General Mathematics

Recommended Prerequisites

Mathematics A from the Portuguese High School Curriculum.   

Teaching Methods

Classes are theoretical and theoretical-practical. Teaching methods are predominantly expository in theoretical components. In the practical components, problems are solved under the guidance of the teacher. In the exhibition, a strong interaction prevails between the concepts and their concrete application, giving a central role to the visualization and analysis of particular situations. The use of technologies in the classroom is promoted, namely symbolic and graphic computing software, as it is understood that these tools facilitate the understanding of the various concepts.

Learning Outcomes

The aim of this curricular unit is to strengthen students' mathematical bases, namely in the knowledge and treatment of functions of 1 and 2 variables, and in differential and integral calculus. These concepts will be fundamental in subsequent units of the course and it is essential to ensure that all students have an adequate level of knowledge in this area. It is also intended to develop critical thinking and the ability to interpret real problems, through an applied approach, considering the specific course in which it is inserted. The use of technological tools in the classroom is encouraged, namely symbolic and graphical computing software, promoting the ability to learn and explore independently.

Work Placement(s)

No

Syllabus

I. Real functions of real variable

I.1 Trigonometric functions and their inverses

I.2 Exponential function and logarithm

I.3 Limits and continuity of real functions of a real variable

I.4 Functions of 2 variables

I.4 Applications to practical problems

II Differential Calculus

II.1 First derivative of a function and derivatives of higher orders

II.2 Derivatives of Functions of Two Variables - Partial Differentiation, Derivation Rules and Directional Derivatives

II.3 Applications to determination of maxima and minima and optimization problems

III Integral calculus

III.1 Primitive of a function

III.2 Definite integral and improper integrals

III.3 Double integral

III.4 Applications to practical problems of calculating the length of a curve, areas and volumes.

Head Lecturer(s)

Stéphane Louis Clain

Assessment Methods

Assessment
2 mid-term exams: 100.0%

Bibliography

[1] James Stewart: Cálculo, Volumes I e II., Cengage Learning, (tradução da 8ª edição norte-americana) 2017.

[2] Jaime Carvalho e Silva: Princípos de Análise Matemática Aplicada, McGraw-Hill, Lisboa (1994).

[3] Earl W. Swokowski, Cálculo com geometria analítica Vol I e Vol II, Makron Books (1995).

[4] Ana d'Azevedo Breda, Joana Nunes da Costa: Cálculo com funções de várias variáveis. McGraw-Hill, Lisboa (1996).