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
Manuel Messias Rocha de Jesus
Weekly hours
5
Total hours
67
Teaching language
Português
Objectives
Elementary knowledge in agreement with the program.
Prerequisites
The student must have elementary knowledge in analysis, namely, sequences of real numbers, 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 are available in the Portuguese version, under the title Programa.
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
Theoretical lectures and practical lectures of problem-solving.
Evaluation method
There are two possible types of evaluation: evaluation by tests or by a final exam.
Evaluation by tests - this type of evaluation is more suitable for students that want to do a progressive learning and a progressive evaluation process.
This evaluation consists of 3 tests, each test with the maximum classification of 20. Only the students with more than two thirds of presences in the problem-solving sessions (aulas práticas), until the test date, are admitted.
Final results:
1. The final grade is the average of the arithmetic sum of the 3 grades obtained in each test; if the grade of the last test is not lower than 7. For a grade lower or equal to 9.4, the student is admitted to the evaluation by final exam.
2. For grades between 9.5 and 16.4, students are approved.
3. For grades above 16.5, the final grade is 16, unless the students have decided to be submitted to a supplementary evaluation to decide the final grade.
Evaluation by final exam – this type of evaluation can be used by all students that have failed in the evaluation by tests and that have more than two thirds of presences in the problem-solving sessions (aulas práticas), until the exam date.
For exam grades lower or equal to 9.4, students have failed. For exam grades above 9.5 the students are approved and the final grade is obtained by the same process described in the previous sections, points 3 and 4.
More detailed rules are available in the Portuguese version, under the title Regras de Avaliação