Shells I: Mechanics of Slender Structures

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Geometric Surfaces: Paraboloid and Hyperboloid Concepts

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Plates II: Föppl-von Kármán Equations

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

Surfaces with Variable Curvature

Explores surfaces with variable curvature, discussing their construction and properties.

Shells II: Mechanics of Slender Structure

Covers the expression of energy, dimensional reduction, equilibrium equations, and the relationship between covariant and contravariant components in shell mechanics.

Differential Geometry: Curves

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

Cylinders: Pressure and Geometry

Explores cylindrical pressure vessels, surfaces parametrization, and geometrical properties computation.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Mechanics of Slender Structure

Covers the expression of the Kirchhoff-St. Venant energy in a covariant setting and the equilibrium equations for spherical shells, among other topics.

Geometric Principles in Architecture: Hyperboloids and Paraboloids

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.