Page - 10 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

10 1 TheFirstFewSteps 1.2.4 MathematicalNotationVersusCoding Make sure you understand that, from the outset, we had a pure mathematical formulationofour formula y=v0t−0.5gt2, which does not contain any connection to programming at all. Remember, this formula was derived hundreds of years ago, long before computers entered the scene!Whenwenextwrotea pieceofcode thatapplied this formula, that codehad to obey the rules of the programming language, which in this case is Python. This means,forexample,thatmultiplicationhadtobewrittenwithastar,simplybecause that is the way multiplication is coded in Python. In some other programming language, the multiplication could in principle have been coded otherwise, but the mathematical formulationwouldstill read thesame. We have seen how the equals sign (=) is interpreted in Python code. This interpretation is very different from the interpretation in mathematics, as might be illustratedby the following little example. Inmathematics,x=2−xwould imply that 2x = 2, giving x = 1. In Python code, however, a code line like x = 2 - xwould be interpreted, not as an equation, but rather as an assignment statement: compute the righthandside bysubtracting thecurrentvalueofx from2 and let the resultbe thenewvalueofx. In thecode, thenewvalueofxcould thusbeanything, alldependingon thevaluexhadabove theassignmentstatement! 1.2.5 WriteandRunYourFirstProgram Reading only does not teach you computer programming: you have to program yourself and practice heavily before you master mathematical problem solving via programming. In fact, this is very much like learning to swim. Nobody can do that by just reading about it! You simply have to practice real swimming to get good at it. Therefore, it is crucial at this stage that you start writing and running Python programs. We just went through the programball.py above, so let us next write andrun thatcode. But first a warning: there are many things that must come together in the right way for ball.py to run correctly. There might be problems with your Python installation, with your writing of the program (it is very easy to introduce errors!), orwith thelocationof thefile, just tomentionsomeofthemostcommondifficulties forbeginners.Fortunately,suchproblemsaresolvable,andifyoudonotunderstand how to fix the problem,ask somebody.Very often the guy next to you experienced thesameproblemandhasalreadyfixed it! Start up Spyder and, in the editor (left pane), type in each line of the program ball.pyshownearlier.Thenyousavetheprogram(selectFile->save as)where you prefer and finally run it (selectRun ->Run, ...or press F5). With a bit of luck, youshouldnowget thenumber1.2342out intherightmostlowerpaneintheSpyder GUI. If so, congratulations,you have just executedyourfirst self-written computer programinPython!