Joseph Fourier
The life of Joseph Fourier - The Revolutionary Who Solved Heat.
Fourier Series
Introduced in 1807, this idea was initially controversial for claiming arbitrary functions could be represented by trigonometric series.
\[ f(x) = a_0 + \sum_{n=1}^{\infty} \left(a_n \cos nx + b_n \sin nx\right) \]
Fourier Transform
Developed from Fourier’s heat theory, this transform later became essential to physics, engineering, and signal processing.
\[ \hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)e^{-2\pi i \xi x}dx \]
Heat Equation
Fourier formulated this equation in 1807 while studying heat diffusion, laying groundwork for modern partial differential equations.
\[ \frac{\partial u}{\partial t} = \alpha \nabla^2 u \]
Sources: https://mathshistory.st-andrews.ac.uk/Biographies/Fourier/
