Matemática

Base Knowledge

Contents covered in Mathematics in primary and secondary education.

Teaching Methodologies

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.

Learning Results

 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 It is intended that students:

a) operate with matrices and calculate determinants in order to discuss and solve systems of linear equations using matrix representation and selecting appropriate methods;

b) deepen and extend their knowledge of real functions of real variables, in particular

  1. distinguish and characterise the behaviour of several families of functions;
  2. calculate the derivative function of a real function of real variables and, from its analysis, deduce characteristics of the function, using consistent reasoning;
  3. calculate indefinite and definite integrals of real functions of real variable, apply them to the calculation of areas of plane regions by deducing the appropriate expressions.

c) Characterise real functions of several variables and develop the appropriate concept of derivative by deducing the partial derivatives of a function of this type.

Program

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.

 

Curricular Unit Teachers

Internship(s)

NAO

Bibliography

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. J. & Reynolds, J. J. (2019). Mathematical Applications for the Management, Life, and Social Sciences (12th Ed.). Cengage.

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