Semester August 2021 - January 2022
Schedule
Lectures
Thursday, Friday 4:00 - 6:00 pm
Problem Session
Wednesday 5:00 - 6:00 pm
Office Hour
Tuesday 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 notesJ. 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 Wednesday at 12:00 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 pmAdditional examinations
- Extraordinary: January 19, 4:00 pm
- Regularization: January 26, 4:00 pm
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