Svein Linge - Programming for Computations - Python: A Gentle Introduction to Numerical Simulations with Python 3.6, 2nd Edition
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- Book:Programming for Computations - Python: A Gentle Introduction to Numerical Simulations with Python 3.6, 2nd Edition
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This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.
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More information about this series at http://www.springer.com/series/5151
Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
This Springer imprint is published by the registered company Springer Nature Switzerland AG.
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To My Family
Thanks to my dear wife, Katrin, and our lovely children, Stian, Mia, and Magnus, for their love, support, and patience. I am a very lucky man.
To Hans Petter
Dear friend and coauthor, it is so sad you are no longer among us.Thank you for everything. I dedicate this second edition of our book to you.
Porsgrunn, NorwaySvein Linge
June 2018
Computing, in the sense of doing mathematical calculations, is a skill that mankind has developed over thousands of years. Programming, on the other hand, is in its infancy, with a history that spans a few decades only. Both topics are vastly comprehensive and usually taught as separate subjects in educational institutions around the world, especially at the undergraduate level. This book is about the combination of the two, because computing today becomes so much more powerful when combined with programming.
Most universities and colleges implicitly require students to specialize in computer science if they want to learn the craft of programming, since other student programs usually do not offer programming to an extent demanded for really mastering this craft. Common arguments claim that it is sufficient with a brief introduction, that there is not enough room for learning programming in addition to all other must-have subjects, and that there is so much software available that few really need to program themselves. A consequence is that engineering students often graduate with shallow knowledge about programming, unless they happened to choose the computer science direction.
We think this is an unfortunate situation. There is no doubt that practicing engineers and scientists need to know their pen-and-paper mathematics. They must also be able to run off-the-shelf software for important standard tasks and will certainly do that a lot. Nevertheless, the benefits of mastering programming are many.
Ready-made software is limited to handling certain standard problems. What do you do when the problem at hand is not covered by the software you bought? Fortunately, a lot of modern software systems are extensible via programming. In fact, many systems demand parts of the problem specification (e.g., material models) to be specified by computer code.
With programming skills, you may extend the flexibility of existing software packages by combining them. For example, you may integrate packages that do not speak to each other from the outset. This makes the work flow simpler, more efficient, and more reliable, and it puts you in a position to attack new problems.
It is easy to use excellent ready-made software the wrong way. The insight in programming and the mathematics behind is fundamental for understanding complex software, avoiding pitfalls, and becoming a safe user.
Bugs (errors in computer code) are present in most larger computer programs (also in the ones from the shop!). What do you do when your ready-made software gives unexpected results? Is it a bug, is it the wrong use, or is it the mathematically correct result? Experience with programming of mathematics gives you a good background for answering these questions. The one who can program can also make tailored code for a simplified problem setting and use that to verify the computations done with off-the-shelf software.
Lots of skilled people around the world solve computational problems by writing their own code and offering those for free on the Internet. To take advantage of this truly great source of software in a reliable way, one must normally be able to understand and possibly modify computer code offered by others.
It is recognized worldwide that students struggle with mathematics and physics. Too many find such subjects difficult and boring. With programming, we can execute the good old subjects in a brand new way! According to the authors own experience, students find it much more motivating and enlightening when programming is made an integrated part of mathematics and physical science courses. In particular, the problem being solved can be much more realistic than when the mathematics is restricted to what you can do with pen and paper.
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