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The primary purpose of this book is to help scientists and engineers work­ ing intensively with computers to become more productive, have more fun, and increase the reliability of their investigations. Scripting in the Python programming language can be a key tool for reaching these goals [27,29]. The term scripting means different things to different people. By scripting I mean developing programs of an administering nature, mostly to organize your work, using languages where the abstraction level is higher and program­ ming is more convenient than in Fortran, C, C++, or Java. Perl, Python, Ruby, Scheme, and Tel are examples of languages supporting such high-level programming or scripting. To some extent Matlab and similar scientific com­ puting environments also fall into this category, but these environments are mainly used for computing and visualization with built-in tools, while script­ ing aims at gluing a range of different tools for computing, visualization, data analysis, file/directory management, user interfaces, and Internet communi­ cation. So, although Matlab is perhaps the scripting language of choiee in computational science today, my use of the term scripting goes beyond typi­ cal Matlab scripts. Python stands out as the language of choice for scripting in computational science because of its very elean syntax, rieh modulariza­ tion features, good support for numerical computing, and rapidly growing popularity. What Scripting is About.

Python (Computer program language) --- Python (Langage de programmation) --- Science --- 681.3*D3 --- 681.3*G4 --- Electronic data processing --- Scripting languages (Computer science) --- Data processing. --- Programming languages --- Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*G4 Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*D3 Programming languages --- Data processing --- Computer mathematics. --- Physics. --- Software engineering. --- Computational intelligence. --- Computational Science and Engineering. --- Numerical and Computational Physics, Simulation. --- Software Engineering/Programming and Operating Systems. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer software engineering --- Engineering --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Computer mathematics --- Mathematics --- Langages de programmation --- Programming languages (Electronic computers) --- Ordinateurs --- Python (langage de programmation) --- Programmation.

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During the last decades there has been a tremendous advancement of com­ puter hardware, numerical algorithms, and scientific software. Engineers and scientists are now equipped with tools that make it possible to explore real­ world applications of high complexity by means of mathematical models and computer simulation. Experimentation based on numerical simulation has become fundamental in engineering and many of the traditional sciences. A common feature of mathematical models in physics, geology, astrophysics, mechanics, geophysics, as weH as in most engineering disciplines, is the ap­ pearance of systems of partial differential equations (PDEs). This text aims at equipping the reader with tools and skills for formulating solution methods for PDEs and producing associated running code. Successful problem solving by means of mathematical models inscience and engineering often demands a synthesis of knowledge from several fields. Besides the physical application itself, one must master the tools of math­ ematical modeling, numerical methods, as weH as software design and im­ plementation. In addition, physical experiments or field measurements might play an important role in the derivation and the validation of models. This book is written in the spirit of computational sciences as inter-disciplinary activities. Although it would be attractive to integrate subjects like mathe­ matics, physics, numerics, and software in book form, few readers would have the necessary broad background to approach such a text.

519.63 --- Differential equations, Partial --- -519.6 --- 681.3 *G18 --- Partial differential equations --- Numerical methods for solution of partial differential equations --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Data processing. --- Diffpack (Computer file) --- Diffpack (Computer file). --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.63 Numerical methods for solution of partial differential equations --- 519.6 --- Numerical solutions&delete& --- Data processing --- Computer mathematics. --- Computational intelligence. --- Mathematical analysis. --- Analysis (Mathematics). --- Physics. --- Computer programming. --- Computational Mathematics and Numerical Analysis. --- Computational Intelligence. --- Analysis. --- Mathematical Methods in Physics. --- Numerical and Computational Physics, Simulation. --- Programming Techniques. --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- 517.1 Mathematical analysis --- Mathematical analysis --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Mathematics --- Programming

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The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology, and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background, and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science.

Electronic books. -- local. --- Python (Computer program language). --- Python (Computer program language) --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Computer Science --- Mathematics. --- Software engineering. --- Computer programming. --- Computer science --- Computer mathematics. --- Physics. --- Computational Science and Engineering. --- Programming Techniques. --- Software Engineering/Programming and Operating Systems. --- Mathematics of Computing. --- Numerical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Computer software engineering --- Engineering --- Math --- Science --- Programming --- Scripting languages (Computer science) --- Computer science. --- Numerical and Computational Physics, Simulation. --- Informatics --- Computer science—Mathematics.

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The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen … does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. … Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python…” Joan Horvath, Computing Reviews, March 2015 .

Mathematics. --- Computer programming. --- Computer science --- Computer mathematics. --- Physics. --- Computational Science and Engineering. --- Programming Techniques. --- Mathematics of Computing. --- Numerical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Math --- Mathematics --- Programming --- Computer science. --- Numerical and Computational Physics, Simulation. --- Informatics --- Science --- Python (Computer program language) --- Computer science—Mathematics. --- Coding theory --- Physical sciences --- Dynamics

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The second edition features lots of improvements and new material. The most significant additions include - finite difference methods and implementations for a 1D time-dependent heat equation (Chapter 1. 7. 6), - a solver for vibration of elastic structures (Chapter 5. 1. 6), - a step-by-step instruction of how to develop and test Diffpack programs for a physical application (Chapters 3. 6 and 3. 13), - construction of non-trivial grids using super elements (Chapters 3. 5. 4, 3. 6. 4, and 3. 13. 4), - additional material on local mesh refinements (Chapter 3. 7), - coupling of Diffpack with other types of software (Appendix B. 3) - high-level programming offinite difference solvers utilizing the new stencil (finite difference operator) concept in Diffpack (Appendix D. 8). Many of the examples, projects, and exercises from the first edition have been revised and improved. Some new exercises and projects have also been added. A hopefully very useful new feature is the compact overview of all the program examples in the book and the associated software files, presented in Chapter 1. 2. Errors have been corrected, many explanations have been extended, and the text has been upgraded to be compatible with Diffpack version 4. 0. The major difficulty when developing programs for numerical solution of partial differential equations is to debug and verify the implementation. This requires an interplay between understanding the mathematical model,the in­ volved numerics, and the programming tools.

Differential equations, Partial --- Numerical solutions --- Data processing. --- Diffpack (Computer file). --- 681.3 *G18 --- 519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations --- Numerical solutions&delete& --- Data processing --- Diffpack (Computer file) --- Computers. --- Mathematical analysis. --- Analysis (Mathematics). --- Software engineering. --- Computer mathematics. --- Computational intelligence. --- Mathematical physics. --- Theory of Computation. --- Analysis. --- Software Engineering/Programming and Operating Systems. --- Computational Mathematics and Numerical Analysis. --- Computational Intelligence. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Electronic data processing --- Mathematics --- Computer software engineering --- Engineering --- 517.1 Mathematical analysis --- Mathematical analysis --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace