Course detail
Mathematics IV
FAST-HA01Acad. year: 2011/2012
Complex-valued functions, limit, continuity and derivative. Cauchy-Riemann conditions, analytic functions. Conformal mappings performed by analytic function.
Curves in space, curvature and torsion. Frenet frame, Frenet formulae.
Explicit, implicit and parametric form of the equation of the surface in the space, first fundamental form of a surface and its applications, second fundamental form of a surface, normal and geodetic curvature of a surface, curvature and asymptotic lines on a surface, mean and total curvature of a surface, elliptic, parabolic, hyperbolic and rembilical points of a surface.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Understanding the basics of the theory of functions of a complex variable.
Understanding the basics of differential geometry of 3D curves and surfaces.
Prerequisites
Basics of calculus. Differentiation.
Basics of calculus of two- and more-functions. Partial differentiation.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
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.
Work placements
Aims
Understanding the basics of differential geometry of 3D curves and surfaces.
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
ERWIN KREYSZIG: Differential geometry. Akademische Verlagsgesellschaft, Leipzig, 1957. (EN)
S.P.FINIKOV: Diferencialnaja geometrija. Moskva, 1961. (RU)
Recommended reading
Classification of course in study plans