The first programming encounter: a formula

Using a program as a calculator

About programs and programming

Tools for writing programs

Writing and running your first Python program

Warning about typing program text

Verifying the result

Using variables

Names of variables

Reserved words in Python

Comments

Formatting text and numbers

Computer science glossary

Another formula: Celsius-Fahrenheit conversion

Potential error: integer division

Objects in Python

Avoiding integer division

Arithmetic operators and precedence

Evaluating standard mathematical functions

Example: Using the square root function

Example: Computing with \( \sinh x \)

A first glimpse of rounding errors

Interactive computing

Using the Python shell

Type conversion

IPython

Complex numbers

Complex arithmetics in Python

Complex functions in Python

Unified treatment of complex and real functions

Symbolic computing

Basic differentiation and integration

Equation solving

Taylor series and more

Summary

Chapter topics

Example: Trajectory of a ball

About typesetting conventions in this book

Exercises

Exercise 1: Compute 1+1

Exercise 2: Write a Hello World program

Exercise 3: Derive and compute a formula

Exercise 4: Convert from meters to British length units

Exercise 5: Compute the mass of various substances

Exercise 6: Compute the growth of money in a bank

Exercise 7: Find error(s) in a program

Exercise 8: Type in program text

Exercise 9: Type in programs and debug them

Exercise 10: Evaluate a Gaussian function

Exercise 11: Compute the air resistance on a football

Exercise 12: How to cook the perfect egg

Exercise 13: Derive the trajectory of a ball

Exercise 14: Find errors in the coding of formulas

Exercise 15: Explain why a program does not work

Exercise 16: Find errors in Python statements

Exercise 17: Find errors in the coding of a formula

Exercise 18: Find errors in a program

References

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 \( \sin x \), 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 document 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 GitHub repository 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...*.