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  3. Licenciatura em Sistemas e Tecnologias de Informação
  4. Análise Matemática I

Análise Matemática I

Objetivos

In this curricular unit it is intended that students develop their logical reasoning and calculation skills, essential for the learning of other curricular units of their cycle of studies. The main goals are the learning and consolidation of fundamental knowledge of Differential and Integral Calculus for real functions of a real variable.

Caracterização geral

Código

100008

Créditos

5.0

Professor responsável

Patrícia Santos Ribeiro

Horas

Semanais - A disponibilizar brevemente

Totais - A disponibilizar brevemente

Idioma de ensino

Português. No caso de existirem alunos de Erasmus, as aulas serão leccionadas em Inglês

Pré-requisitos

It is recommended the frequency of Mathematic A in secondary education.

Bibliografia

Sydsæter, K, Hammond, P., Essential Mathematics for Economic Analysis, 2nd ed., Prentice Hall, 2006.

Sarrico, Carlos, Mathematical Analysis, Readings and Exercises, Gradiva.

Azenha, A., Jerónimo, M.A., Differential and Integral Calculus Elements in IR and IRn, McGraw-Hill, 1995

Método de ensino

Aulas teóricas e aulas práticas para resolução de exercícios.

Método de avaliação

Continuous Assessment (1st period)

The continuous assessment consists of conducting, during the academic semester, 2 tests T1, T2 and a final exam E. The tests have no minimum grade.  The exam has minimum grade of 8.5.

The final grade is calculated as follows: 20%T1+20%T2+60%

If, exceptionally, it is not possible to carry out an assessment in person, there will be the possibility of do the same online followed by an oral exam, but the situation will be analyzed case by case.

Exam Assessment (only 2nd period)

Final exam (100%) (face-to-face and with minimum score of 9.5).

Conteúdo

1. The IR set 

1.1 Basic concepts. 

1.2 Topological notions. 

2. Real functions of one real variable 

2.1 Generalities about real functions of one real variable. 

2.2 Notion of limit; lateral limts, properties and operations. 

2.3 Continuous functions: definition and properties of continuous functions. 

2.4Theorems of Bolzano and Weierstrass .

3. Differential Calculus on IR 

3.1 Derivative of a function: definition of the tangent line equation. 

3.2 One-sided derivatives; differentiability; relationship between differentiability and continuity of a function; derivation rules; derivative of the composite function. 

3.3 Fundamental theorems: theorems of Rolle, Lagrange and Cauchy; Cauchy rule; indeterminate forms. 

3.4 Derivatives from the higher order; formula of Taylor and MacLaurin. 

3.5 Extremes of functions; concavity and inflection points; asymptotes; sketch graph of a function. 

4. Integral Calculus in IR 

4.1 Antiderivative: definition;

4.2 General methods to compute antiderivatives.

4.3 Integral Calculus: Riemann integral;

4.4 Fundamental theorems of integral calculus;

4.5 Calculation of areas of plane figures.