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Introduction to differential geometry

Code: 45747
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Željka Milin Šipuš - Lectures
Lecturers: Domagoj Lacmanović, mag. math. - Exercises
prof. dr. sc. Željka Milin Šipuš - Exercises
dr. sc. Martina Stojić - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: Students will be introduced to the basic concepts of differential geometry of curves and surfaces in space in the local aspect. The geometric point of view will be emphasized. Mathematica/Maple software will be used to visualize introduced concepts.

COURSE DESCRIPTION AND SYLLABUS:
1. Curves in space. Regular curves. Arc length. Parametrization by the arc length. Frenet's moving frame. Frenet's formulas. Flexion and torsion. Fundamental theorem for space curves.
2. Surfaces in space. Regular surfaces. Tangent plane. Differential of a mapping. First fundamental form. Orientation of a surface. Shape operator (Weingarten map). Second fundamental form. Normal curvature. Principal curvatures and vectors. Gaussian and mean curvature.
3. Special curves on a surface: lines of curvatures, asymptotic lines, geodesics. Parallel transport. Local isometry of surfaces. Christoffel symbols. Gauss's Theorema Egregium. Fundamental theorem for surfaces in space.
Literature:
  1. A. Pressley: Elementary Differential Geometry
  2. W. Kühnel: Differential geometry- Curves- Surfaces- Manifolds
  3. A. Grey: Modern differential geometry of curves and surfaces with Mathematica
  4. M. P. do Carmo: Differential Geometry of Curves and Surfaces
  5. R. S. Millman, G. D. Parker: Elements of Differential Geometry
  6. B. O'Neill: Elementary Differential Geometry
1. semester
Geometrija i topologija - Regular study - Mathematics Education

2. semester
Geometrija i topologija - Regular study - Mathematics Education
Consultations schedule:

Content

Link to the course web page: https://web.math.pmf.unizg.hr/nastava/udg/