Course detail
Differential Geometry
FSI-SDG Acad. year: 2023/2024 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
Entry knowledge
Linear algebra, analytic geometry, differential and integral calculus of functions of one and several variables.
Rules for evaluation and completion of the course
Active attendance at the seminars and written test.
In a 120-minute written test, students have to solve assigned problems.
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.
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.
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.
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.