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Real Analysis, 2021


Semester August 2021 - January 2022


Schedule

Lectures

Thursday, Friday 4:00 - 6:00 pm

Problem Session

Wednesday 5:00 - 6:00 pm

Office Hour

Monday 6:00 - 7:00 pm


Content

This is a first course of modern Real Analysis, where we will study the main theorems concerning complete metric spaces, in particular the space of continuous functions, as the Bolzano-Weierstrass, Heine-Borel, Arzelà-Ascoli, and Stone-Weierstrass theorems. We will also study the early theory of Functional Analysis and its applications to Differential Equations.

Syllabus

Homeworks & remarks

All homework assignments and course resources will be posted in the course Classroom page.

Bibliography

R. A. Sáenz, Análisis real: primer curso, Class notes
J. E. Marsden & M. J. Hoffman, Elementary Classical Analysis, 2nd ed., W. H. Freeman, 1993
A. N. Kolmogorov & S. V. Fomin, Introductory Real Analysis, Dover, 1975
W. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, 1976
G. B. Folland, Real Analysis: Modern Techniques and Their Applications, Wiley, 1999
H. L. Royden, Real Analysis, 3rd ed., Macmillan, 1988
H. Hochstadt, Integral Equations, John Wiley & Sons, 2011

Midterm evaluations

There will be two midterm evaluations, each with homework and a written examination.

Homework (40%)

Problems will be assigned weekly, each Friday, to be submitted by next Friday at 5:00 pm.

Written exam (60%)

A written one-hour exam will evaluate the material of the course, focusing on the previous 8 weeks.

Calendar

  • First midterm: October 13, 5:00 pm

  • Second midterm: December 8, 5:00 pm

Final

The final evaluation will consist of a final project and a final written examination, each worth 50% of the final grade.

Written essay

Each student will be assigned a final project, extending the results from class. A report must be submitted before the written examination.

Exam

A two-hour written examination, evaluating the material of the course.

Date

December 15, 4:00 pm

Additional examinations

  • Extraordinary: January 19, 4:00 pm

  • Regularization: January 26, 4:00 pm

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