An approximate method for calculating the steady, incompressible, viscous flow over an airfoil, including regions of separated flow, is presented. The finite-difference equations resulting from an integral method for the laminar and turbulent boundary layers are solved simultaneously in a line-relaxation procedure with the equations for the outer, inviscid flow. These coupled equations allow direct interaction between the viscous and inviscid regions, thus eliminating the mathematical difficulties usually associated with separation. A distributed source on the upper surface of the airfoil provides an outflow to simulate the displaced boundary, and a distributed sink downstream of the trailing edge closes the wake. Computed results, which are compared with measurements for an NACA 4412 airfoil, are quite satisfactory for engineering purposes. / Ph. D.