Mathematics I

Code:

LEC103

Acronym:

MAT I

Keywords
Classification	Keyword
OFICIAL	Mathematics and Informatics

Instance: 2005/2006 - 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	417	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.

Students should be able to use some rigor when exposing the subjects and to develop logic reasoning.

Program

1. Functions of several variables
1.1. Topics of topology in IRn
1.2. Graphs and level surfaces
1.3. Limits
1.4. Continuity
1.5. Partial derivatives
1.6. Diferenciability
1.7. Approximation of functions; Taylor polynomial
1.8. The chain rule
1.9. Directional derivatives
1.10. Homogeneous functions
1.11. Implicit functions
1.12. Convex and concave functions
1.13. Extrema
1.14. Extrema of implicit functions
1.15. Extrema with equality constraints; Lagrange multipliers
1.16. Extrema with inequality constraints

Main Bibliography

- M. Aguiar, J.M. Oliveira, "Texto de apoio às aulas de Matemática I - 2005/06"
- S. C. Gothen, "Estudo de funções reais de várias variáveis", apontamentos de aula, FEP, 2002.
- A. Breda, J. Costa, "Cálculo com funções de várias variáveis", McGraw-Hill, 1996
- C. Pires, "Cálculo para Economistas", McGraw-Hill, 2001

Complementary Bibliography

- J.E. Marsden, A.J. Tromba, "Vector Calculus", W.H. Freeman and Company, San Francisco, 1976
- A. Chiang, Matemática para Economistas, McGraw-Hill, 1982.
- A. Cerqueira, P. Vasconcelos, "Funções reais definidas em R^n", Litexa Editora

Teaching methods and learning activities

Theoretical-practical classes

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 ).