Table of contents : Front Matter....Pages I-XII The basic equation of fluid dynamics....Pages 1-52 Partial differential equations: analytic aspects....Pages 53-80 Finite volume and finite difference discretization on nonuniform grids....Pages 81-109 The stationary convection-diffusion equation....Pages 111-161 The nonstationary convection-diffusion equation....Pages 163-226 The incompressible Navier-Stokes equations....Pages 227-262 Iterative methods....Pages 263-303 The shallow-water equations....Pages 305-338 Scalar conservation laws....Pages 339-396 The Euler equations in one space dimension....Pages 397-466 Discretization in general domains....Pages 467-502 Numerical solution of the Euler equations in general domains....Pages 503-530 Numerical solution of the Navier-Stokes equations in general domains....Pages 531-566 Unified methods for computing incompressible and compressible flow....Pages 567-601 Back Matter....Pages 603-644