👉 The created math, often associated with the work of mathematician and philosopher Joseph Fourier and others in the field of harmonic analysis, introduces a novel approach to solving partial differential equations (PDEs) by representing functions as infinite series of orthogonal basis functions, typically trigonometric polynomials like sine and cosine. This method, known as Fourier series or Fourier transforms, allows for the decomposition of complex functions into simpler components, making it easier to solve PDEs by converting them into algebraic equations. The orthogonality of these basis functions ensures that the coefficients in the series expansion can be computed independently, simplifying the solution process. This approach is particularly powerful for problems with periodic boundary conditions or defined on finite intervals, enabling efficient computation and analysis of solutions in fields like physics, engineering, and signal processing.
