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Browse materialsMIT 18.102 · Spring 2009

Introduction to Functional Analysis

Subjects: Algebra · Linear Algebra · Mathematics

Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain

Instructor: Prof. Richard Melrose
Term: Spring 2009
Level: Undergraduate
What's inside: 10 problem sets · 1 exam · 15 solutions · 1 lecture note · 31 other files · 3 web pages
Materials open: MIT OCW

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18.102 · Spring 2021 · Study here
18.102 · Spring 2009 · Study here (this version)

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About this course

Source: MIT OpenCourseWare 18.102 Introduction to Functional Analysis, Spring 2009, Prof. Richard Melrose — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Has MIT solutions 15 files in this course are named by MIT as solutions.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

How this course was organized

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Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes

26 files

Assignments

24 problem sets

Exams

Other materials from this course

Patriot ProblemsPDF Download

MIT OpenCourseWare, Prof. Richard Melrose, 18.102 Introduction to Functional Analysis, Spring 2009.

License: CC BY-NC-SA 4.0 · Edition: Spring 2009 · Open the original course on OCW ↗

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Introduction to Functional Analysis

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Exams

Other materials from this course

Lecture 1: Linear spaces, metric spaces, normed spaces ( PDF )

Lecture 2: Linear maps between normed spaces ( PDF )

Lecture 3: Banach spaces ( PDF )

Lecture 4: Lebesgue integrability ( PDF )

Lecture 5: Lebesgue integrable functions form a linear space ( PDF )

Lecture 6: Null functions ( PDF )

Lecture 7: Monotonicity, Fatou’s Lemma and Lebesgue dominated convergence ( PDF )

Lecture 8: Hilbert spaces ( PDF )

Lecture 9: Baire’s theorem and an application ( PDF )

Lecture 10: Bessel’s inequality ( PDF )

Lecture 11: Closed convex sets and minimizing length ( PDF )

Lecture 12: Compact sets. Weak convergence. Weak compactness ( PDF )

Lecture 13: Baire’s theorem. Uniform boundedness. Boundedness of weakly convergent sequences ( PDF )

Lecture 14: Fourier series and L² ( PDF )

Lecture 15: Open mapping and closed graph theorems ( PDF )

Lecture 16: Bounded operators. Unitary operators. Finite rank operators ( PDF )

Lecture 17: The second test ( PDF )

Lecture 18: Compact operators ( PDF )

Lecture 19: Fredholm operators ( PDF )

Lecture 20: Completeness of the eigenfunctions ( PDF )

Lecture 21: Dirichlet problem for a real potential on an interval ( PDF )

Lecture 22: Dirichlet problem (cont.) ( PDF )

Lecture 23: Harmonic oscillator ( PDF )

Lecture 24: Completeness of Hermite basis ( PDF )

Lecture 25: The fourier transform on the line ( PDF )

Lecture 26: Hahn-Banach and review ( PDF )