Curves and surfaces with Mathematica

General data

Course ID:	1000-1M13KPM
Erasmus code / ISCED:	(unknown) / (unknown)
Course title:	Curves and surfaces with Mathematica
Name in Polish:	Krzywe i powierzchnie z Mathematicą
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Main fields of studies for MISMaP:	applied geology astronomy computer science geography geology mathematics physics
Type of course:	elective monographs
Prerequisites (description):	Analysis I, II, Linear algebra, basic computer skills.
Short description:	The course supplements analysis and differential geometry I. In the problem classes we shall use Mathematica for symbolic and numerical calculations and visualisations.
Full description:	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.
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)
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 methods and assessment criteria:	Exam or a project (theoretical and/or using the program Mathematica) and its presentation (student's choice)

This course is not currently offered.

Course descriptions are protected by copyright.
Copyright by University of Warsaw.