Seite - 12 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

12 1 TheFirstFewSteps 1.5 MoreBasicConcepts Sofarwehaveseena fewbasicexamplesonhowtoapplyPythonprogrammingto solvemathematical problems. Beforewe can go onwith other andmore realistic examples, we need to briefly treat some topics thatwill be frequently required in later chapters. These topics include computer science concepts like variables, ob- jects, errormessages, andwarnings;morenumericalconcepts like roundingerrors, arithmetic operator precedence, and integer division; in addition to more Python functionalitywhenworkingwitharrays,plotting, andprinting. 1.5.1 UsingPythonInteractively Python can also be used interactively. That is, we do not first write a program in a file and execute it, butwe give statements and expressions towhat is known as a Python shell. We recommend to use IPython as shell (because it is superior to alternativePythonshells).WithSpyder,Ipython is availableat startup, appearing as the lower right window. Following the IPython prompt In [1]: ( a prompt meansa“readysign”, i.e. theprogramallowsyoutoenteracommand,anddifferent programsoftenhavedifferent lookingprompts),youmaydocalculations: In [1]: 2+2 Out [1]: 4 In [2]: 2*3 Out [2]: 6 In [3]: 10/2 Out [3]: 5 In [4]: 2**3 Out [4]: 8 The response fromIPython is precededbyOut [q]:,whereqequalspwhen the response is to input “number”p. Note that, as in a program, youmay have to use import before using pi or functions likesin,cos, etc. That is, at the prompt, do the commandfrom math import *beforeyouusepiorsin, etc. Importingothermodules thanmathmay berelevant,dependingonwhatyouraim iswith thecomputations. Youmayalsodefinevariablesanduse formulas interactivelyas In [1]: v0 = 5 In [2]: g = 9.81 In [3]: t = 0.6 In [4]: y = v0*t - 0.5*g*t**2 In [5]: print y ------> print(y) 1.2342