Symmetries in Mechanics and Wave Equations

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Explores the symmetries of Newtonian Mechanics, Lagrangian mechanics, and the conservation of energy.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Explores Lorentz transformations, boosts, and symmetries in Newtonian mechanics.

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

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

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

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

Covers the preservation of isometry by rotations and symmetries.

Explores the Hamiltonian formalism, conservation laws, preserved quantities, and differential equations in classical physics.

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.