x
Preface
how to think like a programmer, rather than focusing on technical language
details. Thus, the book should put the reader in a good position for learning other
programming languages later, including the classic ones: Fortran, C, and C++.
How This Book Is Different There are numerous texts on computer programming
and numerical methods, so how does the present one differ from the existing
literature? Compared to standard books on numerical methods, our book has a much
stronger emphasis on the craft of programming and on verification. We want to give
students a thorough understanding of how to think about programming as a problemsolving method and how to provide convincing evidence for program correctness.
Even though there are lots of books on numerical methods where many algorithms have a corresponding computer implementation (see, e.g., [1, 3–6, 10, 15–
17, 20, 23, 25, 27–31]—the latter two apply Python), it is often assumed that the
reader “can program” beforehand. The present book teaches the craft of structured
programming along with the fundamental ideas of numerical methods. In this book,
unit testing and corresponding test functions are introduced early on. We also put
much emphasis on coding algorithms as functions, as opposed to “flat programs,”
which often dominate in the literature and among practitioners. Functions are
reusable because they utilize the general formulation of a mathematical algorithm
such that it becomes applicable to a large class of problems.
There are also numerous books on computer programming, but not many that
really emphasize how to think about programming in the context of numerical
methods and scientific applications. One such book is [11], which gives a comprehensive introduction to Python programming and the thinking about programming
as a computer scientist.
Sometimes, however, one needs a text like the present one. It does not go so
deep into language-specific details, but rather targets the shortest path to reliable
mathematical problem-solving through programming. With this attitude in mind, a
lot of topics were left out of the present book, simply because they were not strictly
needed in the mathematical problem-solving process. Examples of such topics are
object-oriented programming and Python dictionaries (of which the latter omission
is possibly subject to more debate). If you find the present book too shallow, [11]
might be the right choice for you. That source should also work nicely as a more
in-depth successor of the present text.
Whenever the need for a structured introduction to programming arises in science
and engineering courses, the present book may be your option, either for self-study
or for use in organized teaching. The thinking, habits, and practice covered herein
will put readers in a firm position for utilizing and understanding the power of
computers for problem-solving in science and engineering.
Changes to the First Edition
1. All code is now in Python version 3.6 (the previous edition was based on Python
version 2.7).
2. In the first edition, the introduction to programming was basically covered in 50
pages by Chap. 1 (The First Few Steps) and Chap. 2 (Basic Constructions). This
is enough to get going, but many readers soon want more details. In this second
edition, these two chapters have therefore been extended and split up into five
Preface
how to think like a programmer, rather than focusing on technical language
details. Thus, the book should put the reader in a good position for learning other
programming languages later, including the classic ones: Fortran, C, and C++.
How This Book Is Different There are numerous texts on computer programming
and numerical methods, so how does the present one differ from the existing
literature? Compared to standard books on numerical methods, our book has a much
stronger emphasis on the craft of programming and on verification. We want to give
students a thorough understanding of how to think about programming as a problemsolving method and how to provide convincing evidence for program correctness.
Even though there are lots of books on numerical methods where many algorithms have a corresponding computer implementation (see, e.g., [1, 3–6, 10, 15–
17, 20, 23, 25, 27–31]—the latter two apply Python), it is often assumed that the
reader “can program” beforehand. The present book teaches the craft of structured
programming along with the fundamental ideas of numerical methods. In this book,
unit testing and corresponding test functions are introduced early on. We also put
much emphasis on coding algorithms as functions, as opposed to “flat programs,”
which often dominate in the literature and among practitioners. Functions are
reusable because they utilize the general formulation of a mathematical algorithm
such that it becomes applicable to a large class of problems.
There are also numerous books on computer programming, but not many that
really emphasize how to think about programming in the context of numerical
methods and scientific applications. One such book is [11], which gives a comprehensive introduction to Python programming and the thinking about programming
as a computer scientist.
Sometimes, however, one needs a text like the present one. It does not go so
deep into language-specific details, but rather targets the shortest path to reliable
mathematical problem-solving through programming. With this attitude in mind, a
lot of topics were left out of the present book, simply because they were not strictly
needed in the mathematical problem-solving process. Examples of such topics are
object-oriented programming and Python dictionaries (of which the latter omission
is possibly subject to more debate). If you find the present book too shallow, [11]
might be the right choice for you. That source should also work nicely as a more
in-depth successor of the present text.
Whenever the need for a structured introduction to programming arises in science
and engineering courses, the present book may be your option, either for self-study
or for use in organized teaching. The thinking, habits, and practice covered herein
will put readers in a firm position for utilizing and understanding the power of
computers for problem-solving in science and engineering.
Changes to the First Edition
1. All code is now in Python version 3.6 (the previous edition was based on Python
version 2.7).
2. In the first edition, the introduction to programming was basically covered in 50
pages by Chap. 1 (The First Few Steps) and Chap. 2 (Basic Constructions). This
is enough to get going, but many readers soon want more details. In this second
edition, these two chapters have therefore been extended and split up into five