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

Preface xi chapters. Explanations are now more complete, previous examples have been modified,newexampleshavebeenadded,andmore. Inparticular, the importing of code is now elaborated on in a greater detail, so is the making of modules. Also,Sect.4.2 isnew,illustratingthe importantstepwisestrategyofcodewriting througha dedicated example.The five first chaptersnow coverabout 150 pages that explain, in a brief andsimple manner, all the code basics required to follow the remainingpartsof thebook. 3. The new Chap.6 (Computing Integrals and Testing Code) and Chap.7 (Solving NonlinearAlgebraicEquations)are seen asgentlefirst applicationsofprogram- ming to problem-solving in mathematics. Both these chapters now precede the mathematically more challenging Chaps.8 and 9, which treat basic numerical solving of ODEs and PDEs, respectively (the chapter Solving Nonlinear Alge- braic Equations was, in the first edition, the final chapter of the book, but it seems more appropriate to let it act as a “warm-up” chapter, together with the newChap.6, for the twofinalchaptersondifferentialequationsolving). 4. Section 8.1 (Filling a Water Tank: Two Cases) is new, particularly written for readerswho lackexperiencewith differentialequations. 5. Section8.5 (RateofConvergence) isnew,explainingconvergencerate related to differentialequations. 6. New exercises have been added, e.g., on Fibonacci numbers, the Leapfrog method,Adams-Bashforthmethods,andmore. 7. Errors and typos have been corrected, and many explanations have been refor- mulated throughout. Supplementary Materials All program and data files referred to herein are available fromthe book’s (2ndedition)primarywebsite: https://github.com/slgit/prog4comp_2. Acknowledgments We want to thank all students who attended the courses FM1006Modellingandsimulationofdynamicsystems,FM1115ScientificComput- ing, FB1012 Mathematics, and FB2112Physics at the University of South-Eastern Norway over the last 5–10 years. They worked their way throughearly versionsof this textandgaveusconstructiveandpositivefeedbackthathelpeduscorrecterrors andimprovethebookinsomanyways.Specialacknowledgmentgoes toGuandong Kou,EdirisingheV.P.J.Manjula,andYapiDonatienAchoufortheircarefulreading of the manuscript (first edition)and constructivesuggestions for improvement.The constructive feedback and good suggestions received from Om Prakash Chapagain (secondedition) is also highlyappreciated.We thankall ourgoodcolleaguesat the University of South-Eastern Norway, the University of Oslo, and Simula Research Laboratoryfortheircontinuedsupportandinterest, for theenlighteningdiscussions, andforprovidingsuchan inspiringenvironmentfor teachingandscience. Special thanks go to Prof. Kent-Andre Mardal, the University of Oslo, for his insightfulcommentsandsuggestions.