Functional analysis helps to solve problems where the vector space is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics will include normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of Lᵖ spaces; Hilbert spaces; compact and self-adjoint operators; and the spectral theorem.