Czech

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

Students will achieve the subject's main objectives:
Understanding the basics of the theory of functions of a complex variable.
Understanding the basics of differential geometry of 3D curves and surfaces.

Basic properties of complex numbers as taught at secondary schools.
Basics of calculus. Differentiation.
Basics of calculus of two- and more-functions. Partial differentiation.

Not applicable.

Not applicable.

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1. Complex numbers, basic operations, displaying, n-th root. Complex finctions.
2. Limit, continuity, derivative of a complex function, Cauchy-Rieman 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 ofa 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.

The seminars follow the lectures.

Not applicable.

Understanding the basics of the theory of functions of a complex variable.
Understanding the basics of differential geometry of 3D curves and surfaces.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Not applicable.

Not applicable.

DIRK J. STRUIK. Lectures on classical differential geometry. Dover Publications, 1988 (EN)
ERWIN KREYSZIG: Differential geometry. Akademische Verlagsgesellschaft, Leipzig, 1957. (EN)
S.P.FINIKOV: Diferencialnaja geometrija. Moskva, 1961. (RU)

Not applicable.