The main feature of this text is the discussion on how modern concepts in computer science can be applied in order to develop scientific software that is easier to extend, maintain and use than the more traditional counterparts.

Part 1 Numerical software tools: object-oriented numerics; basic tools for linear algebra; software tools for modelling scattered data; a comprehensive set of tools for solving partial differential equations - Diffpack; on the numerical efficiency of C++ in scientific computing. Part 2 Partial differential equations: basic equations in Eulerian continuum mechanics; a mathematical model of macrosegregation formation in binary alloy solidification; computation of macrosegregation due to solidification shrinkage; a mathematical model for the melt spinning of polymer fibres; finite element methods for two-phase flow in heterogeneous porous media; splines and ocean wave modelling; Krylov sybspace iterations for sparse linear systems; preconditioning linear saddle point problems. Part 3 Geometric modelling: surface modelling from scattered geological data; varioscale surfaces in geographic information systems; surface modelling from biomedical data; data reduction of Piecewise linear curves; aspects of algorithms for manifold intersection; surface editing.