Homogeneity
Homogeneity [ edit ] Homogenous : An integral equation is called homogeneous if the known function � is identically zero. [1] Inhomogenous : An integral equation is called homogeneous if the known function � is nonzero. [1] Regularity [ edit ] Regular : An integral equation is called regular if the integrals used are all proper integrals. [7] Singular or weakly singular : An integral equation is called singular or weakly singular if the integral is an improper integral. [7] This could be either because at least one of the limits of integration is infinite or the kernel becomes unbounded, meaning infinite, on at least one point in the interval or domain over which is being integrated. [1] Examples include: [1] � ( � ) = ∫ − ∞ ∞ � − � � � � ( � ) � � � [ � ( � ) ] = ∫ 0 ∞ � − � � � ( � ) � � These two integral equations are the Fourier transform and the Laplace transform of u(x) , respectively, with both being Fredholm equations of th...