### Fourier Series 101

In mathematics, a Fourier series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. With appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). As such, the summation is a synthesis of another function.

... from Wikipedia.

So what does that mean in everyday English?

Mathematicians do have a tendency to make things much more complex than they are.

I found this wonderful explanation of what is a Fourier Series on YouTube recently. It's well worth a watch.

So now the explanation at Wikipedia starts to make some sense.

and Mathworld at Wolfram had this to say which also now starts to make sense

Encyclopedia of Math was not helpful at all at least to me.

Just for fun from Wolfram Demonstration. Just play with the buttons and sliders.

Fourier Synthesis for Selected Waveforms by Kenny F Stephens.
"Combine up to nine harmonic frequencies to visualize the resulting waveform using Fourier synthesis. Several standard waveforms are provided (sine, square, sawtooth, and triangle)."

### Mikes Notes

• Video big picture the best approach to learning new maths
• Use Wolfram CDF
• Jupyter?