General Covariance in Gravitational Field

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General Covariance in Gravity

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

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Scalar Gravity: Einstein Equations

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

Flat Space-Time: Conditions and Theorems

Covers the necessary conditions and theorems to have flat space-time and discusses the symmetry properties of the Riemann tensor.

Special and General Relativity

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

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.

Einstein Equations

Covers the derivation of Einstein equations and the Schwarzschild metric.

Gaussian Curvature in Plates

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

Plates II: Föppl-von Kármán Equations

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.