Curves, surfaces and discretization
- Code: DT0837
- Unit Coordinator: Giuseppe Pipoli
- Programme: Double Degrees
- ECTS Credits: 6
- Semester: 2
- Year: 1
- Campus: University of L'Aquila
- Aims:
Learning Objectives.
The course aims at providing the basics of the geometry of curves and surfaces, continuous and discrete.
Those objectives contribute to the learning goals of the entire course of studies, as the inner coherence was verified at the time of the planning of the program.
Learning Outcomes
At the end of the course, the student should
1. know the fundamentals of geometry of curves and surfaces, as tangent and normal space, curvature in the smooth and discrete setting;
2. understand and be able to explain thesis and proofs in geometry of curves and surfaces;
3. have strengthened the logic and computational skills;
4. be able to read and understand other mathematical texts on related topics. - Content:
Geometry of curves: parametrization, Frenet frame, curvature and torsion.
Geometry of surfaces: parametrization, tangent and normal spaces, mean curvature and Gaussian curvature. - Pre-requisites:
Calculus in several variables, fundamental of Mathematical Analysis.
- Reading list:
Manfredo Do Carmo, Differential geometry of curves and surfaces.
Alexander I. Bobenko, Yuri B. Suris, Discrete Differential Geometry: Integrable Structure.
