On what basis?
-------------------


    * **Topic:** basis sets, series expansions, Fourier analysis
    * **Task A:** 
        1. Simulate the wave using a complex Fourier transformation. What type of a
           boundary does it implement?
        2. Try reconstructing the solution using only a few expansion coefficients. 
           How does this change the outcome?
        3. Try simulations with different initial shapes.
    * **Task B:** 
        1. Implement the method to reconstruct the function as a sine series.
           You can look at the cosine series for guidance.
        2. Simulate the wave using sine and cosine series expansions. What types of a boundaries
           do these correspond to?
        3. Try simulations with different initial shapes.
    * **Template:** 
        - `fourier.py <http://users.utu.fi/tejohy/teaching/simu/templates/fourier.py>`_
    * **Further reading:**         
        - https://en.wikipedia.org/wiki/Fourier_series
        - `https://en.wikipedia.org/wiki/Basis_(linear_algebra) <https://en.wikipedia.org/wiki/Basis_(linear_algebra)>`_
        - `https://en.wikipedia.org/wiki/Basis_set_(chemistry) <https://en.wikipedia.org/wiki/Basis_set_%28chemistry%29>`_
        - https://en.wikipedia.org/wiki/Fast_Fourier_transform


fourier.py
#################

.. automodule:: fourier
    :members:
    :undoc-members: