Introduction to Functional Analysis

Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed space that is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics include normed spaces, completeness, functionals, the 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.

The syllabus, on MIT OpenCourseWare

The full course — syllabus, assigned readings, problem sets, exams, and lecture notes — lives on OCW. These open the real thing: