Lectures related to Orthogonal coordinates

Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Finite Element Modeling: Systematization and Construction

Covers the systematization and construction of a 2D finite element model.

Regular Curves: Parametrization and Tangent Vectors

Explores regular curves, examples like segments and functions, and curvilinear integrals along regular curves.

Change of Variables in Double Integrals

Explores changing variables in double integrals through examples and curvilinear coordinates.

Parametric Equations and Cartesian Coordinates

Explores parametric equations, Cartesian coordinates, lines equations, and geometric angles between lines.

Finite Element Modeling: Systematization

Covers the systematization of 2D finite element modeling and treatment of curvilinear integrals.

Orthogonality and Orthogonal Bases

Explains orthogonal bases, angles between vectors, and uniqueness of coefficients.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

Orthogonal Vectors and Projections

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Finite Element Method: Construction and Integration

Explores the construction of a 2D finite element model and the treatment of curvilinear integrals.

Signal Approximation and Orthogonal Bases

Explores signal approximation, orthogonal bases, Fourier series, correlation, and vector geometry.

Orthogonal Sets and Bases

Introduces orthogonal sets and bases, discussing their properties and linear independence.

Curvilinear Integrals and Green's Theorem

Introduces curvilinear integrals, parameterization, and Green's Theorem for conservative fields.

Analytical Geometry: Mixed Product and Determinant

Covers the analytical expression of the mixed product and its applications.

Gradient: Scalar Field

Explores gradient in scalar fields, directional derivatives, and level sets.

Curvilinear Integrals

Covers the calculation of curvilinear integrals for a continuous function in R^n and the interpretation of the integral as the sum of small segments along a curve.

Curvilinear Integrals and Conservative Fields

Explores curvilinear integrals, conservative fields, and domain potentials through practical examples and calculations.

Gateways to the Moon and Local Floer Homology

Explores the problem of a falling stone hitting the moon, focusing on gateways to the moon and local Floer homology.