Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.
