# 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