Matemática

Contents covered in Mathematics in primary and secondary education.

The following teaching methodologies are used in this curricular unit:

1) Verbal methods (say), making use of the following educational resources: Exposition, Explanation, Dialogue and questioning;

2) Intuitive Methodologies (show), making use of the following educational resources: Demo, Audiovisual, written texts;

3) Active Methodologies (doing), making use of pedagogical resources: problem solving; technology.

 Being an instrumental course unit it is intended to develop in students a set of interpretation, calculation and relational skills associated with mathematical content relevant to the acquisition of knowledge and skills in other curricular units.

In particular, students should be able to

a) operate with matrices and calculate determinants;

b) represent matrices, discuss and solve systems of linear equations using appropriate methods;

c) identify and characterize different types of families of real functions of real variable, analytically and graphically.

d) calculate and analyze the derivative function and deduce characteristics of the function, using consistent reasoning;

e) calculate indefinite and definite integrals, using immediate primitivization and primitivization methods;

f) Deduce the value of the area of a flat region by applying definite integrals.

g) characterize functions of several variables, develop the notion of appropriate derivative and calculate partial derivatives.

1. Matrices and Systems of linear equations:Matrices: definition and algebraic operations; Gauss elimination method; Determinants; Cramer’s rule; Inverse matrix and the Gauss-Jordan method.

2.Real functions of a real variable: Introduction; Injective, surjective and Bijective function; inverse function; Main types of functions and their characterization; Equations involving exponentials and logarithms.

3. Functions of several variables: Functions of several variables; Partial derivatives: basic rules, second derivatives and optimization.

4. Differential calculus: Limits and continuity; Slope of a non-linear function; Differentiability and continuity, derivation rules, higher order derivatives;

5. Integral Calculus: Indefinite integral: rules for calculation; Definite integral: Fundamental Theorem of Calculus and properties; Integration by substitution, integration by parts and integration of rational fractions.

NAO

Adams, R. A. (2013). Calculus: a complete course (8th ed.). Prentice Hall.

Anton, H., Bivens, I., & Stephen, D. (2014). Cálculo, Vol. I (10ª ed.). Bookman.

Anton, H., Rorres, C. (2013). Elementary Linear Algebra with Application (11th Ed.). Wiley.

Campos Ferreira, J. (2014). Introdução à Análise Matemática (11ª ed.), F. Calouste Gulbenkian.

Dowling, E. T. (2009). Mathematical Methods for Business and Economics, Mc Graw Hill.

Harshbarger, R., Reynolds, J. (2006). Matemática Aplicada: Administração, Economia e Ciências Sociais e Biológicas, 7.ª edição. McGraw Hill.

Stewart, J., Clegg, D.C., & Watson (2021). Calculus: Early Transcendentals, Metric Edition (9th ed.). Cengage.

Khan Academy Portugal: Matemática. https://pt-pt.khanacademy.org/math/