Page - 3 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

1.2 APythonProgramwithVariables 3 arguments toother functions, there isgoodsupport for interfacingC,C++andFor- tran code (i.e., a Python programmay use codewritten in other languages), and functions explicitlywritten for scalar input oftenworkfine (withoutmodification) alsowithvector input.Another important thing, is thatPython isavailable for free. It canbedownloadedfromthe Internetandwill runonmostplatforms. Readers who want to expand their scientific programming skills beyond the introductory level of the present exposition, are encouraged to study the book A Primer on Scientific Programming with Python [13]. This comprehensive book is as suitable for beginners as for professional programmers, and teaches the art of programming through a huge collection of dedicated examples. This book is considered the primary reference, and a natural extension, of the programming matters in thepresentbook. Somecomputerscienceterms Note that, quite often, the terms script and scripting are used as synonyms for programandprogramming, respectively. The inventor of thePerl programming language,LarryWall, tried to explain thedifferencebetweenscript andprograminahumorousway(fromperl.com1): Suppose you went back to Ada Lovelace2 and asked her the difference between a script and a program. She’d probably look at you funny, then say something like: Well, a script is what you give the actors, but a program is what you give the audience. That Ada was one sharp lady ... Since her time, we seem to have gotten a bit more confused about what we mean when we say scripting. It confusesevenme, andI’msupposed tobe oneof theexperts. Therearemanyotherwidelyusedcomputersciencetermstopickup.Writing a program (or script or code) is often expressed as implementing the program. Executing a programmeans running the program. An algorithm is a recipe for how to construct a program. A bug is an error in a program, and the art of trackingdownandremovingbugs iscalleddebugging.Simulatingorsimulation refers to using a program tomimic processes in the real world, often through solvingdifferential equations thatgovern thephysicsof theprocesses. 1.2 APythonProgramwithVariables Ourfirst example regardsprogrammingamathematicalmodel thatpredicts thepo- sition of a ball thrown up in the air. FromNewton’s 2nd law, and by assuming negligibleair resistance,onecanderiveamathematicalmodel thatpredicts thever- tical positiony of theball at time t. Fromthemodelonegets the formula yDv0t 0:5gt2; where v0 is the initial upwards velocity and g is the acceleration of gravity, for which 9:81ms 2 is a reasonable value (even if it depends on things like location on the earth). With this formula at hand, andwhenv0 is known, youmayplug in avalue for timeandgetout thecorrespondingheight. 1http://www.perl.com/pub/2007/12/06/soto-11.html 2http://en.wikipedia.org/wiki/Ada_Lovelace