Code: | M355 | Acronym: | M355 |
Keywords | |
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Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Physics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:AST | 1 | Plano de Estudos a partir de 2008 | 3 | - | 7,5 | - | |
L:F | 0 | Plano de estudos a partir de 2008 | 3 | - | 7,5 | - | |
L:M | 11 | Plano de estudos a partir de 2009 | 1 | - | 7,5 | - | |
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Students should acquire knowledge about the application of methods of differential and integral calculus to the study of geometry with emphasis on the differential geometry of surfaces. They should be able to apply this knowledge independently to analyze and solve mathematical problems in contexts where methods of differential geometry are relevant.
Described in the Learning Outcomes.
Basic point set topology necessary for the development of the theory. Smooth surfaces and implicitly defined surfaces. Differentiable functions on surfaces and maps between surfaces. Tangent plane. Orientation. First fundamental form. Area. Geodesics and normal curvature. Geodesic curves. The second fundamental form. Curvature of surfaces. Gauss' Theorema Egregium. The Gauss-Bonnet theorem.
Additionally, one or more of the following optional topics will be treated:
- Global differential geometry of curves and surfaces;
- Classification of topological surfaces;
- Surfaces and abstract manifolds;
- Surfaces of constant curvature and the parallel axiom;
- Differential forms and applications;
- Variational problems and minimal surfaces;
- Applications of differential geometry to physics.
Classes: Lectures, problem sessions, student presentations.
designation | Weight (%) |
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Teste | 100,00 |
Total: | 100,00 |
Attendance (50% of each type of class).
The final mark is the average of the marks of the tests.
Working students: according to the rules for students of the ordinary regime.
Remaining cases: by a single exam, if the right to a special exam exists.
By a single exam, in one of the two exam periods immediately following the one in which the student passed the course.
Pre-requisites: Fundamentals of Linear Algebra, Calculus, Geometry and Analysis in R^n. (Vector Analysis / Multivariable Calculus)