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  • Open Access
  • © 2020

Programming for Computations - Python

A Gentle Introduction to Numerical Simulations with Python 3.6

  • Easy-to-read text offering a gentle introduction to the necessary mathematics and computer science concepts

  • Focuses on explaining all details of how to construct programs to solve mathematical problems

  • Further emphasizes verification procedures and how to embed them in automatic test frameworks

Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 15)

Buying options

Hardcover Book USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)

Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxiii
  2. The First Few Steps

    • Svein Linge, Hans Petter Langtangen
    Pages 1-38Open Access
  3. A Few More Steps

    • Svein Linge, Hans Petter Langtangen
    Pages 39-58Open Access
  4. Loops and Branching

    • Svein Linge, Hans Petter Langtangen
    Pages 59-77Open Access
  5. Functions and the Writing of Code

    • Svein Linge, Hans Petter Langtangen
    Pages 79-102Open Access
  6. Some More Python Essentials

    • Svein Linge, Hans Petter Langtangen
    Pages 103-130Open Access
  7. Computing Integrals and Testing Code

    • Svein Linge, Hans Petter Langtangen
    Pages 131-174Open Access
  8. Solving Nonlinear Algebraic Equations

    • Svein Linge, Hans Petter Langtangen
    Pages 175-201Open Access
  9. Solving Ordinary Differential Equations

    • Svein Linge, Hans Petter Langtangen
    Pages 203-285Open Access
  10. Solving Partial Differential Equations

    • Svein Linge, Hans Petter Langtangen
    Pages 287-309Open Access
  11. Back Matter

    Pages 311-332

About this book

This book is published open access under a CC BY 4.0 license.

This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected.

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.

The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.


  • programming
  • Python
  • verification
  • numerical methods
  • differential equations
  • open access


“This book merits careful study. It gives readers what they need to develop numeric and graphical solutions to problems in engineering, science, and mathematics: the necessary theoretical background, plus sufficient Python and a solid grasp of the programming process. Science and engineering students would obviously benefit from this book. It would also be useful to applied mathematics students and to professionals interested in learning Python or in seeing it applied to solve scientific problems.” (Edgar R. Chavez, Computing Reviews, December 7, 2021)

Authors and Affiliations

  • Fac of Tech, Natural Sci & Maritime Sci, University of South-Eastern Norway, Porsgrunn, Norway

    Svein Linge

  • Simula Research Laboratory BioComp, Lysaker, Norway

    Hans Petter Langtangen

About the authors

Svein Linge is a professor of modelling and simulation at the University College of Southeast Norway and holds a Dr. Scient. degree in biomechanics from the Norwegian School of Sport Sciences. He works part-time at a Norwegian Center of Excellence: "Center for Biomedical Computing", at Simula Research Laboratory, to which he has been linked for the last 13 years. His main research interests includes cerebrospinal fluid dynamics, cardiac electro-mechanics and sport biomechanics. Over the last decade, Linge has been particularly engaged in reforming the engineering education in mathematics and physics to take advantage of computer programming and simulation.

Hans Petter Langtangen (1962 - 2016) was a professor of computer science at the University of Oslo. He was formerly a professor of mechanics and was the Director of "Center for Biomedical Computing", a Norwegian Center of Excellence at the Simula Research Laboratory in Oslo. Langtangen has more than 100 scientific publications, including journal papers and many books, e.g., the bestseller TCSE 6 "A Primer on Scientific Programming with Python" (editions 1 - 5). He has also developed open source and commercial software systems for computational sciences.”

Bibliographic Information

Buying options

Hardcover Book USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)