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 , Cód. 61422.
Lecturer
- Paula Cristina Miguel da Silva (2)
- Eugénio Manuel Carvalho Pina de Almeida (1)(2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Objectives
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.
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, graphs, properties and applications
1.2.2 Polynomial functions and rational functions
1.2.3 Exponential and logarithmic functions
1.2.4 Derivatives of a function
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; sin, cos, tg and cotg of an angle.
3. Vectors. Operations with vectors.
3.1 General notions
3.2 Operations with Vectors
3.2.1 Adding and Subtracting Vectors
3.2.2 Multiplying a Vector by a Scalar
3.2.3 Scalar product of vectors
3.2.4 Angle between two vectors
4. Matrix calculation
4.1 General notions
4.2. Operations on matrices
4.2.1 Addition and subtraction of matrices
4.2.2 Multiplying a scalar by a matrix
4.2.3 Matrix multiplication
4.2.4 Matrix Potentisation
4.2.5 Transposed Matrix
4.3 Application of matrices to solving systems of linear equations - Gauss elimination method
4.3.1 Systems of linear equations. Classification of systems of linear equations.
4.3.2 Gauss Elimination Method
5 Introduction to propositional logic
5.1 Propositions and logical operators on propositions
5.2 Truth tables
5.3 DeMorgan's Laws
Evaluation Methodology
Rating: 0 to 20 values.
Final approval with a minimum of 10 values
Minimum grade for admission to the 2nd frequency: 7.0 values
Evaluation:
1. Continuous assessment: two written tests containing development problems and questions; 1st frequency in the middle of the semester and 2nd frequency at the end of the semester with a weighting of 50% each, for the final grade.
2. Final written test for the student who has not been approved in continuous assessment (or who wants to improve the grade) in the Exam and/or Appeal Exam, with a weighting of 100% for the final grade.
Bibliography
- Barnett, R. e Ziegler, M. e Byleen, K. e Sobecki, D. (2011). College Algebra with Trigonometry. (Vol. 1). New York: McGraw-Hill
- Larson, R. e Et al, . (2006). Cálculo. (Vol. 1). São Paulo: McGraw-Hill
- M., F. e Amaral, I. (2008). Álgebra Linear -Matrizes e Determinantes. (Vol. 1). Portugal: Sílabo
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.
