Geometric Transformations in R2 and R3: Visualizations and Rotations

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

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

Covers velocity, acceleration, dynamics, moments of inertia, and kinetic energy storage systems.

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

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

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

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

Explores the concept of angles in circular trigonometry, emphasizing geometric angles and their properties.

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Covers the preservation of isometry by rotations and symmetries.