Differential Geometry of Surfaces

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Second Fundamental Tensor

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

Gaussian Curvature in Plates

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

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Coordinate Systems: Polar and Spherical

Covers polar and spherical coordinate systems, position vectors, equations of motion, and Frenet frame concepts.

Tensors & Indices Recap

Covers the basics of tensors and indices, including contravariant vectors and tensor operations.

Covariance and Contravariance of Vectors

Explains covariance and contravariance of vectors in multilinear algebra and tensor analysis, focusing on their behavior under changes in basis and scale.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Indicial Notation and Vectors

Explores indicial notation, vectors, and the transformation law in the context of mass flux density.

Curves in the Oriented Plane

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.