A worked example on scientific computing with Python

Optimal background for reading this note

some interest in exploring physics through numerical simulation
some very basic knowledge of

differential equations
finite difference approximations
Python or Matlab

significant interest in exploring Python for scientific computations to solve a real-world physical problem (with low mathematical complexity)

You can read in two ways: either as a detailed example on using Python for solving differential equations (some very basic Python knowledge is preferred) or just to get an impression of how Python can be used in a Matlab-like fashion.

If you need motivation for using Python as programming language, see Appendix: Quick motivation for programming with Python. Lists of many useful tutorials and introductions to Python, with emphasis on scientific computing, are found in Appendix: Scientific Python resources.