Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Explores the well-posedness of elliptic partial differential equations with various boundary conditions, emphasizing the weak formulation and coercivity.
Explores semigroups of linear operators, contraction semigroups, infinitesimal generator, and Riemann integral properties.
