ABSTRACT
F (s) = ∫ b
f(x)K(s, x) dx,
provided F (s) exists, where s denotes the variable of the transform, F (s) is the integral transform of f(x), and K(s, x) is known as the kernel of the transform. An integral transform is a linear transformation, which, when applied to a linear initial or boundary value problem, reduces the number of independent variables by one for each application of the integral transform. Thus, a partial differential equation can be reduced to an algebraic equation by repeated application of integral transforms. The algebraic problem is generally easy to solve for the function F (s), and the solution of the problem is obtained if we can obtain the function f(x) from F (s) by some inversion formula. The integral transform methods are used to solve a diverse range of initial and boundary value problems, such as problems of circuits, current flow, heat flow, fluid flow, elastic deformation, and control theory.
