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layout: page | ||
title: 18.102 Introduction to Functional Analysis | ||
permalink: /courses/mit/course-18/18-102/ | ||
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**Catalog description:** | ||
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Normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators. Lebesgue measure, measurable functions, integrability, completeness of L-p spaces. Hilbert space. Compact, Hilbert-Schmidt and trace class operators. Spectral theorem. | ||
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Also see the math department's [subject overview](https://math.mit.edu/academics/undergrad/subjects/181x.html) for courses on analysis. | ||
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### Resources: | ||
- 18.102 Spring 2021 [OCW](https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/) (homework, exams, lecture notes, [lecture videos](https://www.youtube.com/playlist?list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_)) | ||
- 18.102 Spring 2021 [in-class scribe lecture notes](https://web.stanford.edu/~lindrew/18.102.pdf) | ||
- 18.102 Spring 2017 [class website](https://math.mit.edu/~rbm/18-102-S17/) (homework, exams, lecture notes) | ||
- 18.102 Spring 2009 [OCW](https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2009/) (homework, solutions, exams, lecture notes) |
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title: 18.112 Functions of a Complex Variable | ||
permalink: /courses/mit/course-18/18-112/ | ||
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**Catalog description:** | ||
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Studies the basic properties of analytic functions of one complex variable. Conformal mappings and the Poincare model of non-Euclidean geometry. Cauchy-Goursat theorem and Cauchy integral formula. Taylor and Laurent decompositions. Singularities, residues and computation of integrals. Harmonic functions and Dirichlet's problem for the Laplace equation. The partial fractions decomposition. Infinite series and infinite product expansions. The Gamma function. The Riemann mapping theorem. Elliptic functions. | ||
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Also see the math department's [subject overview](https://math.mit.edu/academics/undergrad/subjects/181x.html) for courses on analysis. | ||
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### Resources: | ||
- 18.102 Fall 2019 [in-class scribe lecture notes](https://web.stanford.edu/~lindrew/18.112.pdf) | ||
- 18.112 Fall 2008 [OCW](https://ocw.mit.edu/courses/18-112-functions-of-a-complex-variable-fall-2008/) (homework, solutions, exams, lecture notes) |