Mathematics I

Code:

LEC103

Acronym:

MAT I

Keywords
Classification	Keyword
OFICIAL	Mathematics and Informatics

Instance: 2004/2005 - 1S

Active?	Yes
Responsible unit:	Matematics and Informatics Group
Course/CS Responsible:	ECONOMICS

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
ECO	469	Official Curricular Structure since 2004	1	3		-

Objectives

The students should understand the main definitions and results, be able to relate them and apply them to practical and theoretical problems.

Program

1. Indefinite integrals
1.1. Definition
1.2. Properties
1.3. Techniques of integration: integration by parts and by substitution
1.4. Integration of rational functions
2. Definite integrals
2.1. Definition
2.2. Properties
2.3. The average value of a function
2.4. The definite integral as a function of the upper limit
2.5. The fundamental Theorem of Calculus
2.6. Integration by parts and by substitution
2.7. Areas
2.8. Integral definido de funções seccionalmente contínuas
3. Improper integrals
3.1. Definition
3.2. Tests of convergence
4. Functions of several variables
4.1. Topics of topology in IRn
4.2. Graphs and level surfaces
4.3. Limits
4.4. Continuity
4.5. Partial derivatives
4.6. Diferenciability
4.7. The chain rule
4.8. Directional derivatives
4.9. Homogeneous functions
4.10. Aproximation of functions; Taylor polynomial

Main Bibliography

F. Durão, Lições de Matemática: funções contínuas e deriváveis, séries, integral indefinido e integral definido; Manuais da Universidade Portucalense, 1991.
S. C. Gothen, Estudo de funções reais de várias variáveis, apontamentos de aula, FEP, 2002.
J. Stewart, Calculus, Brooks/Cole, ,1999.

Complementary Bibliography

Chiang, "Fundamental Methods of Mathematical Economics", McGraw-Hill, 1984.
N. Piskounov, Cálculo Diferencial e Integral, Lopes da Silva Editora, 1977.

Teaching methods and learning activities

Theoretic-pratical classes

Software

Maple

Evaluation Type

Calculation formula of final grade

The best of the following marks (regular season):
-- exam mark or average of the test marks
-- 4/5*(exam mark or average of the test marks)+ 1/5*(average of the short-test marks ).