Page - 5 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

1.2 APythonProgramwithVariables 5 To download Anaconda, you must pick the Anaconda version suitable for your machine (Windows/Mac/Linux) and choose which version of Python you want (3.6 is used for this book). When the download has completed, proceed with the installationofAnaconda. After installation, you may want to (search for and) start up Spyder to see what it looks like (see also Appendix A). Spyder is an excellent tool for developing Pythoncode.So,unlessyouhavegoodreasonstochooseotherwise,werecommend Spyder tobeyourmain“working”environment,meaningthat to read,writeandrun code you start Spyder and do it there. Thus, it is a good idea to make Spyder easy accessibleonyourmachine. With Anaconda installed, the only additional package you need to install is Odespy.3 Odespy is relevant for thesolvingofdifferentialequations thatwetreat in Chaps.8and9. In Appendix A you will find more information on the installation and use of Python. 1.2 APythonProgramwithVariables Our first example regards programming a mathematical model that predicts the height of a ball thrown straight up into the air. From Newton’s 2nd law, and by assuming negligible air resistance, one can derive a mathematical model that predicts theverticalpositiony of the ball at time t: y=v0t−0.5gt2. Here,v0 is the initialupwardsvelocityandg is theaccelerationofgravity,forwhich 9.81ms−2 is a reasonable value (even if it depends on things like location on the earth). With this formula at hand, and when v0 is known, you may plug in a value for timeandgetout thecorrespondingheight. 1.2.1 TheProgram Letusnext lookat aPythonprogramforevaluating this simple formula.Todo this, we need some values for v0 and t, so we pick v0 = 5ms−1 and t = 0.6s (other choiceswouldof coursehave been just as good).Assume the programis contained as text inafile namedball.py, reading # Program for computing the height of a ball in vertical motion v0 = 5 # Initial velocity g = 9.81 # Acceleration of gravity 3 The original version of Odespy (https://github.com/hplgit/odespy) was written in Python 2.7 by H.P. Langtangen and L. Wang. However, since the sad loss of Prof. Langtangen in 2016, Ode- spy has been updated to Python 3.6 (https://github.com/thomasantony/odespy/tree/py36/odespy), thanks to Thomas Antony. Thisversion is theone used herein.