Philosophy of computational fluid dynamics The governing equations of fluid dynamics: their derivation, a discussion of their physical meaning Mathematical behavior of partial differential equations: the impact on CFD Basic aspects of discretization Grids with appropriate transformations Some simple CFD techniques: a beginning Some aplications Numerical solutions of quasi - one dimensional nozzle flows Numerical solution of two dimensional supersonic flow: prandtl meyer expansion wave Incompressible couette flow: numerical solutions by means of an implicit method and the pressure correction me Supersonic flow over a flat plate: numerical solution by solving the complete navier stokes equations Other topics Some advanced topics in modern CFD: A discussion The future of CFD Thomas' algorithm for the solution of a tridiagonal system of equatioins