# Introduction to Functional Analysis

- Institution: Massachusetts Institute of Technology
- Department: Mathematics
- Teacher: Dr. Casey Rodriguez
- Term: Spring 2021
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [MIT OpenCourseWare](https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/)
- Licence: [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) (Non-commercial use only.)
- Syllabus: [at the source](https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/pages/syllabus/)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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.

## Lectures

1. [Lecture 1: Basic Banach Space Theory](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/27e96eeeb33c) (Video)
2. [Lecture 2: Bounded Linear Operators](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/a4c83542c698) (Video)
3. [Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/2d137fae061f) (Video)
4. [Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/a1702bcd6137) (Video)
5. [Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/32f63b3b433c) (Video)
6. [Lecture 6: The Double Dual and the Outer Measure of a Subset of Real Numbers](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/3c2846d4dcaf) (Video)
7. [Lecture 7: Sigma Algebras](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/ecb28843d61e) (Video)
8. [Lecture 8: Lebesgue Measurable Subsets and Measure](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/191e403f20ca) (Video)
9. [Lecture 9: Lebesgue Measurable Functions](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/e6093feeb220) (Video)
10. [Lecture 10: Simple Functions](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/f394542996d2) (Video)
11. [Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/99a6cd0d436a) (Video)
12. [Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence Theorem](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/3cbd9d1463a6) (Video)
13. [Lecture 13: Lp Space Theory](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/b95f94f4bc6d) (Video)
14. [Lecture 14: Basic Hilbert Space Theory](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/6180e0a2e04d) (Video)
15. [Lecture 15: Orthonormal Bases and Fourier Series](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/4db67eeedb15) (Video)
16. [Lecture 16: Fejer’s Theorem and Convergence of Fourier Series](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/7160486fbcc5) (Video)
17. [Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/1b5dbbfc6a69) (Video)
18. [Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/72ad70b12dc5) (Video)
19. [Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/f501cda3d344) (Video)
20. [Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/2c42ae89ed25) (Video)
21. [Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint Operators](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/0ef358822cb1) (Video)
22. [Lecture 22: The Spectral Theorem for a Compact Self-Adjoint Operator](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/2143e99974bd) (Video)
23. [Lecture 23: The Dirichlet Problem on an Interval](https://invisiblenetwork.ai/learn/mit/18-102-introduction-to-functional-analysis-spring-2021/85e8248b6f96) (Video)