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Browse materialsMIT 18.102 · Spring 2021

Introduction to Functional Analysis

Subjects: Algebra · Linear Algebra · Mathematics

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

Instructor: Dr. Casey Rodriguez
Term: Spring 2021
Level: Undergraduate
What's inside: 23 videos · 1 exam · 3 lecture notes · 82 other files · 3 web pages
Materials open: Videos here · files on MIT OCW

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

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About this course

Source: MIT OpenCourseWare 18.102 Introduction to Functional Analysis, Spring 2021, Dr. Casey Rodriguez — 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.

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Lecture Notes and Readings

49 files

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12 files

Other materials from this course

Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence Theorem transcriptPDF Download

MIT OpenCourseWare, Dr. Casey Rodriguez, 18.102 Introduction to Functional Analysis, Spring 2021.

License: CC BY-NC-SA 4.0 · Edition: Spring 2021 · 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 and Readings

Assignments and Exams

Other materials from this course

Lecture 1: Basic Banach Space Theory

Lecture 2: Bounded Linear Operators

Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem

Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem

Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem

Lecture 6: The Double Dual and the Outer Measure of a Subset of Real Numbers

Lecture 7: Sigma Algebras

Lecture 8: Lebesgue Measurable Subsets and Measure

Lecture 9: Lebesgue Measurable Functions

Lecture 10: Simple Functions

Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems

Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence Theorem

Lecture 13: Lp Space Theory

Lecture 14: Basic Hilbert Space Theory

Lecture 15: Orthonormal Bases and Fourier Series

Lecture 16: Fejer’s Theorem and Convergence of Fourier Series

Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem

Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space

Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators

Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space

Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint Operators

Lecture 22: The Spectral Theorem for a Compact Self-Adjoint Operator

Lecture 23: The Dirichlet Problem on an Interval