Curves and surfaces with Mathematica 1000-1M13KPM
The course supplements analysis and differential geometry I. In the problem classes we shall use Mathematica for symbolic and numerical calculations and vizualizations.
The topics include: plane curves, evolutes, involutes, global properties of plane curves, curves in R^3, Frenet basis, curvature, torsion, fundamental theorem, knots. Surfaces, Gauss map, tangent plane, metrics, mean curvature, Gauss curvature, asmptotic curves. Ruled surfaces, surfaces of constant Gauss curvature, minimal, rotation surfaces, Theorema Egregium, geodesic curvature, geodesics, Christoffel's symbols, Gauss-Bonnet theorem.
Main fields of studies for MISMaP
geology
astronomy
physics
mathematics
computer science
geography
Type of course
Prerequisites (description)
Learning outcomes
The student knows the fundamental notions of differential geometry and is able to perform symbolic computations and create graphical representations related to these notions in Mathematica.
Assessment criteria
Exam or a project (theoretical and/or using the program Mathematica) and its presentation (student's choice)
Bibliography
A. Gray, Modern differential geometry of curves and surfaces with Mathematica, CRC, 1998.
(there is a newer edition: E. Abbena, S. Salamon, A. Gray, Modern differential geometry of curves and surfaces with Mathematica,Third Edition, CRC 2006)
J. Oprea, Differential geometry and its applications (available online in BUW)
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: