Flat Space-Time: Conditions and Theorems

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General Covariance in Gravity

Explores general covariance in gravity, covering equations, curvature tensor, and static gravity field.

Scalar Gravity: Einstein Equations

Introduces scalar gravity, covering covariant derivatives, Ricci tensor, Einstein Equivalence Principle, and the generalization of Newtonian gravity equations.

Gravitational Field Equations

Covers the formulation of gravitational field equations and the motion of particles in gravitational fields.

Lorentz Transformations and Covariant Tensors

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Tensor Analysis: Coordinate Systems

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

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Differential Geometry of Surfaces

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

Elements of Lie Groups and Algebras

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

Indicial Notation and Vectors

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

Linear Shell Theory: Equilibrium Equations

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