Here you can find lists of great Numerical Methods books are or have been used to teach courses at Harvard.
By: Parviz Moin
By: Tao Pang
By: Sauro Succi
By: Michael T. Heath
By: William H. Press, Saul A. Teukolsky, William T. Vetterling
By: Lloyd N. Trefethen
By: Jorge Nocedal, Stephen Wright
By: Bengt Fornberg