Excellent overview at grad. Emphasis toward solution of elliptic PDE's, but good description of methods to get there including linear algebra, Matrix techniques, ODE solving methods, and interpolation theory.
Biggest strength is it provides a coherent framework and structure to attach most commonly used num.
This helps understanding about why to use one method or another. Applications to plasmas, astronmy, and solid state are discussed. Emphasis is on description of algortihms. Some results shown. Source codes shown.