Elements of Differential Geometry

This chapter introduces fundamental elements of the differential geometry that deal with vector algebra and calculus in curvilinear coordinatesCurvilinear coordinates. The covariant and contravariant basis vectorsContravariant basis vectors, surface and volume mapping and the gradient operator in curvilinear coordinates are presented and discussed. In this textbook, the curvilinear coordinates are suitably introduced in order to define the transfer functions collected in the aerodynamic matrixAerodynamic matrix resulting from the BEM solutions presented in Chaps. 4 and 6 .