Basic mathematical relations of fluid dynamics for modified panel methods

Classical panel methods need some modifications in order to account for important features of real flow fields. The list of these features includes a wide spectrum of effects (appearing in many fluid dynamics problems), and their mathematical description is non-standard in some cases. Fundamental relationships and boundary conditions can have different, although equivalent forms. The paper presents foundation of potential flows and is prepared as a common foundation for any next papers devoted to the review of selected modified panel methods and their application to complex flow field calculations.