Cursos / 1º Ciclo / / Faculty of Economy and Business Management :: Economics
MATEMÁTICAS GERAIS - 2017/2018
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
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
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.
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 consists of two written examinations with the duration of about one hour each. 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 evaluations the students can use the scientific calculating machine.
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 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 |