Texts in Computational Science and Engineering

Hans Petter Langtangen · Svein Linge · Alfio Quarteroni · Fausto Saleri · John A. Trangenstein

Latest release: July 11, 2023

Series

Books

Computational Partial Differential Equations: Numerical Methods and Diffpack Programming, Edition 2

Book 1·Dec 2012

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.

Scientific Computing with MATLAB and Octave: Edition 2

Book 2·Jun 2007

0.0

Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game that computers adopt when storing and operating with realand complex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raised through exercises and examples, often stemming from s- ci?c applications.

Scientific Computing with MATLAB and Octave: Edition 3

Book 2·May 2010

4.0

Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game thatcomputersadoptwhenstoringandoperatingwith realandcomplex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raisedthrough exercises and examples, often stemming from s- ci?c applications.

Scientific Computing with MATLAB

Book 2·Dec 2012

0.0

"It is important to prove, is more but it important to improve." This textbook is an introduction to Scientific Computing. We will illustrate several numerical methods for the computer solution of cer tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. With this aim, in Chapter 1 we will illustrate the rules of the game that computers adopt when storing and operating with real and complex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will adopt the programming environment MATLAB ® 1 as a faithful companion. We will gradually discover its principal commands, statements and con structs. We will show how to execute all the algorithms that we intro duce throughout the book. This will enable us to furnish an immediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raised through exercises and examples, often stemming from specific ap plications.

Python Scripting for Computational Science: Edition 2

Book 3·Feb 2006

5.0

The second edition features new material, reorganization of text, improved examples and software tools, updated information, and correction of errors. This is mainly the result of numerous eager readers around the world who have detected misprints, tested program examples, and suggested alternative ways of doing things. I am greatful to everyone who has sent emails and contributed with improvements. The most important changes in the second edition are brie?y listed below. Already in the introductory examples in Chapter 2 the reader now gets a glimpse of Numerical Python arrays, interactive computing with the IPython shell, debugging scripts with the aid of IPython and Pdb, and turning “?at” scripts into reusable modules (Chapters 2. 2. 5, 2. 2. 6, and 2. 5. 3 are added). Several parts of Chapter 4 on numerical computing have been extended (- pecially Chapters 4. 3. 5, 4. 3. 7, 4. 3. 8, and 4. 4). Many smaller changes have been implemented in Chapter 8; the larger ones concern exemplifying Tar archives instead of ZIP archives in Chapter 8. 3. 4, rewriting of the material on generators in Chapter 8. 9. 4, and an example in in Chapter 8. 6. 13 on adding new methods to a class without touching the original source code and without changing the class name. Revised and additional tips on op- mizing Python code have been included in Chapter 8. 10. 3, while the new Chapter 8. 10.

Python Scripting for Computational Science: Edition 3

Book 3·Dec 2007

4.1

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.

Python Scripting for Computational Science

Book 3·Mar 2013

3.0

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.

Design Patterns for e-Science

Book 4·May 2007

1.0

This is a book about a code and about coding. The code is a case study which has been used to teachcourses in e-Science atthe Australian NationalUniv- sity since 2001. Students learn advanced programming skills and techniques TM in the Java language. Above all, they learn to apply useful object-oriented design patterns as they progressively refactor and enhance the software. We think our case study,EScope, is as close to real life as you can get! It is a smaller version of a networked, graphical, waveform browser which is used in the control rooms of fusion energy experiments around the world. It is quintessential “e-Science” in the sense of e-Science being “computer science and information technology in the service of science”. It is not, speci?cally, “Grid-enabled”, but we develop it in a way that will facilitate its deployment onto the Grid. The standard version ofEScope interfaces with a specialised database for waveforms, and related data, known asMDSplus. On the acc- panying CD, we have provided you with software which will enable you to installMDSplus,EScope and sample data ?les onto Windows or Linux c- puters. There is much additional software including many versions of the case study as it gets built up and progressively refactored using design patterns. There will be a home web-site for this book which will contain up-to-date information about the software and other aspects of the case study.

Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications

Book 5·Aug 2007

0.0

Particle models play an important role in many applications in physics, chemistry and biology. They can be studied on the computer with the help of molecular dynamics simulations. This book presents in detail both the necessary numerical methods and techniques (linked-cell method, SPME-method, tree codes, multipole technique) and the theoretical background and foundations. It illustrates the aspects modelling, discretization, algorithms and their parallel implementation with MPI on computer systems with distributed memory. Furthermore, detailed explanations are given to the different steps of numerical simulation, and code examples are provided. With the description of the algorithms and the presentation of the results of various simulations from the areas material science, nanotechnology, biochemistry and astrophysics, the reader of this book will be able to write his own programs for molecular dynamics step by step and to run successful experiments.

A Primer on Scientific Programming with Python

Book 6·Aug 2009

5.0

Theaimofthisbookistoteachcomputerprogrammingusingexamples from mathematics and the natural sciences. We have chosen to use the Python programming language because it combines remarkable power with very clean, simple, and compact syntax. Python is easy to learn and very well suited for an introduction to computer programming. Python is also quite similar to Matlab and a good language for doing mathematical computing. It is easy to combine Python with compiled languages, like Fortran, C, and C++, which are widely used languages forscienti?ccomputations.AseamlessintegrationofPythonwithJava is o?ered by a special version of Python called Jython. The examples in this book integrate programming with appli- tions to mathematics, physics, biology, and ?nance. The reader is - pected to have knowledge of basic one-variable calculus as taught in mathematics-intensive programs in high schools. It is certainly an - vantage to take a university calculus course in parallel, preferably c- taining both classical and numerical aspects of calculus. Although not strictly required, a background in high school physics makes many of the examples more meaningful.

A Primer on Scientific Programming with Python: Edition 2

Book 6·Mar 2011

5.0

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.

A Primer on Scientific Programming with Python: Edition 3

Book 6·Jul 2012

0.0

A Primer on Scientific Programming with Python: Edition 4

Book 6·Aug 2014

0.0

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

A Primer on Scientific Programming with Python: Edition 5

Book 6·Jul 2016

3.7

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

“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

Elements of Scientific Computing

Book 7·Sep 2010

0.0

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.

Fundamentals of Scientific Computing

Book 8·Jun 2011

0.0

The book of nature is written in the language of mathematics -- Galileo Galilei

How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built?

The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation.

This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.

Space-Filling Curves: An Introduction with Applications in Scientific Computing

Book 9·Oct 2012

5.0

The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings.

The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.