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)
- Carlos Filipe Perquilhas Baptista (1)(2)
(1) Lead Professor
(2) Teaching Professor
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
Continuous assessment: two closed-book written tests, each graded from 0 to 10 points. The final grade (rounded to the nearest whole number) will be the sum of the grades from the two written tests (unrounded grades). The student is exempt from the exam if they obtain a final grade greater than or equal to 10 points and if they obtain at least 3.5 points on the first written test (the minimum grade for admission to the second written test is therefore 3.5 unrounded points).
Exam assessment: a closed-book written test, graded from 0 to 20 points, covering all taught syllabus throughout the semester. The student passes the course if, on this test, they obtain a grade greater than or equal to 10 points.
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; scientific calculating machines.
