Mean and Gaussian Curvature

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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

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

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Covers the application of the Weingarten map on regular surfaces and the shape operator.