I am looking at a research paper that mentions integral operators (which in this case is brought up in reference to shading equations that are integral operators) and it says that we can create a matrix representation of integral operators using Galerkin projections. I am having difficulty finding specific literature on Galerkin projections. When I speak of integral operators $\textbf{K}$ of the form:
$$g(y) = K f |\_{y} = \int\_X k(x,y)f(x)dx$$
where $k(x,y): X\times X\rightarrow \mathbb{R}$ is the kernel of the integral operator. Thanks for any help!



Galerkin Projection on Integral Operators
The idea of the Galerkin method is similar for partial differential equations and for integral equations, hence, any book on numerics of PDEs (that does finite elements) should be a good reference, and also every book on numerical methods for integral equations, e.g. 


* "Integral Equations: Theory and Numerical Treatment" by Hackbusch or
* "Computational Methods for Integral Equations" by Delves and Mohamed.


There is also the original article ["The discrete Galerkin method for integral equations" by Atkinson and Bogomolny](http://www.jstor.org/discover/10.2307/2007830?uid=3737864&uid=2129&uid=2&uid=70&uid=4&sid=21104819443411)


