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An integral equation is an equation in which an unknown function appears under one or more integration signs. Integral equations also form one of the most useful tools in many branches of pure analysis, such as functional analysis and stochastic processes.

There is also a close connection between integral and differential equations, and some problems may be formulated either way (for example, Green's function, Fredholm theory, and Maxwell's equations). Many initial and boundary value problems associated with ODE(ordinary differential equations) and PDE(partial differential equations) can be transformed into problems of solving some approximate integral equations.

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