Mathematical Analysis I A
Objectives
Available soon
General characterization
Code
10969
Credits
9.0
Responsible teacher
Oleksiy Karlovych
Hours
Weekly - 6
Total - Available soon
Teaching language
Português
Prerequisites
Available soon
Bibliography
Campos Ferreira, J. - Introdução à Análise Matemática, Fundação Calouste Gulbenkian, 1982.
Demidovitch, B. - Problemas e exercícios de análise matemática, Mir, Moscovo, 1987 (ou qualquer outra edição).
Elon Lages Lima - Curso de Análise - Projeto Euclides, Rio de Janeiro, 1989.
Figueira, M. - Fundamentos de Análise Infinitesimal, Textos de Matemática, vol. 5, Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, 1996.
Santos, J.P. - Cálculo numa variável real, IST Press, 2012.
Sarrico, C. - Análise Matemática, Leitura e Exercícios, Gradiva, 1997.
Teaching method
Available soon
Evaluation method
Available soon
Subject matter
1. Real numbers. Topological notions in IR. Mathematical induction.
2. Sequences of real numbers: Limits. Infinite limits. Limits at infinity. Monotone sequences. Convergent sequences. Subsequences. Upper limit and lower limit. Cauchy sequence. Completeness of IR.
3. Single real variable functions: limits and continuity. Properties of continuous functions; Bolzano’s theorem. Weierstrass theorem. Uniform continuity. Lispschitz continuous functions. Cantor’s theorem.
4. Differential calculus: Derivatives, physical and geometric interpretations and properties. Fundamental theorems: Rolle, Darboux, Lagrange and Cauchy. Cauchy rule. Taylor’s formula and applications. Extrema, concavity and inflection points.