# Mathematical Analysis I

Year
1
2019-2020
Code
01001647
Subject Area
Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
7.5
Type
Compulsory
Level
1st Cycle Studies

## Recommended Prerequisites

Secondary School Mathematics

## Teaching Methods

The theoretical lectures are mainly expositive. The tutorial lectures are used to solve problems under the guidance of the teacher. During tutorial lectures, students are encouraged to solve problems by their own. Concerning the theoretical lectures, a strong interaction between concepts and their concrete application prevails. Before a new concept is introduced in an abstract way, attention is given to the visualization and analysis of particular situations related with the new concept. The transformation of concepts into working tools will be achieved by the individual work of each student, encouraged by the teacher.

## Learning Outcomes

To provide the students with the basic knowledge of differential and integral calculus in R and give the fundamental concepts for the study of plane curves. It is intended that students acquire calculation skills. It is also intended that students acquire a critical knowledge of the concepts in such way that they understand the scope and limitations of the studied material as well as their applications.

No

## Syllabus

1.  Real functions of one real variable
1.1  Limits, continuity and derivatives
1.2  Defined Integral and applications
1.3  Improper integral
2. First order differential equations: linear differential equations and separable variables differential equations
3. Parametric equations and polar coordinates, including the study of curves in parametric equations and curves in polar coordinates.

## Bibliography

Stewart, J. Cálculo , 4ª ed., Vol 1 e Vol.2 , Pioneira, São Paulo, 2001

Carvalho e Silva, J., Princípos de Análise Matemática Aplicada, McGraw-Hill, Lisboa, 1994

Campos Ferreira, J., Introdução à Análise Matemática, Fundação Calouste Gulbenkian, 1993.