Differential Geometry of Surfaces

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Related lectures (31)

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Shells I: Mechanics of Slender Structures

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

Shells I

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

Differential Geometry of Surfaces

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

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Shells I: Mechanics of Slender Structure

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

Special Relativity

Covers the main points of special relativity, including symmetries, transformations, 4-vectors, Maxwell equations, and proper time.

Linear Shell Theory: Equilibrium and Energy

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Linear Shell Theory: Equilibrium Equations

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Tensor Analysis: Coordinate Systems

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

Differential Geometry: Parametric Curves & Surfaces

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