Part of this Programme
Level of Qualification|Semesters|ECTS
Bachelor | Semestral | 5
Year | Type of course unit | Language
2 |Mandatory |Português
Total of Working Hours | Duration of Contact (hours)
140 | 60
Recommended complementary curricular units
Prerequisites and co-requisites
Series. Definition. Convergence. Geometric and Mengoli Series, Non Negative Terms. Simple and absolute convergence. Leibniz's criterion. Series of Powers. Domain of convergence. Power series development. Taylor series. Ordinary Differential Equations. Introduction. Directional fields. Models containing order EDO 1. Growth models. Logistic models. Mixing and heating problems. Algebraic methods for the resolution of First Order Differential Equations. Separation of variables, variation of parameters. Applications of First Order Differential Equations to Engineering Problems. Differential Equations of Second Order. Algebraic and numerical methods for the solution of Second order Differential Equations. Applications of Second Order Differential Equations to Engineering Problems. Vibrating Models. Vector fields. Conservative vector fields. Curvilinear integrals. Work done by a force. Independence of the way.
Domain of the main calculation techniques in the Real Multivariate Analysis. Determine the nature of a series, determine the radius of convergence of a series of powers, calculate areas, volumes and masses. Integrate vector functions on lines and surfaces for application in the resolution of engineering problems Application of the concepts and techniques inherent to the principles of differential equations for application to the resolution of engineering problems, namely vibratory problems and others.
Knowledge, abilities and skills to be acquired
Acquiring global skills to use in solving various problems.
Teaching methodologies and assessment
In the presentation of the material, concrete examples are presented and students are invited to analyze the concepts involved in the examples, and the definitions and propositions arise naturally. Illustrative examples and counterexamples are presented. In practical classes, students are invited to analyze and solve problems involving the concepts presented in the theoretical classes. Students are encouraged to try various resolution strategies. Continuous endorsement: 2 frequencies to be carried out during the semester, the 1st with a weighting of 45% and the 2nd of 50%. The active participation of the students during the classes with a weighting of 5% will be considered. have a mean of 9.5 val and have a attendance of not less than 75% of the total number of classes provided they are not covered by special statutes / situations. End-of-term assessment: two exam periods. Students who score = or> 9.5 val in one of the periods are considered approved.
Apostol, T.M.(2004). Cálculo, vol. 1, 2ª ed.; Reverté.
Larson, R. and Hostetler, R. and Edwards, B. (2006). Cálculo, 8ªEd., McGraw-Hill.
Howard Anton (1999). Calculus, 9th Edition, John Wiley & Sons.
Piskounov, N. (1992). Cálculo Diferencial e Integral, Editora Lopes da Silva.
Simmons, G., Cálculo com Geometria Analítica, McGraw Hill.
Swokowski, Earl W., Cálculo com Geometria Analítica, volumes 1 e 2, McGraw Hill.