Four new books from Hans Petter Langtangen

This year Hans Petter Langtangen has published four new books. Simula congratulates Langtangen on this achievement!

Two of the books are written together with Svein Linge, Professor at Telemark University College, and one with Geir K. Pedersen, Professor at the University of Oslo.

– I am astonished by this extraordinary accomplishment; I have never heard of anyone completing four books in a year and I will probably never hear it again. But it comes as no surprise that this record achievement was performed by Hans Petter whose productivity is simply unbelievable, says Managing Director Aslak Tveito. He continues: – All texts are open access so please download, read and learn! 

The new books

All four books are Open Access and freely available online to anyone.

Finite Difference Computing with Exponential Decay Models by Hans Petter Langtangen

This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular.

Scaling of Differential Equations by Hans Petter Langtangen and Geir K. Pedersen

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

Programming for Computations - MATLAB/Octave by Hans Petter Langtangen and Svein Linge

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book; this one is for MATLAB. 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.

Programming for Computations - Python  A Gentle Introduction to Numerical Simulations with Python by Svein Linge and Hans Petter Langtangen 

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book; this one is 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.