@inproceedings{PourEl1989ComputabilityIA,
title={Computability in analysis and physics},
author={M. B. Pour-El and J. I. Richards},
booktitle={Perspectives in Mathematical Logic},
year={1989}
}

This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning. Among the topics dealt with are: classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The book is self-contained, and yet sufficiently detailed to provide an introduction to research in this area.