Mathematics I

Code:

LEC103

Acronym:

MAT I

Keywords
Classification	Keyword
OFICIAL	Mathematics and Informatics

Instance: 2006/2007 - 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	371	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 - 2006/07", FEP, 2006
- 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

- Larson, Hostetler, Edwards, "Cálculo", Volume II, McGraw-Hill, 8ª edição.
- J.E. Marsden, A.J. Tromba, "Vector Calculus", W.H. Freeman and Company, San Francisco, 1976
- A. Chiang, "Fundamental Methods of Mathematical Economics", McGraw-Hill, 1984.
- A. Cerqueira, P. Vasconcelos, "Funções reais definidas em R^n", Litexa Editora

Teaching methods and learning activities

Theoretical-practical classes

Evaluation Type

Distributed evaluation with final exam

Eligibility for exams

A student will be approved if he/she obtains a final classification, according to the calculation rules described below, equal or upper to 10 values.

Calculation formula of final grade

If a student has a final classification of N upper than 18, according to the calculation rules described below, he/she should perform an improvement test so that he/she can obtain a final classification upper than 18 (according to the calculation rule described below). Otherwise, his/her final classification will be 18.

The final classification of each student is computed according to the following rules:

- If the student choose to be evaluated through the distributed evaluation rules, N = Maximum{ 0,36 * (M1+M2 +M3)/3 + 0,64 * E, E }, where M1, M2, M3 are the marks of each mini-test and E is the mark of the final exam;

- If the student choose not to be evaluated through the distributed evaluation rules, N = E, where E is the mark of the final exam;

- If N <= 18 then the final classification is N, rounded to units;

- If N > 18 then the final classification is given by 18 + PV * (N-18), rounded to units, being PV the percentage obtained in the improvement test (note that PV = 0 if the student choose not to perform the improvement test).

Observations

In what concerns the discipline evaluation, a student can not be classified according to the distributed evaluation rules if he/she did not have a classification in at least one mini-test, had a classification under 6 values in at least one mini-test or had a classification under 6 values in the final exam.