Part of this Programme
Level of Qualification|Semesters|ECTS
Bachelor | Semestral | 5
Year | Type of course unit | Language
1 |Mandatory |Português
Total of Working Hours | Duration of Contact (hours)
140 | 60
Recommended complementary curricular units
Prerequisites and co-requisites
Three-dimensional Cartesian coordinates. Vectors, scalar product. Lines and planes. Cylindrical and quadric surfaces. The Euclidean space R ^ n, Euclidean metric, topological notions. Vector functions and curves in space. Limits and continuity. Differentiability, vector tangent to a curve. Integration, length of a curve. Generalities about real functions of several real variables. Curves of level. Limits and continuity. Partial derivatives, derived from higher order. Differentiability, differential, tangent planes and linear approximations. Chain rule. Implicit derivation. Directional derivative, vector gradient and its geometric interpretation. Hessian matrix, free ends and saddle points. Extremely conditioned. Double integrals. Triple integrals. Applications. Polar and cylindrical coordinates, change of variable in double and triple integrals. Numerical approximation of multiple integrals.
To confer competences in the techniques and applications of differential and integral calculus with functions of several variables. To master the concepts of limit, continuity and differentiability of functions. Master the calculation of multiple integrals. To be able to solve problems in diverse contexts using differential and integral calculus methods. To know the applications to problems of optimization, of geometric characterization of curves and surfaces and of calculation of volumes and areas. The curricular unit develops the dexterity in the calculus, the capacity of geometric analysis and the logical-mathematical reasoning. Confers skills in the use of quantitative methods in the analysis of diverse subjects. It develops the ability to solve and solve varied problems using the structured language of differential and integral calculus.
Teaching methodologies and assessment
The lecture includes lectures and practical classes. Theoretical classes are essentially expositive. The theorems are presented as well as examples and a strong appeal is made to the students' geometric intuition. In the practical classes exercises cards are solved, including exercises of application to varied areas of knowledge. In this curricular unit the continuous evaluation includes the following elements: 10 homework and a written test. The grade of the set is the arithmetic mean and corresponds to 40% of the final grade. The final compulsory attendance, to be carried out together with the examination of the first period, lasting 150 minutes, and corresponding to 60% of the final grade. The frequency note may not be less than 7,0 values. The weighting of 40% of the grades obtained in the tests will only be considered if the final grade grade is lower than that. Otherwise, the final grade will correspond only to the grade obtained in the final frequency.
Stewart, J.; Cálculo, vol. 2, 5ª ed.; Thomson Learning; 2007.
Simmons, G.F.; Cálculo com Geometria Analítica, vol. 2; Makron Books; 1987.
Apostol, T.M.; Cálculo, vol. 2, 2ª ed.; Reverté; 2004.