Elements of Analysis and Algebra II
Code
8789
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Maria do Céu Cerqueira Soares
Weekly hours
6
Total hours
67
Teaching language
Português
Objectives
The student must acquire basic knowledge of numerical series and series of functions, differential and integral calculus for functions of several variables, resolution of differential equations and characterization of groups, isometries and symmetries.
Prerequisites
The student must have elementary knowledge in analysis, namely differential and integral calculus in R.
Subject matter
1. Series of real numbers, power series; Taylor expansions.
2. Functions of several real variables: continuity, differentiation and multiple integrals.
3. Ordinary differential equations (first and second order).
4. Elementary group theory. Groups of symmetries.
More detailed information is available in the Portuguese version.
Bibliography
[1] Sá, A. & Louro, B. – Sucessões e Séries, Escolar Editora, 2009.
[2] Sarrico, C. - Análise Matemática, Gradiva, 1997.
[3] Sarrico, C. - Cálculo Diferencial e Integral para funções de várias variáveis, Esfera do Caos, 2009.
[4] Monteiro, A. & Matos, I. - Álgebra, Escolar Editora, 2001.
Teaching method
In this course there are lectures (3 hours weekly) and solving-problems classes (3 hours weekly).
Students have, in advance, at their disposal a guide with all the theoretical and practical notes for classes.
There is also some office hours where each student can individually talk to and/or seek the help of the teacher.
Evaluation method
Conditions for evaluation admittance:
• for freshmen student - maximum of 3 unjustified absences to classes;
• for other students - maximum of 8 unjustified absences to classes.
Evaluation can be done through tests during classes period, or by final exam.
More details available in the portuguese version.