1807 – Fourier analysis

Harmonic analysis deals with the mathematical representation of combinations of waves. In the abstract worlds of mathematics, trigonometric functions (like a sine wave) are often used to represent waveforms, but these usually present simple waves. In the real world, waves tend to be more complex. By combining the simple waveforms in many different ways, these complex forms can be constructed and studied.

Primitive harmonic series were used by the Babylonians to construct tables of the positions of astronomical bodies.

1759 – values for a sine series representing a vibrating string are computed – Lagrange
1768 – Fourier – bio
1770 – “Réflexions sur la résolution algébrique des équations” cubic equation solutions studied using decomposition – Lagrange
1828 – convergence of trig series to represent arbitrary functions – Dirichlet

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