Page - 7 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

1.3 APythonProgramwithaLibraryFunction 7 Butfirst awarning: there aremany things thatmust come together in the right way for ball.py to run correctly on your computer. There might be problems with your Python installation, with your writing of the program (it is very easy to introduce errors!), or with the location of the file, just tomention some of the most commondifficulties for beginners. Fortunately, such problems are solvable, and if you do not understand how to fix the problem, ask somebody. Typically, once you are beyond these common start-up problems, you canmove on to learn programmingandhowprogramscandoalotofotherwisecomplicatedmathematics foryou. Wedescribe the first steps using theSpyder graphical user interface (GUI), but youcanequallywelluseastandard texteditor forwriting theprogramanda termi- nalwindow(TerminalonMac,PowerShellonWindows) for running theprogram. Start upSpyder and type in each lineof theprogramball.pyshownearlier. Then run theprogram.Moredetailed descriptionsofoperatingSpyder are found inAp- pendixA.3. If youhave had the necessary luck to get everything right, you should nowget the number 1.2342 out in the rightmost lower window in the Spyder GUI. If so, congratulations! You have just executed your first self-written computer program inPython,andyouare ready togoonstudying thisbook!Youmay like to save the programbeforemovingon (File,save as). 1.3 APythonProgramwithaLibraryFunction Imagineyoustandonadistance, say10maway,watchingsomeone throwingaball upwards. A straight line from you to the ball will thenmake an angle with the horizontalthat increasesanddecreasesastheballgoesupanddown.Letusconsider theball at aparticularmoment in time, atwhich it hasaheightof10m. What is the angle of the line then? Again, this could easily bedonewith a cal- culator, but we continue to address gentlemathematical problemswhen learning to program. Before thinking of writing a program, one should always formulate thealgorithm, i.e., the recipe forwhatkindofcalculations thatmustbeperformed. Here, if the ball isxmaway andymup in the air, it makes an angle with the ground,where tan Dy=x. Theangle is then tan 1.y=x/. LetusmakeaPythonprogramfordoingthesecalculations.Weintroducenames xandy for thepositiondatax andy, and thedescriptivenameangle for theangle . Theprogramis stored inafileball_angle_first_try.py: x = 10 # Horizontal position y = 10 # Vertical position angle = atan(y/x) print (angle/pi)*180 Beforewe turn our attention to the running of this program, let us take a look at one new thing in the code. The line angle = atan(y/x), illustrates how the function atan, corresponding to tan 1 in mathematics, is called with the ratio