Mathematics Darboux's Theorem This post gives a detailed overview of Darboux's theorem, discussing the significance of the theorem and providing two different proofs.
Physics Hamiltonian Mechanics This post introduces Hamiltonian mechanics using the formalism of differential geometry, culminating in Noether's theorem, which describes the correspondence between certain symmetries and conservation laws.
Mathematics The Euclidean Metric in Spherical Coordinates This post discusses the derivation of the expression for the Euclidean metric in spherical coordinates.
Physics The Einstein-Hilbert Action This post describes how to derive the field equation of General Relativity from the Einstein-HIlbert action.
Differential Geometry Covariant Derivatives of Tensor Fields This post discusses covariant derivatives of tensor fields.
Mathematics Curvature Tensors This post discusses the concept of curvature in manifolds and various tensor fields which measure this curvature.
Mathematics Covariant Derivatives This post discusses the concept of a covariant derivative on a smooth manifold.
Differential Geometry Smooth Manifolds This post examines the basic properties of smooth manifolds and gives a few detailed examples.
Mathematics Tangent Spaces This post contains a detailed explanation of the concept of the tangent space at a point on a smooth manifold.
