Oct 22, 2020   12:29 p.m. Sergej

# Course syllabus I1-DG - Differential geometry (FCE - WS 2020/2021)

Information sheet          ECTS          Syllabus

Slovak          English

University:
Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit code:
I1-DG
Course unit title: Differential geometry
Mode of delivery, planned learning activities and teaching methods:
 lecture 2 hours weekly (on-site method) seminar 2 hours weekly (on-site method)

Credits allocated: 5

Recommended semester/trimester: Mathematical and Computational Modeling - master (compulsory), 1. semester
Level of study:
2.
Prerequisites for registration:
none

Assesment methods:
During the semester - presence in lectures and seminars, earning at least 56% of points from both theoretical and practical assignments
During the examination period - written and oral exam, earning at least 56% of both.

Learning outcomes of the course unit:
After completing this course, the student should be familiar with important concepts of classical differential geometry. He should be able to understand important results concerning curves in Eucledian spaces including the proofs. He should be able to apply the knowledge - the exercise is focused on application and illustration of the concepts by means of simple Mathematica programs.

Course contents:
- Parametric curve.
- Plane and space curves - length, curvature and torsion.
- Jordan's curve theorem.
- Isoperimetric inequality.
- Evolution of plane curves.
- Parametric surface.
- First fundamental form.

Basic:
 PRESSLEY, A. Elementary Differential Geometry. London: Springer, 2012. GRAY, A. -- SALAMON, S. -- ABBENA, E. Modern Differential Geometry of Curves and Surfaces with Mathematica. London: Chapman&Hall, 2006. 1016 p.

Language of instruction: slovak

Notes:

Courses evaluation:
Assessed students in total: 48

ABC
D
E
FX
12,5 %
25,0 %
29,2 %
22,9 %
2,1 %
8,3 %
Name of lecturer(s):
prof. RNDr. Karol Mikula, DrSc. (person responsible for course)
Ing. Peter Sarkoci, PhD. (examiner, instructor, lecturer) - slovak, english
doc. Mgr. Mariana Sarkociová Remešíková, PhD. (examiner, instructor, lecturer) - slovak, english
Ing. Mgr. Lukáš Tomek, PhD. (examiner, instructor, lecturer)

Last modification:
30. 3. 2020
Supervisor:
prof. RNDr. Karol Mikula, DrSc. and programme supervisor

Last modification made by Ing. Marián Dubík on 03/30/2020.

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