- #1
neelakash
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Homework Statement
Given [tex]\frac{1}{| \int\ f(\ x)\ g(\ x)\ d\ x\ |}=\int \frac{\ f(\ x)}{\ g(\ x)}\ d\ x[/tex]
Does the above put any condition on f(x) and g(x)?
An integral equation is an equation that contains an unknown function within an integral sign. It relates the value of a function to its integral over a given domain.
The solution of an integral equation is important in many areas of mathematics and physics, as it allows us to find an unknown function from its integral. This can help in understanding physical phenomena and in solving differential equations.
There are several methods for solving integral equations, such as the method of successive approximations, the method of moments, and the Fredholm and Volterra methods. The choice of method depends on the type of equation and the properties of the unknown function.
A Volterra integral equation has a kernel that depends only on the current value of the unknown function, while a Fredholm integral equation has a kernel that depends on both the current value and past values of the unknown function. This means that the solution to a Fredholm equation is more sensitive to initial conditions than a Volterra equation.
Yes, integral equations have many applications in physics, engineering, economics, and other fields. They are used to model various physical phenomena, such as heat transfer, diffusion, and fluid flow. They are also used in signal processing and image reconstruction.