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Lecture
2D Transformations: Linear Maps & Matrices
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Isometries in Euclidean Spaces
Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.
Isometries: Definition and Examples
Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.
Laws of Transformation of Velocities and Accelerations
Covers the laws of transformation of speeds and accelerations, including the rotation of points and dynamic movement principles.
3D Transformations: Basics and Euler Angles
Covers 3D transformations, Euler angles, and rotation in computer graphics.
Isometries & Orientation in Modern Geometry
Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.
Rotations (2D): Definitions and Analytical Expressions
Covers the concept of 2D rotations and their analytical expressions.
Symmetry in Modern Geometry
Delves into modern geometry, covering transformations, isometries, and symmetries.
Galilean Transformations: Spacetime and Measurements
Explores Galilean transformations in spacetime, focusing on measurements and coordinate transformations.
Rotation Dynamics: Symmetry Axis
Explores rotation dynamics around a symmetry axis, covering angular momentum, center of mass theorem, and solid body movement.
Matrices and Orthogonal Transformations
Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.