Mathematical Analysis I

Recommended Prerequisites

High School Mathematics.

Teaching Methods

The theoretical lectures are predominantly expository. In practical classes the students will solve exercises under the guidance of the instructor. In the theoretical classes it will prevail a strong interaction between concepts and their practical application, giving, as much as possible, a central role to visualization and analysis of particular situations before making a progressive approach to more abstract notions. The transformation of concepts into working tools will be achieved by encouraging personal work. The formal lectures will be complemented by periods of individual attendance.

Learning Outcomes

To provide students with basic knowledge of differential and integral calculus for real functions as well as the fundamental concepts in the study curves in the plan. It is intended that the students acquire computational skills, and abilities to solve first order differential equations. It is also intended that the students acquire an understanding of the concepts that will enable them to evaluate the scope and limitations of the materials studied and their applications.

Work Placement(s)

No

Syllabus

Functions of one real variable

    Limits, continuity and derivatives

    The definite integral and its applications

    Improper integrals

First order differential equations (separable variables and linear differential equations) and applications Parametric equations and polar coordinates (study of curves).

Head Lecturer(s)

Isabel Maria Narra de Figueiredo

Assessment Methods

Continuous
Continuous evaluation is done throughout the semester amd may consist of tests, quizzes or homework. The weight of each of these components for the final classification depends on the material under evaluation. Those students who obtain a grade higher or equal to 10 (out of 20) are exempted from the exams.: 100.0%

Final assessment
The final evaluation requires an exam quoted for 20.: 100.0%

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, Fund. Calouste

Gulbkenkian 1993.