Mathematics I

Code:

LGE101

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:	Business Administration

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
GES	199	Official Curricular Structure since 2004	1	3		-

Objectives

It is aimed that the student will acquire the competence of doing the complete study of real functions of several real variables.
The developing of the student's geometrical way of thinking is also a goal to achieve.

Program

Real functions of several real functions:
1. Graphs and domain
2. Limits and Continuity
3. Partial derivatives; differentiable functions; gradient; tangent plane
4. Differentiability; appoximation of functions (differential of a function, Taylor formula); chain rule
5. Homogeneous functions
6. Theorem of the implicit function.
7. Maxima and minina: extrema of functions
8. Lagrange multipliers

Main Bibliography

A. Cerqueira e P. Vasconcelos,
"Funções Reais Definidas em IRn : Exercícios e Aplicações",
Litexa, 1997.
S. Castro Gothen,
"Estudo de Funções de Várias Variáveis",
Apontamentos de aula, FEP, 2002.

Complementary Bibliography

J.E. Marsden e A.J. Tromba,
"Vector Calculus",
W.H. Freeman and Company, San Francisco, 1976.
C. Pires,
"Cálculo para Economistas",
Mc-Graw-Hill, Lisboa, 2001.

Teaching methods and learning activities

Mixed type of lectures: the lecturer presents the topics - concepts and theory - and solves practical exercises.

Evaluation Type

Observations

The mathematical materials studied at school before entering in the university are considered prerequisites