Math 175: Elementary Functional Analysis (Winter 2019)
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Course Information
- Instructor: Yiran Wang
- Email: yrw(at)stanford.edu
- Office hours: M, F 2:30pm-4pm at 380-384C.
- Course assistant: Francisco Arana Herrera
- Email: farana(at)stanford.edu
- Office hours: Tue 4pm-7pm at 380-381F.
- Textbook: Introduction to Hilber space by N. Young.
- Notes on Lebesgue integrals by Prof. Luk.
- Syllabus
- Grades (on Canvas)
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Exam Information
- Midterm exam: Monday, February 11th, in class.
- Midterm will cover Chapter 1-6 and the Lebesgue integrals.
- Additional office hours for the midterm:
Feb. 5 and 7, 9am-11am at 380-384C.
- Final exam: Wednesday, March 20th,
3:30pm-6:30pm at 380-380D.
- Additional office hours for the final:
Mar. 13 (Wed), 8:30am-10am at 380-384C.
Mar. 14 (Thu), 9am-11am at 380-384C.
Mar. 18 (Mon), 2:30pm-4pm at 380-384C.
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Homemork
(Note: HW solutions are posted on Canvas.)
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Running schedule
- 01/07: Vector space, inner product space.
- 01/09: Normed spaces, metric space.
- 01/11: Finite vs infinite dimensional normed spaces.
- 01/14: Completeness; closed point property.
- 01/16: Orthogonality; Fourier series.
- 01/18: Separable spaces; orthogonal complements.
- 01/21: Holiday, no class.
- 01/23: Classiclal Fourier series.
- 01/25: Classiclal Fourier series.
- 01/28: Lebesgue integrals on [a, b], properties.
- 01/30: Completeness of L1.
- 02/01: Completeness of L2.
- 02/04: Linear functionals, dual spaces.
- 02/06: Riesz representation theorem.
- 02/08: Hahn-Banach theorem.
- 02/11: Midterm
- 02/13: Banach space of bounded operators.
- 02/15: Inverses of operators.
- 02/18: Holiday, no class.
- 02/20: Adjoints of operators.
- 02/22: Spectrum, compact operators.
- 02/25: Compact operators, Fredholm alternative.
- 02/27: Hilbert-Schmidt operators.
- 03/01: The spectral theorem.
- 03/04: The spectral theorem.
- 03/06: Sturm-Liouville problem.
- 03/08: Green's function.
- 03/11: Green's function.
- 03/13: Applications to PDE.
- 03/15: Review.
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