Mathematical Analysis II A
Code
10972
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
78
Teaching language
Português
Objectives
Intuitive and rigorous comprehension of the concepts of integral and functional convergence.
Good skills handling primitives, series and integrals.
Comprehension of the importance of Taylor’s formula in approaching functions by polynomials.
Prerequisites
Background in Análise Matemática I A.
Subject matter
1. Primitives. Primitivation by parts and by change of variables. Computation of primitives of rational, irrational and transcendent functions.
2. Integral calculus. Fundamental theorem of calculus; mean value theorem; Barrow’s formula. Computation of areas of plane figures.
3. Improper integrals. Criterea of convergence for improper integrals. Computation of areas of unbounded domains. Beta and Gamma functions.
4. Series of real numbers. Series of non negative terms. Alternate series. Absolute convergence. Products of series.
5. Series of functions. Ponctual and uniform convergence. Power series. Taylor series.
Bibliography
1 - Campos Ferreira, J. - Introdução à Análise Matemática – Edição da Fundação Calouste Gulbenkian, Lisboa
2 - Figueira, M. - Fundamentos de Análise Infinitesimal- Textos de Matemática nº 5 - Edição do Departamento de Matemática da F.C.U.L.
3 - Guerreiro, J. - Curso de Matemáticas Gerais - Escolar Editora, Lisboa
4 - Lages Lima, E. - Curso de Análise – Projecto Euclides, Rio de Janeiro
5 - Alves de Sá, A. & Louro, B. – Análise Matemática I B, C, D, E, (Departamento de Matemática da F.C.T-U.N.L.)
6 - Alves de Sá, A. & Louro, B. – Sucessões e Séries, Teoria e Prática. Escolar Editora, 2008
7 - Sarrico, C. - Análise Matemática - Gradiva, Trajectos Ciência, Lisboa 1997
Teaching method
In this course there are lectures (3 hours weekly) and practical 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 help from any teacher of the discipline.
Evaluation method
Conditions for evaluation admittance:
• for freshmen student - maximum of 4 unjustified absences to classes;
• for other students - attendence on 2/3 of classes, at least.
Evaluation can be done through tests during classes period, or by final exam.
More details available in the portuguese version.