Mathematics

TeSP - Animação e Modelação 3D, Publication in the Diário da República - Aviso n.º 11775/2016 - 27/09/2016

5 ECTS; 1º Ano, 1º Semestre, 60,0 TP

Lecturer
- Rui Manuel Domingos Gonçalves
- Eugénio Manuel Carvalho Pina de Almeida

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
- Larson, L. (2006). Cálculo . (Vol. vol 1). S. Paulo: Mc Graw-Hill
- Almeida, E. (2020). Apontamentos e exercícios de Matemática. IPT: UDMF-ESTT-IPT

Method of interaction
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