Tensors and Normal Coordinates

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Vector Transformation and Tense

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

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Elements of Lie Groups and Algebras

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

Special and General Relativity

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Chemical Environments: Representations and Correlations

Explores chemical environment representations, symmetrized correlations, and machine learning applications at the atomic scale.

Intersection of Manifolds in Exercise 8.2

Covers the intersection of manifolds in exercise 8.2 and fiscal year 8.8.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Gaussian Curvature in Plates

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