Hans Petter Langtangen - Böcker

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 2010Those 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 2011This 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

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi­ neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati­ cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high­ quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil­ ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu­ ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in­ vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work­ shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe­ matics and the Departments of Informatics and Mathematics at the Uni­ versity of Oslo.

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi­ neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati­ cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high­ quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil­ ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu­ ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in­ vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work­ shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe­ matics and the Departments of Informatics and Mathematics at the Uni­ versity of Oslo.

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.

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms.

This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization.

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style 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 the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

The book serves both as a reference forvarious scaled models with corresponding dimensionless numbers, and as aresource for learning the art of scaling. A special feature of the book is the emphasis on how to create softwarefor scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is amathematical technique that greatly simplifies the setting of input parameters innumerical simulations. Moreover, scaling enhances the understanding of howdifferent physical processes interact in a differential equation model.Compared to the existing literature, where the topic of scaling is frequentlyencountered, but very often in only a brief and shallow setting, the presentbook gives much more thorough explanations of how to reason about finding theright scales. This process is highly problem dependent, and therefore the bookfeatures a lot of worked examples, from very simple ODEs to systems of PDEs,especially from fluid mechanics.The text is easily accessible andexample-driven. The first part on ODEs fits even a lower undergraduate level,while the most advanced multiphysics fluid mechanics examples target thegraduate level. The scientific literature is full of scaled models, but in mostof the cases, the scales are just stated without thorough mathematicalreasoning. This book explains how the scales are found mathematically.This book will be a valuable read for anyonedoing numerical simulations based on ordinary or partial differential equations.

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs.This book is open access under a CC BY license.

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods.

This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization.

This book presents computer programming as a key method for solving mathematical problems. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students.

This book presents computer programming as a key method for solving mathematical problems. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students.

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods.

This book is about solving partial differential equations (PDEs). Such equa­ tions are used to model a wide range ofphenomena in virtually all fields ofsci­ ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in­ tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech­ niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor­ der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff­ pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple­ mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.

Numerous readers of the second edition have noti?ed me about misprints and possible improvements of the text and the associated computer codes. The resulting modi?cations have been incorporated in this new edition and its accompanying software. The major change between the second and third editions, however, is caused by the new implementation of Numerical Python, now called numpy. The new numpy package encourages a slightly di?erent syntax compared to the old Numeric implementation, which was used in the previous editions. Since Numerical Python functionality appears in a lot of places in the book, there are hence a huge number of updates to the new suggested numpy syntax, especially in Chapters 4, 9, and 10. The second edition was based on Python version 2.3, while the third edition contains updates for version 2.5. Recent Python features, such as generator expressions (Chapter 8.9.4), Ctypes for interfacing shared libraries in C (Chapter 5.2.2), the with statement (Chapter 3.1.4), and the subprocess module for running external processes (Chapter 3.1.3) have been exempli?ed to make the reader aware of new tools. Chapter 4.4.4 is new and gives a taste of symbolic mathematics in Python.

Numerous readers of the second edition have noti?ed me about misprints and possible improvements of the text and the associated computer codes. The resulting modi?cations have been incorporated in this new edition and its accompanying software. The major change between the second and third editions, however, is caused by the new implementation of Numerical Python, now called numpy. The new numpy package encourages a slightly di?erent syntax compared to the old Numeric implementation, which was used in the previous editions. Since Numerical Python functionality appears in a lot of places in the book, there are hence a huge number of updates to the new suggested numpy syntax, especially in Chapters 4, 9, and 10. The second edition was based on Python version 2.3, while the third edition contains updates for version 2.5. Recent Python features, such as generator expressions (Chapter 8.9.4), Ctypes for interfacing shared libraries in C (Chapter 5.2.2), the with statement (Chapter 3.1.4), and the subprocess module for running external processes (Chapter 3.1.3) have been exempli?ed to make the reader aware of new tools. Chapter 4.4.4 is new and gives a taste of symbolic mathematics in Python.

The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. It is our goal to teach principles and ideas that carry over from field to field.

Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.