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  5. Elements of Analysis and Algebra II

Elements of Analysis and Algebra II

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.

General characterization

Code

8789

Credits

6.0

Responsible teacher

Fábio Augusto da Costa Carvalho Chalub

Hours

Weekly - 5

Total - 67

Teaching language

Português

Prerequisites

The student must have elementary knowledge in analysis, namely differential and integral calculus in R.

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. 

Evaluation method

Details available in the portuguese version.

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.