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Publication in the Diário da República: Despacho n.º 8838/2020 de 14-09-2020 + Despacho n.º 3463/2023 de 16/03/2023

6 ECTS; 1º Ano, 1º Semestre, 56,0 TP

- Rui Manuel Domingos Gonçalves
- Eugénio Manuel Carvalho Pina de Almeida
- Carla Sofia Costa Pott Larsen


The objectives of this course are the acquisition and consolidation of some fundamental knowledge about: functions, trigonometry, matrix and vector calculus and propositional logic. Learning outcomes of the course unit at the end - the student should be able to: a) recognize, operate and apply the fundamental concepts inherent to the study of kings of real variables; b) calculate the trigonometric ratios for a given acute angle of a right triangle; c) handle trigonometric formulas and apply those formulas to solve geometric problems; d) operate with matrices and use matrix techniques to solve systems of linear equations; e) operate with vectors in geometric and analytical form; f) apply vector calculus to solve some geometric problems; g) identify and use the logical operations defined between propositions and build the respective truth tables; h) use the main calculation tools of this curricular unit in the analysis, interpretation and resolution of problematic situations within the scope of the Higher Professional Technical Course in question.

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 score if it is> = 9.5 values (part of the material is evaluated). Approval: Final grade> = 9.5 points

- Larson, R. e Et al, . (2006). Cálculo. (Vol. 1). São Paulo: McGraw-Hill
- Barnett, R. e Ziegler, M. e Byleen, K. e Sobecki, D. (2011). College Algebra with Trigonometry. (Vol. 1). New York: McGraw-Hill
- M., F. e Amaral, I. (2008). Álgebra Linear -Matrizes e Determinantes. (Vol. 1). Portugal: Sílabo
- F. Paixão, J. (2020). Sebenta Matemática. IPT: UDMF- IPT

Teaching Method
Lectures with presentation of themes and problem solving. Some of the exercises are specific to the course in question. The use of calculator and free software as an aid to problem solving is permitted.

Software used in class
E-learning platform; MAFA plotter and scientific calculating machines.




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