Lectures related to Normal coordinates

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers the exponential map, covariant derivatives, connection coefficients, and Riemann curvature tensor.

Introduces one-forms, tensors, normal coordinates, and metric tensors in differential geometry.

Covers coordinates, midpoints, and abscissa in analytical geometry, providing practical problem-solving examples.

Explores Taylor polynomials of order 2 and their applications in differential calculus and polar coordinates.

Explores surface integrals, change of variables, and properties of regular surfaces.

Explores the Schwarzschild metric in General Relativity, focusing on singularities and spherically symmetric solutions.

Covers the calculation of the center of gravity in analytical geometry.

Explores the properties of bisectors and areas in Analytical Geometry.

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

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

Explores stereographic projection and sphere parameterization, emphasizing regularity and line independence.

Discusses the geometry of least squares, exploring row and column perspectives, hyperplanes, projections, residuals, and unique vectors.

Covers cylindrical and spherical coordinates, position, velocity, and acceleration vectors.

Simplifies electric field calculations using Gauss's law and symmetry arguments.

Covers geometric projections using Monge's method, focusing on representing three-dimensional points through their orthogonal projections.

Explores rotation in analytical geometry, including center coordinates and fixed points.

Covers the precise description of the relative positioning of objects in space.