1. Complex numbers, basic operations, displaying, n-th root. Complex functions. 2. Limit, continuity, derivative of a complex function, Cauchy-Riemann conditions. 3. Analytical functions. Conform mapping implemented by an analytical function. 4. Conform mapping implemented by an analytical function. 5. Planar curves, singular points on a curve. 6. 3D curves, curvature and torsion. 7. Frenet trihedral, Frenet formulas. 8. Explicit, implicit, and parametric equations of a surface. 9. The first basic form of a surface and its use. 10. The second basic form of a surface. Normal and geodetic curvature of a surface. Meusnier's theorem. 11. Asymptotic curves on a surface. 12. Mean and total curvature of a surface. 13. Elliptic, hyperbolic, parabolic and circular points of a surface.

1. Complex numbers, basic operations, displaying, n-th root. Complex functions. 2. Limit, continuity, derivative of a complex function, Cauchy-Riemann conditions. 3. Analytical functions. Conform mapping implemented by an analytical function. 4. Conform mapping implemented by an analytical function. 5. Planar curves, singular points on a curve. 6. 3D curves, curvature and torsion. 7. Frenet trihedral, Frenet formulas. 8. Explicit, implicit, and parametric equations of a surface. 9. The first basic form of a surface and its use. 10. The second basic form of a surface. Normal and geodetic curvature of a surface. Meusnier's theorem. 11. Asymptotic curves on a surface. 12. Mean and total curvature of a surface. 13. Elliptic, hyperbolic, parabolic and circular points of a surface. Seminar evaluation.