Part of this Programme
Industrial Engineering and Management.
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
Real functions of real variable. Trigonometric and inverse trigonometric functions. Generalities about real functions of real variable. Elementary functions and composition of functions. Composite and inverse function. Limits and continuity of functions. Bolzano's theorem. Derivative and differential of a function. Geometric interpretation. Derivation rules. Derivative of the compound function and the inverse function. Derived from implicitly defined functions. Cauchy's Rule. Complete study of functions. Calculation integral in IR. Meaning of primitive. Primitivation techniques (immediate, parts, powers of trigonometric functions, rational functions, by substitution). Definition of integral of Riemann. Properties of integral. Criteria for integrability. The fundamental theorem of integral calculus. Average value theorem for definite integrals Applications of the integral: Calculation of areas of flat surfaces, lengths of flat lines and volumes of solids of revolution. Integral integrals.
Mastering of the main calculation techniques in the real analysis. To allow a greater knowledge of the concepts of limit, continuity, derivative, primitive and integral and of the relation between these concepts. Application of concepts and techniques to solve engineering problems.
Knowledge, abilities and skills to be acquired
Acquisition of competences to use the differential and integral calculus in solving various problems.
Teaching methodologies and assessment
In the presentation of the subject concrete examples are presented and the 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 the practical classes, the 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 assessment: two frequencies to be carried out during the semester, the first with a weighting of 45% and the second of 50%. The active participation of the students during classes will be considered with a weighting of 5%. Students who obtain an average of 9.5 val higher or higher and who attend at least 75% of the total number of classes are considered approved. Final evaluation: two examination periods. Students who obtain a grade of 9.5 or higher 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.