are in so widespread useyou should be familiar with them too howeverfor the most part in this book we shall do from numpy import from matplotlib pyplot import for convenience and for making python programs that look very similar to their matlab counterparts the function linspace takes parametersand is generally called as linspace(startstopnthis is our first example of python function that takes multiple arguments the linspace function generates equally spaced coordinatesstarting with start