The Fredholm equation is an integral equation of the form:

```       /b
g(t) = |  K(s,t) f(s) ds
/a
```

where `g(t)` is often called the "data" and `K(s,t)` is the kernel of the equation. Fredholm equations are linear transformations of a function `f(t)`, and as such, they can be seen as a convolution of `f(t)` with a varying impulse response. Of particular interest is the case where `f(t)` is unknown; one then can find `f(t)` from `g(t)` and `K(s,t)`, if the kernel is invertible (that is, non singular).

If the upper limit of the integral is replaced by variable `t`, i.e.:

```       /t
g(t) = |  K(s,t) f(s) ds ,
/a
```

we get a Volterra equation. In this case, it is always possible to retrieve `f(t)` from `g(t)` since the discontinuity in the integration range breaks any smoothness that the kernel may have at `s = t`. This is analogous to the case of a matrix equation involving a lower triangular matrix.

Fredholm and Volterra equations of this form are said to be "of the first kind"; the second kind being

```         /b
f(t) = k |  K(s,t) f(s) ds + g(t)
/a
```

for the Fredholm equation, and of course

```         /t
f(t) = k |  K(s,t) f(s) ds + g(t)
/a
```

for the Volterra equation, where `k` is a given constant. Those last equations are analoguous to matrix eigenvalues problems.

A nonlinear Fredholm equation would be of the general form:

```       /t
g(t) = |  f(s) K(s,t,f(s)) ds
/a
```