Real Analysis II


At the end of this course the student will have acquired knowledge and skills that will enable him (i) to understand that the completeness of R previously studied is a common characteristic to R^n and the importance of this property to optimization problems and equations, (ii) to deal with concepts and results previously studied from a calculus perspective in the curricular unit Cálculo II, from an analytic and abstract point of view, (iii) to make a transition to the more abstract context of metric spaces being acknowledged with topological notions in these spaces and understanding its possible lack of completeness.

General characterization





Responsible teacher

Oleksiy Karlovych


Weekly - 6

Total - Available soon

Teaching language



Available soon


W. Fleming, Functions of Several Variables, second edition, Springer, 1977.

L. Loomis, S. Sternberg, Advanced Calculus, Jones and Bartlett Publishers, 1990.

Teaching method

Classes are theoretical/practical with oral presentation of concepts and results together with their proofs and complemented with examples and applications. The student is encouraged to present and discuss the topics under study. A list of exercises is provided to the students to be solved independently. Specific student difficulties will be addressed during classes or in individual sessions scheduled with the professor. Continuous evaluation is based on two tests. If a student does not obtain approval through continuous evaluation, he can try it in an additional assessment.

Evaluation method

Available soon

Subject matter

Available soon