Riemann Tensor and Ricci Scalar

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Symmetries and Conservation Laws

Explores Killing vectors, conserved quantities, symmetric spaces, and the Riemann curvature tensor properties.

Linear Shell Theory: Equilibrium Equations

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

Plates II: Föppl-von Kármán Equations

Covers the framework for plates, bending and stretching energies, and Föppl-von Kármán Equations, exploring mean and Gaussian curvatures.

Differential Geometry of Surfaces

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Symmetry in Modern Geometry

Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.

Differential Geometry of Surfaces

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

Tensors and Lorentz Transformations

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.

Curves and Isometries

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Curvature and Osculating Circle

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