Lectures related to General Transformations

Symmetries of Navier-Stokes Equations

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Conformal Transformations: Part 1

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Geometric Transformations Compositions

Covers the composition of geometric transformations in 2D, focusing on rotations and reflections to achieve specific results.

Rotations (2D): Definitions and Analytical Expressions

Covers the concept of 2D rotations and their analytical expressions.

Rotations and Symmetries

Covers the preservation of isometry by rotations and symmetries.

Isometries: Definition and Examples

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Geometric Transformations: Rotations

Covers the analytical expression of rotations in different coordinate systems.

Geometric Rotations in 2D

Covers the geometric definition of rotations in 2D and analytical expressions for rotations using matrices.

Geometric Transformations in R2 and R3: Visualizations and Rotations

Covers visualizations in orthonormal bases in R2, focusing on rotations and reflections.

Geometric Transformations in the Plane: Orientation

Covers the concept of orientation in the plane and transformations using matrices.

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Symmetries in Mechanics and Wave Equations

Explores symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.

Lie Algebra of Lorentz Group

Covers the Lie algebra of the Lorentz group, focusing on boosts, rotations, and transformations.

Analytical Geometry: Rotation and Center

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

Isometries: Final Panorama

Explores the synthesis of plane isometries and their composition through axial reflections, rotations, translations, and glided reflections.

Rotations: Angular Momentum

Covers angular momentum in rotations, including preservation of angles and vector products.

Geometry: Reflections and Transformations

Explores geometry transformations, emphasizing isometries, point reflections, rotations, and translations to illustrate fundamental geometric principles.

Geometry: Transformations and Isometries

Explores transformations and isometries in geometry, preserving properties through translations, rotations, and reflections.