Integraalvõrranditeks

Integraalvõrranditeks are mathematical equations where the unknown function appears under an integral sign. They are a generalization of algebraic equations and differential equations. In their simplest form, an integral equation involves an unknown function, say $y(x)$, and an integral of this function, possibly multiplied by a known kernel function, that is set equal to another known function.

There are several types of integral equations. Fredholmi integraalvõrrandid are characterized by fixed integration limits, typically from a constant $a$ to a constant $b$. Volterra integraalvõrrandid, on the other hand, have at least one variable limit of integration, usually from a constant $a$ to the variable $x$.

Furthermore, integral equations can be classified as linear or nonlinear, depending on whether the unknown function appears linearly. They can also be homogeneous or nonhomogeneous, based on whether the right-hand side of the equation is zero or not. The study of integral equations is crucial in many areas of physics and engineering, including the solution of boundary value problems, wave propagation, and radiative transfer. Techniques for solving them include methods of successive approximations and the use of Green's functions.