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

viii Preface shift inpopularity fromthesecompiled languages tomorehigh-levelandeasier-to- readlanguages likeMatlab,Python,R,Maple,Mathematica,andIDL, for instance. This latter classof languages is computationally less efficient,but superiorwith re- spect to overall humanproblem solving efficiency. This book emphasizes how to think like a programmer, rather than focusingon technical languagedetails. Thus, the book should put the reader in a goodposition for learning other programming languages later, including theclassicones: Fortran,C, andC++. Howthis book is different There are numerous texts on computer programming and numericalmethods, so howdoes the present one differ from the existing lit- erature? Compared tobooksonnumericalmethods, ourbookhas amuchstronger emphasisonthecraftofprogrammingandonverification.Wewant togivestudents a thoroughunderstandingofhowonethinksaboutprogrammingasaproblemsolv- ingmethodandhowonecanbesure thatprogramsarecorrect (well, youcannever be completely sure, but we show how you can provide convincing evidence for correctness). Even though there are lots of books on numericalmethodswheremany algo- rithmshave a corresponding computer implementation (see, e.g., [1, 3–6, 11, 16– 18, 21, 24, 26–31] – the latter two are the only textswe know that applyPython), it is assumed that the reader “canprogram”beforehand. Thepresent book teaches the craft of structured programming alongwith the fundamental ideas of numeri- calmethods. Furthermore,we have so far not foundanyother numericalmethods book that has a strong emphasis on verifying implementations. In this book, unit testingandcorresponding test functionsare introducedearlyon.Wealsoputmuch emphasis on codingalgorithmsas functions, as opposed to “flat programs”,which often dominate in the literature and among practitioners. Functions are reusable because theyutilize thegeneral formulationof amathematical algorithmsuch that it becomesapplicable toa largeclassofproblems. Therearealsonumerousbooksoncomputerprogramming,but toourknowledge only one [13] that aims to teach how to think about programming in the context of numericalmethods and scientific applications. That book [13] has its primary focus on teaching Python and is a very comprehensive introduction to Python as alanguageandthethinkingaboutprogrammingasacomputerscientist. Sometimes one needs a text that does not go so deep into the language-specific details, but instead targets the shortest path to reliablemathematical problemsolving through programming.With this attitude inmind,a lotof topicswere leftoutof thepresent book, simply because theywere not strictly needed in themathematical problem solving process. Examples of such topics are object-oriented programming and Pythondictionaries(ofwhichthelatteromissionispossiblysubject tomoredebate). Ifyoufindthepresentbooktooshallow,[13]mightbetherightchoiceforyou.That sourceshouldalsoworknicelyas amore in-depthsuccessorof thepresent text. Whenever the need for a structured introduction to programming arises in sci- enceandengineeringcourses, thisbookmaybeyouroption,either forself-studyor foruse inorganizedteaching.Thethinking,habits, andpracticecoveredinacouple ofhundredpageswill put readers inafirmposition forutilizingandunderstanding thepowerof computers forproblemsolving in scienceandengineering.