Transonic flow characteristics and their applications towards external and internal aerodynamics. Euler, Full-Potential and Transonic Small-Disturbance equations. Shock waves and rotational flows. Method of Characteristics. Finite-Difference schemes (unsteady, rotated). Von Neuman stability analysis. Artificial viscosity and compressibility. Implicit and explicit schemes. Airfoil design in transonic flows. Parameterization of airfoils. Supercritical airfoils. Airfoil optimization problem: inverse and direct formulations. Transonic wings: induced drag, taper ratio, wing-fuselage (area ruling).