Lectures related to Untitled | EPFL Graph Search

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.