Lectures related to Geometric Transformations in R2 and R3

Isometries in Euclidean Spaces

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

Symmetry in Modern Geometry

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

Vector Transformation and Tense

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

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Symmetries of Navier-Stokes Equations

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

Geometric Transformations in the Plane: Orientation

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

Rotations and Symmetries

Covers the preservation of isometry by rotations and symmetries.

Geometric Transformations in R2 and R3: Visualizations and Rotations

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

Isometries: Definition and Examples

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

Matrices and Orthogonal Transformations

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Geometric Transformations Compositions

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

Isometries & Orientation: Modern Symmetry

Explores isometries, reflections, rotations, and translations in space, as well as the structure theorem and configurations of planes and lines.

Symmetry in Modern Geometry

Explores symmetry in modern geometry, focusing on isometries, reflections, rotations, and translations, emphasizing the importance of 180-degree rotations.

Symmetry in the Plane

Explores the modern definition of symmetry and its practical applications.

Symmetries of the Wave Equation

Explores the symmetries of the wave equation under Lorentz transformations and the Poincare group.

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Rotations (2D): Definitions and Analytical Expressions

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

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Translations and Homotheties

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Symmetry in Geometry

Explores symmetry in modern geometry, emphasizing reflections, rotations, and practical applications in computer-aided design.