Hans Petter Langtangen - A Primer on Scientific Programming with Python

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Springer-Verlag Berlin Heidelberg 2016

Hans Petter Langtangen A Primer on Scientific Programming with Python Texts in Computational Science and Engineering 10.1007/978-3-662-49887-3_1

1. Computing with Formulas

Hans Petter Langtangen 1, 2

(1)

Simula Research Laboratory, Fornebu, Norway

(2)

Department of Informatics, University of Oslo, Oslo, Norway

Hans Petter Langtangen

Email:

Our first examples on computer programming involve programs that evaluate mathematical formulas. You will learn how to write and run a Python program, how to work with variables, how to compute with mathematical functions such as e x and , and how to use Python for interactive calculations.

We assume that you are somewhat familiar with computers so that you know what files and folders are (another frequent word for folder is directory), how you move between folders, how you change file and folder names, and how you write text and save it in a file.

All the program examples associated with this chapter can be downloaded as a tarfile or zipfile from the web page http://hplgit.github.com/scipro-primer . I strongly recommend you to visit this page, download and pack out the files. The examples are organized in a folder tree with src as root. Each subfolder corresponds to a particular chapter. For example, the subfolder formulas contains the program examples associated with this first chapter. The relevant subfolder name is listed at the beginning of every chapter.

The folder structure with example programs can also be directly accessed in a on the web. You can click on the formulas folder to see all the examples from the present chapter. Clicking on a filename shows a nicely typeset version of the file. The file can be downloaded by first clicking Raw to get the plain text version of the file, and then right-clicking in the web page and choosing Save As.

1.1 The First Programming Encounter: a Formula

The first formula we shall consider concerns the vertical motion of a ball thrown up in the air. From Newtons second law of motion one can set up a mathematical model for the motion of the ball and find that the vertical position of the ball, called y , varies with time t according to the following formula:

(1.1)

Here, v 0 is the initial velocity of the ball, g is the acceleration of gravity, and t is time. Observe that the y axis is chosen such that the ball starts at y = when t =. The above formula neglects air resistance, which is usually small unless v 0 is large, see Exercise .

To get an overview of the time it takes for the ball to move upwards and return to y = again, we can look for solutions to the equation y =:

That is, the ball returns after seconds, and it is therefore reasonable to restrict the interest of () to .

1.1.1 Using a Program as a Calculator

Our first program will evaluate () we have

(1.2)

This arithmetic expression can be evaluated and its value can be printed by a very simple one-line Python program:

The four standard arithmetic operators are written as + , - , * , and / in Python and most other computer languages. The exponentiation employs a double asterisk notation in Python, e.g., 0.62 is written as 0.6**2 .

Our task now is to create the program and run it, and this will be described next.

1.1.2 About Programs and Programming

A computer program is just a sequence of instructions to the computer, written in a computer language. Most computer languages look somewhat similar to English, but they are very much simpler. The number of words and associated instructions is very limited, so to perform a complicated operation we must combine a large number of different types of instructions. The program text, containing the sequence of instructions, is stored in one or more files. The computer can only do exactly what the program tells the computer to do.

Another perception of the word program is a file that can be run (double-clicked) to perform a task. Sometimes this is a file with textual instructions (which is the case with Python), and sometimes this file is a translation of all the program text to a more efficient and computer-friendly language that is quite difficult to read for a human. All the programs in this chapter consist of short text stored in a single file. Other programs that you have used frequently, for instance Firefox or Internet Explorer for reading web pages, consist of program text distributed over a large number of files, written by a large number of people over many years. One single file contains the machine-efficient translation of the whole program, and this is normally the file that you double-click on when starting the program. In general, the word program means either this single file or the collection of files with textual instructions.

Programming is obviously about writing programs, but this process is more than writing the correct instructions in a file. First, we must understand how a problem can be solved by giving a sequence of instructions to the computer. This is one of the most difficult things with programming. Second, we must express this sequence of instructions correctly in a computer language and store the corresponding text in a file (the program). This is normally the easiest part. Third, we must find out how to check the validity of the results. Usually, the results are not as expected, and we need to a fourth phase where we systematically track down the errors and correct them. Mastering these four steps requires a lot of training, which means making a large number of programs (exercises in this book, for instance!) and getting the programs to work.

1.1.3 Tools for Writing Programs

There are three alternative types of tools for writing Python programs:

• a plain text editor
• an integrated development environment (IDE) with a text editor
• an IPython notebook

What you choose depends on how you access Python. Section H.1 contains information on the various possibilities to install Python on your own computer, access a pre-installed Python environment on a computer system at an institution, or access Python in cloud services through your web browser.

Based on teaching this and previous books to more than 3000 students, my recommendations go as follows.

• If you use this book in a course, the instructor has probably made a choice for how you should access Python follow that advice.
• If you are a student at a university where Linux is the dominating operating system, install a virtual machine with Ubuntu on your own laptop and do all your scientific work in Ubuntu. Write Python programs in a text editor like Gedit, Atom, Sublime Text, Emacs, or Vim, and run programs in a terminal window (the gnome-terminal is recommended).

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