Stereographic Projection and Metric Tensors

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Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Explores the evolution of projective geometry and its applications in architectural representation.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.

Covers DC currents, resistors, capacitors, Kirchhoff's laws, and electromotive force in electric circuits.

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