UE Differential and dynamic geometry

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Degrees incorporating this pedagocial element :

Description

Introduction to curves and surfaces.

Curves: Frénet references, covariant derivatives, reference fields, connection forms, structural equations.

Surfaces: surfaces of R^3, plane tangents, differential forms, differentiable applications between surfaces.

Abstract Variety: Whitney's Theorem

Curvature: Normal curvature, Gauss curvature, Geodesics. Case of surfaces of revolution.

Geometry of the surfaces of R^3: Egregium theorem, Gauss Bonnet's theorem

 Possibility of complement: Transition to sub-varieties of Rn and abstract varieties

 Possibility of complement: Introduction to dynamic systems. Vector fields and dynamic systems on varieties

Recommended prerequisite

Differential calculus of L3