M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2023
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 M4,01024
  • Timetable of Seminar Groups:
M4190/01: Tue 14:00–15:50 M2,01021, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && ( M1100 Mathematical Analysis I || M1100F Mathematical Analysis I ))|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. This covers both the theory of local invariants and also global properties of curves and surfaces.
Learning outcomes
At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curvatures. Covariant derivative, intrinsic and extrinsic geometry of surfaces. Gauss-Bonnet theorem.
Literature
    recommended literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
    not specified
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Two hours of lectures and two hours of problem class.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2023/M4190