﻿ - TeSP - Qualidade AmbientalInstituto Politécnico de Tomar

# IPT

Ano Letivo: 2017/18

Publication in the Diário da República: Aviso nº 1804/2017 de 16/02/2017

5 ECTS; 2º Ano, 1º Semestre, 60,0 TP

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 em 22 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 em 22 de fevereiro de 2016 em http://cmup.fc.up.pt/cmup/apoiomat/manual_apoiomat_v1.pdf

Teaching Method
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.