Análise Matemática II B

At the end of this curricular unit, students should have acquired knowledge, skills and competences that allow them to:

- Work with basic notions of topology in Rn.

- Understand the rigorous notion of limit, continuity and differentiability of vector functions of a real variable.

- Apply vector functions of a real variable in the parameterization and study of curves.

- Understand the rigorous notion of limit and continuity of real and vector functions of several real variables and compute limits.

- Know the notion of partial derivative and differentiability for functions of several real variables.

-Understand and apply the implicit function theorem and the inverse function theorem.

- Know Taylor's formula and applications to the study of functions and its extremums.

- Know the notion of double and triple integral and how to compute these integrals using appropriate coordinates.

- Know some applications of double and triple integrals.

- Know the notion of line integral, its applications, and fundamental results.

- Know the notion of surface integral, its application and fundamental results.