Cursos / 1º Ciclo / Faculty of Economy and Business Management :: Economics

Versao Portuguesa


1º curricular year
Semestralidade: 2nd semester


Leading Teacher: Prof. Doutor Paulo Aguiar
Assistant Professor: Prof. Doutor Paulo Aguiar

Class type and School hours

Orientação Tutorial : 1 Horas
Teórico-prática : 2 Horas

Main Aims/Objectives

We aim at:
a) Equipping the students with the mathematical techniques and concepts that are indispensable for the understanding of the subjects treated in other courses of the degree;
b) Promoting the necessary skills to use mathematics in an effective manner in order to solve "real problems";
c) Promoting the development of reasoning and problem solution skills in general.

Specific Aims/Objectives

We aim at equipping the students with the elementary concepts and techniques of integral calculus in one and two variables, matrix algebra and determinants and with the necessary tools to classify and solve systems of linear equations.

Skills to be acquired

By the end of the course the student should be capable of:
a) Solving integrals in one variables using several methods and applying this knowledge to practical problems;
b) Solving integrals in several variables;
c) Performing the operations of matrix algebra;
d) Finding matrix determinans;
e) Finding inverse matrices;
f) Using determinants to classify systems of linear equations;
g) Solving systems of linear equations using several methods.

Teaching Procedures

The contents are presented following an expository methodology. When appropriate, texts are made available that further develop the subjects. The student is presented with problems that he or she must solve, being assisted during the tutorials.


I. Integral calculus

1. Primitives and indefinite integrals
2. Chain rule and change of variables in integration
3. Integration by parts
4. Area and the fundamental theorem of calculus
5. Other application of integrals
6. Improper integrals
7. Double integrals and applications

II. Matrices and systems of linear equations

1. Matrices
2. Matrix algebra
3. Homogeneous linear equations and elimination
4. Operations in lines and Gaussian elimination
5. Elementary matrices
6. Application to the calculation of the inverse matrix

III. Determinants

1. Determinants of order 2
2. Determinants of order 3 and higher
3. Some results on inverse matrices
4. Cramer´s rule

Evaluation Type

The continuous assessment consists of two written examinations each with the duration of about one hour and half. The first one covers the first half of the course contents and takes place approximately half way through the semester and the second one covers the second half of the course contents and takes place towards the end of the semester.

Teaching Resources

The didactic resources that should be available to the students are the books in the course bibliography and room for study, individually and in small groups.
In the assessment students will be able to use scientific and non-graphing calculators.


Linear Algebra

Main Bibliography

Author Hoffmann, Laurence; Bradley, Gerald; Sobecki, Davi
Title Cálculo: Um Curso Moderno e Suas Aplicações
Edition 11.ª ed.
Place Rio de Janeiro
Editor LTC
Year 2015
Author Lay, David C.
Title Álgebra Linear e Suas Aplicações
Edition 4.ª ed.
Place Rio de Janeiro
Editor LTC
Year 2013
Author Sydsaeter, Knut; Hammond, Peter; Strom, Arne
Title Essential Mathematics for Economic Analysis
Edition 5. ed.
Place Harlow, England
Editor Pearson Education Limited
Year 2016

Complementary Bibliography

Author Lang, Serge
Title Introduction to Linear Algebra
Edition 2.ª ed.
Place New York
Editor Springer
Year 2012
Author Larson, Roland; Edwards, Bruce
Title Cálculo com Aplicações
Edition 6.ª ed.
Place Rio de Janeiro
Editor LTC
Year 2005