MIT 18.102 Introduction to Functional Analysis, Spring 2021

Name: MIT 18.102 Introduction to Functional Analysis, Spring 2021
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What you'll learn

This course includes

30.3 hours of video
Certificate of completion
Access on mobile and TV

Course content

1 modules • 23 lessons • 30.3 hours of video

MIT 18.102 Introduction to Functional Analysis, Spring 2021

23 lessons • 30.3 hours

Lecture 1: Basic Banach Space Theory01:15:19
Lecture 2: Bounded Linear Operators01:24:11
Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem01:04:02
Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem01:14:58
Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem01:10:24
Lecture 6: The Double Dual and the Outer Measure of a Subset of Real Numbers01:20:58
Lecture 7: Sigma Algebras01:20:24
Lecture 8: Lebesgue Measurable Subsets and Measure01:14:02
Lecture 9: Lebesgue Measurable Functions01:24:57
Lecture 10: Simple Functions01:22:55
Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems01:21:38
Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence...01:24:57
Lecture 13: Lp Space Theory01:23:59
Lecture 14: Basic Hilbert Space Theory01:23:24
Lecture 15: Orthonormal Bases and Fourier Series01:16:02
Lecture 16: Fejer’s Theorem and Convergence of Fourier Series01:21:23
Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem01:16:04
Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space01:12:18
Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators01:23:23
Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space01:22:25
Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint...01:10:51
Lecture 22: The Spectral Theorem for a Compact Self-Adjoint Operator01:24:07
Lecture 23: The Dirichlet Problem on an Interval01:23:54