Functional Analysis I: Spectral Theorem

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

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Introduces linear and bounded operators, compact operators, and the Banach space.