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

Versao Portuguesa

MATEMÁTICAS GERAIS - 2021/2022

1º curricular year
Semestralidade: 1st semester
ECTS: 6

Teachers

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

Teaching Language

Portuguese

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

It is intended that students acquire the basic concepts and techniques of the differential calculation of one and several variables and optimize functions with one and two 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.

Programme

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 is based on 2 written tests each containing complementary parts of the program. If the written tests are to be carried out online on the Moodle platform, students who obtain a grade higher than 14.0 on the online platform will need to take an oral test that will more accurately assess their knowledge. Those who do not need this oral exam will get 14 in this exam. Each test will last for 1 hour.

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.
The proposed exercises and other relevant content will be placed on the Moodle platform. This platform may come to be used in online examinations.
In the assessment students will be able to use scientific and non-graphing calculators.

Sustainability Objectives

Keywords

Mathematics
Calculus
Functions
Optimization

Main Bibliography

Author Hoffmann, Laurence; Bradley, Gerald; Sobecki, Davi
Title Cálculo: Um Curso Moderno e suas Aplicações
Edition 11.ª edição
Place Rio de Janeiro
Editor LTC
Year 2015
Author Larson, Roland; Edwards, Bruce
Title Cálculo com Aplicações
Edition 6.ª edição
Place Rio de Janeiro
Editor LTC
Year 2005
Author Sydsaeter, Knut; Hammond, Peter; Strom, Arne
Title Essential Mathematics for Economic Analysis
Edition 5.ª edição
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 edição
Place International Edition
Editor McGraw-Hill
Year 2005
Author Jacques, Ian
Title Mathematics for Economics and Business
Edition 8ª edição
Place Harlow, England
Editor Pearson Education Limited
Year 2015