|
|
|
||
|
A course for students of cartography and geoinformatics explaining the
basic notions of differential geometry of curves and surfaces, spherical trigonometry, graph theory, and simple mappings in the complex plane. It is a continuation of Mathematics for geographers S710P02. Last update: Hladíková Hana, RNDr., Ph.D. (26.11.2019)
|
|
||
|
Rektorys, K.: Přehled užité matematiky. Prometheus, 1995.
Budínský, B.: Analytická a diferenciální geometrie. SNTL, 1983
Struik, D.J.: Lectures on Classical Differential Geometry. Addison-Wesley Publishing Company, Inc., Reading, London, 1961.
Kreyszig, E.: Introduction to Differential Geometry and Riemannian Geometry. University of Toronto Press, 1968.
Kuntz, E.: Kartennetzentwurfslehre, Grunlagen und Anwendungen, Wichmann, Karlruhe, 1990. Last update: Hladíková Hana, RNDr., Ph.D. (26.11.2019)
|
|
||
|
1. Introductory topics: Taylor's theorem, vector functions and differential operations, analytic geometry in 2D and 3D, vector and scalar product, more dimensional integration, basic curves and surfaces.
2. Curves in the plane and in the space, general parametrization, tangent, length of a curve. Formulae of Frenet, curvature and torsion. Osculating, normal and rectifying planes, order of contact of curves. Derivation of radii of curvature for an ellipsoid of revolution.
3. The first and second fundamental form of a surface. Curves on a surface. Meusnier's and Euler's theorem. The total and mean curvature. Geodesic curvature and geodesic lines. Classification of mappings between surfaces.
4. Basic formulae of spherical trigonometry.
5. Several elementary notions from the graph theory.
6. Functions of complex variable, derivative, analytic functions. Simple mapping in complex plane. Last update: Hladíková Hana, RNDr., Ph.D. (26.11.2019)
|