Real Analysis

Semester August 2017 – January 2018


Lecture Office hour Problem session
Monday – Tuesday
4:00 – 6:00 pm
5:00 – 6:00 pm
4:00 – 5:00 pm


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.


Homeworks & remarks


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 (optional) homework and a written examination.

Homework (up to 40%)

Problems will be assigned weekly, to be submitted by each Friday 4:00 pm. Their submission is optional, and, in the case of submitted, each problem set will provide 5% of the midterm grade.

Written exam (60 -100%)

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


  • First midterm: September 29
  • Second midterm: November 24

Final exam

The final (Ordinary) examination will be a two-hour written exam and will evaluate the complete course. It will consist of 50% problem solving and 50% knowledge of the material covered in the course.


December 11, 4:00 pm

Additional examinations

  • Extraordinary: January 9, 4:00 pm
  • Regularization: January 22, 4:00 pm