University of West Bohemia
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for academic year 2024/2025
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Course: Differential Geometry

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Course title Differential Geometry
Course code KMA/DG
Organizational form of instruction Lecture + Seminar
Level of course Bachelor
Year of study 2
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Bizzarri Michal, Doc. RNDr. Ph.D.
  • Vršek Jan, Doc. RNDr. Ph.D.
Course content
1. Vector calculus 2. Curves in En, Frenet equations 3. Planar and spatial curves 4. Surfaces - definition and basic notions 5. First fundamental form, curves on surfaces 6. Weingarten map 7. Curvatures, second fundamental form 8. Minimal surfaces 9. Special curves on surfaces 10.Geodetic curves 11.Paralellel transport 12.Gauss-Bonet theorem I 13.Gauss-Bonet theorem II

Learning activities and teaching methods
Lecture, Practicum
  • Contact hours - 52 hours per semester
  • Preparation for comprehensive test (10-40) - 30 hours per semester
  • Presentation preparation (report) (1-10) - 10 hours per semester
  • Preparation for an examination (30-60) - 50 hours per semester
prerequisite
Knowledge
We require a basic orientation in the concepts and skills of differential and integral calculus of functions of one or more real variables. Basic orientation in the foundations of linear algebra and analytic geometry is also necessary.
Skills
aplikovat dovednosti získané úspěšným zvládnutím základních kurzů matematiky (matematické analýzy) a lineární algebry
teoreticky i prakticky pracovat s pojmy derivace a integrál
řešit soustavy lineárních algebraických rovnic
pracovat s lineárními a kvadratickými objekty (rovnice, společné body)
pracovat s vektory (lineární závislost, vektorový, skalární, smíšený součin)
Competences
N/A
N/A
N/A
N/A
learning outcomes
Knowledge
The student is able to describe curves and surfaces in parametric form (and vice versa, the parametric description to visualize) and from this description to derive important characteristics of the object, especially its curvature.
Skills
pro křivku a plochu vytvořit parametrický popis
z parametrického popisu provést vizualizaci objektu (křivky a plochy)
z popisu odvodit důležité charakteristiky křivky, zejména jeho křivosti (křivost a torze)
z popisu odvodit důležité charakteristiky plochy (1. a 2. tenzor plochy, Gaussova, střední a geodetická křivost)
ze zjištěných charakteristik odvodit vlastnosti popř. typ křivek (rovinnost, obalové křivky, tečné vlastnosti)
ze zjištěných charakteristik odvodit vlastnosti popř. typ ploch (rozvinutelné plochy, minimální plochy, obalové plochy, křivky na plochách)
Competences
N/A
teaching methods
Knowledge
Lecture supplemented with a discussion
Practicum
Skills
Lecture supplemented with a discussion
Practicum
Competences
Lecture supplemented with a discussion
Practicum
assessment methods
Knowledge
Combined exam
Skills
Combined exam
Competences
Combined exam
Recommended literature
  • Oprea, J.: Differential geometry and Its Applications. The Mathematical Association of America, USA 2007..
  • Pressley, A.: Elementary differential geometry. Springer, London 2001..
  • Budinský, B. Analytická a diferenciální geometrie. 1. vyd. Praha : SNTL, 1983.
  • O'Neill, Barrett. Elementary differential geometry. 2nd ed. Amsterdam : Elsevier Academic Press, 2006. ISBN 0-12-088735-5.
  • Struik, Dirk Jan. Lectures on classical differential geometry. Second edition. 1988. ISBN 0-486-65609-8.
  • Tapp, Kristopher. Differential geometry of curves and surfaces. 2016. ISBN 978-3-319-39798-6.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
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Faculty: Faculty of Education Study plan (Version): Geography in Education (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physics in Education (16) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (16) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Geography in Education (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (18) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (18) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Geography in Education (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (16) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (18) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (18) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Music in Education (19) Category: Art and applied art 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physics in Education (19) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (18) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): English Language in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (17) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (17) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (16) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (19) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (19) Category: Physical education and sport 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (19) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (17) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (17) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physics in Education (17) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (19) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (17) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Summer
University of West Bohemia, date of update: 26.07.2024 23:53. Data created for academic year 2024/2025