هندسة تفاضلية - DIFFERENTIAL GEOMETRY

Euclidean 3-space - the theory of curves in the space- Direction fields – Frenet frame- Variable variants of Frenet frame - Curvature and torsion of the curve - Some special curves in the space and their properties - Local surface theory - curves on the surface - The First Fundamental Form, the Second Fundamental Form - Principal Directions and Principal Curvatures - Curvature lines - Convergent lines - Geodesic curves on the surface- Christoffel Symboles – Codazzi and Gauss Equations.

Main Textbook:  Shifrin, T., Differential Geometry: A First Course in Curves and Surfaces, Preliminary Version, 2016 Subsidiary Books:  Talpaert, Y., Differential Geometry with Applications to Mechanics and Physics, 1st Edition, CRC Press, 2000.  Kreyszig, E., Differential Geometry, 1st Edition, Dover Publications, 1991.