Course detail
Differential Geometry
FSI-SDG Acad. year: 2022/2023 Summer semester
The classical differential geometry of curves and surfaces: contact of curves, Frenet formulas, osculating curves, contact of surfaces, the first and the second fundamental form, asymptotic curves, Gauss curvature, ruled surfaces, the intrinsic geometry of a surface. Elements of Tensor Calculus.
Language of instruction
Czech
Number of ECTS credits
4
Department
Learning outcomes of the course unit
Students will be made familiar with classical differential geometry of curves and surfaces. They will be able to apply this theory in various engineering tasks.
Prerequisites
Linear algebra, analytic geometry, differential and integral calculus of functions of one and several variables.
Planned learning activities and teaching methods
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes
Active attendance at the seminars and written test.
In a 120-minute written test, students have to solve assigned problems.
Aims
The course aims to acquaint the students with the basics of classical differential geometry of curves and surfaces. Another goal of the course is to develop the students' logical thinking.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is recommended, attendance at seminars is required. The lessons are planned on the basis of a weekly schedule. The way of compensation for an absence is fully at the discretion of the teacher.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
Week 1: The notion of a curve.
Week 2: The contact of curves.
Week 3: Frenet formulas of a plane curve.
Week 4: Osculating curves.
Week 5: Frenet formulas of a space curve.
Week 6. The notion of a surface.
Week 7: The contact of surfaces.
Week 8: The first fundamental form.
Week 9: The second fundamental form.
Week 10: Asymptotic curves.
Week 11: The Gauss curvature.
Week 12: Ruled surfaces.
Week 13: The intrinsic geometry of a surface.
Exercise
13 hours, compulsory
Teacher / Lecturer
Syllabus
Seminars related to the lectures given in the previous week.