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

Versao Portuguesa


1º curricular year
Semestralidade: 1st 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 differential calculus of functions of one and several real variables.

Skills to be acquired

By the end of the course the student should be capable of:
a) Working with functions of one and several real variables, including graph sketching and differentiation;
b) Applying his or her knowledge of differential calculus to solve practical problems. In particular, students must be able to solve optimization problems of several types.

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. Functions of one real variable

1. Functions, their graphs and symmetries
2. Limits and continuity
3. Introduction to derivatives
4. Differentiation rules
5. Differentials and marginal analysis
6. The chain rule
7. Derivatives of different orders
8. Implicit differentiation
9. Extremes and optimization
10. Characterization of functions and graph sketching

II. Functions of several real variables

1. Definitions
2. Partial derivatives
3. Differentials
4. The chain rule in several variables
5. Optimization with free variables
6. Optimization with constraints

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.



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 2014
Author Larson, Roland; Edwards, Bruce
Title Cálculo com Aplicações
Edition 6.ª ed.
Place Rio de Janeiro
Editor LTC
Year 2005
Author Sydsaeter, Knut; Hammond, Peter; Strom, Arne
Title Essential Mathematics for Economic Analysis
Edition 5.ª ed.
Place Harlow, England
Editor Pearson Education Limited
Year 2016

Complementary Bibliography

Author Chiang, Alpha C.; Wainwright, Kevin
Title Fundamental Methods of Mathematical Economics
Edition 4.ª ed.
Place International Edition
Editor McGraw-Hill
Year 2005
Author Jacques, Ian
Title Mathematics for Economics and Business
Edition 8ª ed.
Place Harlow, England
Editor Pearson Education Limited
Year 2015