Programming for Computations – Python

Programming for Computations – Python on python.engineering

Programming for Computations – Python: a book by Svein Linge · Hans Petter Langtangen

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A Gentle Introduction to Numerical Simulations with Python 3.6. 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.

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332 pages, published in 2020

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Most universities and colleges implicitly require students to specialize in com- puter 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. Why Learn Programming? 1. 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. 2. 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. 3. 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. 4. 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. 5. Lotsofskilledpeoplearoundtheworldsolvecomputationalproblemsbywriting 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. 6. 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. 7. Finally, we launch our most important argument for learning computer program- ming: the algorithmic thinking that comes with the process of writing a program for a computational problem enforces a thorough understanding of both the problem and the solution method. We can simply quote the famous Norwegian computer scientist Kristen Nygaard: “Programming is understanding.”

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