Module fourier_coefficients 

Fourier coefficient computation for PDE solutions

Computes coefficients cₙ for series solutions: u(x,t) = Σ cₙ Xₙ(x) Tₙ(t)

Uses inner product: cₙ = ⟨f, Xₙ⟩ / ⟨Xₙ, Xₙ⟩ Where ⟨f, g⟩ = ∫ f(x)g(x)dx

Functions

compute_coefficients_analytical

Simplified coefficient computation for common cases

compute_fourier_coefficients

Compute Fourier coefficients from initial condition

compute_normalization

Compute normalization constant for an eigenfunction