MATH-213: Differential geometry I - curves and surfaces

Lectures in this course (34)

Explores closed curves in topological spaces, emphasizing their properties and significance in mathematics.

Explores conformal maps, hyperbolic geometry, and isometric properties of disks.

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

Discusses isometries and orthonormal bases in mathematics.

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Covers the basics of linear algebra, including rank, differentiable applications, and submersions.

Covers the concept of osculating planes and parameterized curves, discussing the speed of points and linear independence.

Covers the calculation of the length of curves and the properties of tangent vectors.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

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