**TeSP - Instalações Elétricas e Manutenção Industrial**

5 ECTS; 1º Ano, 2º Semestre, 60,0 TP

**Lecturer**

**Prerequisites**

**Objectives**

a) Retrieve and consolidate knowledge of numbers and algebra;

b ) Acquire knowledge on succession and functions at the secondary level;

c ) Use mathematical skills in problem solving and reality interpretation.

**Program**

1. Numbers and Elementary Algebra

1.1. natural numbers, integers, rational and real - concepts and operative rules;

1.2. Polynomials - factoring polynomials, notable cases of multiplication, integer division of polynomials and simplifying algebraic expressions;

1.3. Equations and inequalities - solving equations and polynomials inequalities and modules, ratios, proportions and percentages.

2. Succession and real functions of real variable

2.1. Overview of numerical sequences;

2.2. monotonous succession and inheritance limited;

2.3. arithmetic progressions and geometric progressions;

2.4. Convergence of a succession - limits, benchmarks and algebra limits;

2.5. Overview of real functions of real variable;

2.6. Limits and continuity of functions;

2.7. Derivative of a function - derivative of a function at a point, geometric interpretation of the derivative; calculating derived using the definition;

2.8. algebraic and transcendental functions.

**Evaluation Methodology**

Two written tests , without consultation, on each of the chapters , with a weight of 75 % . Work group developed in the last five weeks of the semester , with a 25 % weight. The final mark ( continuous evaluation ) is the rounded weighted average.

**Bibliography**

- Sá, A. (2012). *Introdução ao Cálculo*. Lisboa: Escolar Editora

- Educação e Ciência, M. (0). *Manuais recentes de Matemática do Ensino Secundário*.Acedido em22 de fevereiro de 2016 em http://www.dge.mec.pt/sites/default/files/ManuaisEscolares/lista_manuais_disponiveis_2015_2016_ensino_secundario.pdf

- Tavares, J. (0). *Temas de Matemática Elementar*.Acedido em22 de fevereiro de 2016 em http://cmup.fc.up.pt/cmup/apoiomat/manual_apoiomat_v1.pdf

**Method of interaction**

The fundamental principles are transmitted , being described and exemplified their applications . Students are instructed in the use , criticism, analysis and interpretation of principles and calculation methods used and not using calculator.

**Software used in class**

Excel and Wolframalpha online.