Publication in the Diário da República: Aviso n.º 11775/2016 - 27/09/2016
5 ECTS; 1º Ano, 1º Semestre, 60,0 TP , Cód. 62402.
Lecturer
- Rui Manuel Domingos Gonçalves (2)
- Eugénio Manuel Carvalho Pina de Almeida (2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Knowledge of Mathematics in Secondary Education
Objectives
The objectives of this course are the acquisition and consolidation of some knowledge
fundamentals about: functions, trigonometry, matrix and vector calculus and propositional logic.
At the end of this course unit the student should be able to: a) recognize, operate and apply the
fundamental concepts inherent to the study of kings functions of real variable; b) calculate the
trigonometric ratios for a given acute angle of a right triangle; ç)
handle trigonometric formulas and apply those formulas to solve problems
geometric; d) operate with matrices and use matrix techniques in the resolution of information systems
linear equations; e) operate with vectors in geometric and analytical form; f) apply the calculation
vectorial to solve some geometric problems; g) identify and use operations
logic defined between propositions and building the respective truth tables; h) use the
main calculation tools of this course
Program
1. Functions
1.1. Successions
1.1.1 Concept of Succession
1.1.2 Arithmetic and geometric progressions: general term and sum of the first n terms
1.2 Real variable functions
1.2.1 Definitions, graphics, properties and applications
1.2.2. Polynomial functions and rational functions
1.2.3. Functions; exponential and logarithmic
2. Trigonometry
2.1. Trigonometric ratios of acute angles
2.2. Values of trigonometric ratios at particular angles
2.3. Trigonometric circle and its applications
2.4 Trigonometric functions; sen, cos, tg and cotg from an angle.
3. Matrix calculation
3.1. General notions
3.2. Matrix operations
3.3. Application of matrices to the resolution of systems of linear equations - Gaussian elimination method
3.4 Vectors. Operations between vectors.
4 Introduction to propositional logic
4.1. Propositions and logical operators about propositions
4.2. Truth Tables
4.3. DeMorgan Laws
Evaluation Methodology
Continuous assessment - Frequency: two tests 0-20 points (50% each). You can repeat the Exam:
written test 0-20 val. or you can carry a test note as long as it is> = 9.5 values
(part of the material is evaluated). Approval: Final grade> = 9.5 points
Bibliography
- Almeida, E. (2020). Apontamentos e exercícios de Matemática. IPT: UDMF-ESTT-IPT
- Larson, L. (2006). Cálculo . (Vol. vol 1). S. Paulo: Mc Graw-Hill
Teaching Method
Face-to-face classes with exposure of topics and resolution of exercises. Some of the exercises
are specific to the course in question. The use of a calculator and free software such as
problem solving aid
Software used in class
https://pt.symbolab.com/solver/functions-calculator
