Conceptual
Browse Instruct Curate

Heat Equation Solutions and Fourier Series Decomposition in Complex Numbers

The Fourier series theorem states that any periodic function with square-integrable properties can be decomposed into a sum of complex exponential functions representing orthogonal basis vectors at integer frequencies. This decomposition relies on the linearity of partial differential equations, where arbitrary initial conditions are reconstructed as a superposition of eigenmodes to solve heat diffusion problems and other linear dynamical systems.