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

x Preface how to think like a programmer, rather than focusing on technical language details. Thus, the book should put the reader in a good position for learning other programminglanguages later, includingtheclassic ones:Fortran,C, andC++. HowThisBookIsDifferent Therearenumeroustextsoncomputerprogramming and numerical methods, so how does the present one differ from the existing literature?Comparedtostandardbooksonnumericalmethods,ourbookhasamuch strongeremphasison thecraftofprogrammingandonverification.Wewant togive studentsathoroughunderstandingofhowtothinkaboutprogrammingasaproblem- solvingmethodandhowtoprovideconvincingevidenceforprogramcorrectness. Even though there are lots of books on numerical methods where many algo- rithms have a corresponding computer implementation (see, e.g., [1,3–6,10,15– 17,20,23,25,27–31]—the latter two apply Python), it is often assumed that the reader “can program” beforehand.The present book teaches the craft of structured programmingalongwith thefundamental ideasofnumericalmethods. In thisbook, unit testing and corresponding test functions are introduced early on. We also put much emphasis on coding algorithms as functions, as opposed to “flat programs,” which often dominate in the literature and among practitioners. Functions are reusable because they utilize the general formulation of a mathematical algorithm such that it becomesapplicable toa largeclassofproblems. There are also numerous books on computer programming, but not many that really emphasize how to think about programming in the context of numerical methodsand scientific applications. One such book is [11], which gives a compre- hensive introduction to Python programmingand the thinking about programming asa computerscientist. Sometimes, however, one needs a text like the present one. It does not go so deep into language-specific details, but rather targets the shortest path to reliable mathematical problem-solving through programming.With this attitude in mind, a lotof topicswere leftoutof thepresentbook,simplybecause theywerenotstrictly needed in the mathematical problem-solving process. Examples of such topics are object-orientedprogrammingand Pythondictionaries (ofwhich the latter omission is possibly subject to more debate). If you find the present book too shallow, [11] might be the right choice for you. That source should also work nicely as a more in-depthsuccessorof thepresent text. Whenevertheneedforastructuredintroductiontoprogrammingarisesinscience andengineeringcourses, the presentbookmaybe youroption,either for self-study or for use in organized teaching. The thinking, habits, and practice covered herein will put readers in a firm position for utilizing and understanding the power of computersforproblem-solvingin scienceandengineering. Changes to theFirstEdition 1. All codeisnowinPythonversion3.6(thepreviouseditionwasbasedonPython version2.7). 2. In the first edition, the introduction to programmingwasbasically covered in 50 pagesby Chap.1 (The First Few Steps) and Chap.2 (Basic Constructions). This is enough to get going, but manyreaders soon want more details. In this second edition, these two chapters have therefore been extended and split up into five