A Fredholm equation of the first kind is an integral equation of the form $$ \int_{a}^{b} K(x,y) f(y) dy = g(x), \quad \forall x \in [a,b], $$ and a Fredholm equation of the second kind is an integral equation of the form $$ f(x) - \lambda\int_{a}^{b} K(x,y)f(y)dy = g(x), \quad \forall x \in [a, b], $$ where $$ Kf(x) = \int_{a}^{b} K(x,y)f(y)dy, \quad \forall x \in [a, b] $$ is a compact operator in some function space.