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Lecture
Rotations (2D): Definitions and Analytical Expressions
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Geometric Transformations Compositions
Covers the composition of geometric transformations in 2D, focusing on rotations and reflections to achieve specific results.
Reflection and Rotation Composition
Explores reflection and rotation composition in analytical geometry, including finding centers and solving fixed point systems.
Isometries: Definition and Examples
Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.
Isometries in Euclidean Spaces
Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.
Analytical Geometry: Rotation and Center
Explores rotation in analytical geometry, including center coordinates and fixed points.
Geometric Transformations: Rotations
Covers the analytical expression of rotations in different coordinate systems.
Symmetries of Navier-Stokes Equations
Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.
Translations and Homotheties
Covers translations, homotheties, and geometric transformations using vectors and matrices.
Vector Transformation and Tense
Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.
Geometric Transformations in R2 and R3: Visualizations and Rotations
Covers visualizations in orthonormal bases in R2, focusing on rotations and reflections.