Computational Differential Equations - K. Erikson et al.

and

A first course in the numerical analysis of differential equations, A. Iserles

Both books represent a view on "How to tell it to the students: Iserles goes straight to his goal: mathematicians (that special breed, you know) deserve rigorous education. Sometimes he exaggerates, but he succeeds in weaving an interesting red ribbon trough differential equations from ordinary to hyperbolic, in the process he spends a quarter of the text to linear algebra (Gauss, iterative methods, multigrid, fast Poisson solvers). For who can live with his style of treatment this is a very fine book to educate in about 6 hours in a trimester his students in the numerical treatment of differential equations. Those with practical interest will be disappointed, however. The engineering approach is given in Eriksons's book. It treats just about the same subjects, but from a point of view that more relevant from a technical prospect (and, conspicuously, in a different order). The second book is an update of Johnson's book that has been very successful during the past years. It appears that the same verdict can be given to this extended new book. It is nicely crafted and full of interesting details. For me, the question remains whether you should use a comprehensive book like this. For the course on finite elements given at the Eindhoven Technical University this reissue contains redundant information. (R. Mattheij)