Análise Matemática I - F+EF+EB

Ano letivo: 2011-2012
Specification sheet

Specific details
course codecycle os studiesacademic semestercredits ECTSteaching language

Learning goals

Provide students with the basic knowledge of Differential and Integral Calculus in real as well as of the essential concepts in the study of flat curves and basic differential equations. Students are expected to acquire knowledge of the concepts that allow them to assess the range and limitations of the subjects that are studied and their applications.


Real functions of a real variable.

Limit, continuity and derivative.

Definite integral and applications.

Improper Integral.

First Order Differential Equations: separable and linear variables.

Parametric equations and polar coordinates (includes curves study).


Mathematics of the 12th year of high school.

Generic skills to reach
. Competence in analysis and synthesis;
. Competence to solve problems;
. Critical thinking;
. Competence in autonomous learning;
. Competence in organization and planning;
. Competence in oral and written communication;
. Competence in applying theoretical knowledge in practice;
. Self-criticism and self-evaluation;
(by decreasing order of importance)
Teaching hours per semester
theory-practical classes45
total of teaching hours90

Problem solving0<50 %
Mini tests0<50 %
Assessment Tests0<100 %
Exam0<100 %
assessment implementation in 20112012
Isabel Maria Narra de Figueiredo

Bibliography of reference

STEWART, J. (2001). Cálculo. 4ª ed. São Paulo: Pioneira. Vol 1 e Vol.2.

CARVALHO e SILVA, J. (1994). Princípos de Análise Matemática Aplicada. Lisboa: McGraw-Hill.

FERREIRA, Campos J. (1993). Introdução à Análise Matemática. Fund. Calouste Gulbkenkian.

Teaching method

In the theoretical classes the essential concepts will be presented. The theoretical and practical classes are intended to solve problems under the supervision of the teacher. The autonomous resolution of problems will be encouraged. As far as the theoretical lecturing is concerned, a strong interaction will be prevailed, as much as possible, between the concepts and their concrete application, giving a central role to the visualization and analysis of specific situations before carrying out a gradual abstraction of the notions to be presented.  

Resources used