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Lecture

Geometric Rotations in 2D

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Scalar Products in 2D and 3D Geometry

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Rotations: Isometries and Axes

Explores rotations as isometries composed of reflections with common axes and the flexibility in choosing rotation axes.

Isometries in Space: Orientation & Reflections

Explores isometries in space, transformations preserving lengths and angles, including reflections, rotations, and translations.

Geometric Transformations: Rotations

Covers the analytical expression of rotations in different coordinate systems.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Product of 4 Plane Reflections: Normalization

Explores the normalization of the product of 4 plane reflections in space.

Geometric Transformations in the Plane: Examples

Explores geometric transformations in the plane through rotation and reflection examples, emphasizing analytical formulas and characteristic elements.

General Transformations

Covers rotations and general transformations in various dimensions with mathematical formulas and applications.

Symmetries in Mechanics and Wave Equations

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

Rotations: Angular Momentum

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