Matemática III

Theoretical classes introduce concepts, properties and examples, enabling students to understand the exercises proposed and identify the mathematical tools to be used. In the remaining classes, shared, individual and/or group resolution of exercises and activities allows students to develop specific analysis and calculation skills to solve the problems proposed.

The course aims to develop theoretical and applied understanding of fundamental concepts in mathematics, particularly in the field of integral calculus on IRn and series (numerical and power series). In the theoretical classes, an expository teaching method is adopted, through which essential concepts are introduced and illustrative examples of their application are presented. In the remaining classes, an active teaching method is used, focused on solving exercises – individually and/or in groups – promoting the consolidation of content, as well as the development of analysis and problem-solving skills.

1. Integral calculus on IRn – Multiple integrals – double integrals (definition, properties and geometric interpretation, calculation in Cartesian and polar coordinates, applications); triple integrals (definition, properties, calculation of triple integrals, triple integrals in Cartesian, cylindrical and spherical coordinates, applications). Line integrals and vector analysis.
2. Series – Brief review of numerical sequences. Numerical series: definition; nature of a series; properties; examples (geometric series, Dirichlet series and telescopic series); necessary condition for convergence; series of non-negative terms; comparison criteria; integral, root and ratio criteria; absolute convergence and simple convergence; alternating series, Leibniz criterion. Power series: definition; radius and interval of convergence; properties; Taylor series, Taylor series expansions.

• - Tests (90%) and class questions (10%) / Exam (100%) - 100.0%

NAO