Publication in the Diário da República: Despacho n.º 11230/2020 de 13/11/2020 + Despacho n.º 7089/2023 de 03/07/2023
7 ECTS; 1º Ano, 1º Semestre, 30,0 T + 30,0 TP + 2,0 OT , Cód. 61211.
Lecturer
- Rui Manuel Domingos Gonçalves (1)(2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Not applicable
Objectives
The objectives of this class are to acquire and consolidate fundamental knowledge of functions, trigonometry, matrix and vector calculus, derivatives of functions, and complex numbers. Upon completion of this course, students should be able to:
a) recognize, operate, and apply the fundamental concepts inherent in the study of real-valued functions of one real variable; b) identify some applications of differential calculus; c) calculate the trigonometric ratios of a given acute angle of a right triangle and identify the values ??of the trigonometric ratios at particular angles; d) use the trigonometric circle and identify its applications; e) manipulate trigonometric formulas and apply these formulas to solve geometric problems; f) operate with matrices and vectors in matrix form; use matrix techniques to solve systems of linear equations; g) operate with vectors in geometric and analytical forms; h) apply vector calculus to solve some geometric problems; i) represent and operate with complex numbers in trigonometric and algebraic forms; j) use the main calculation tools of this discipline in the analysis, interpretation and resolution of problem situations within the scope of the Higher Professional Technical Course in question.
Program
1. Functions
1.1. Sequences
1.1.1 Concept of Sequence
1.1.2 Arithmetic progressions and geometric progressions: general term and sum of the first n terms
1.2 Real functions of one variable
1.2.1 Definitions, graphs, 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; sin, cos, tan, and cot of an angle
3. Matrix calculus
3.1. General notions
3.2. Operations on matrices
3.3. Application of matrices to solving systems of linear equations - Gaussian elimination method
3.4 Vectors Operations between Vectors
4 Complex Numbers
4.1. Definition; Algebraic and Trigonometric Form
4.2. Geometric Representation
4.3. Operations with Complex Numbers
Evaluation Methodology
Continuous Assessment - Tests: Two written exams worth 0-20 points (weighted 50% each). Students are exempt from the exam if they obtain >= 9.5 points in the continuous assessment.
Bibliography
- Armstrong, B. e Davis, D. (2002). College Mathematics, Solving problems in finite mathematics and calculus. New York: Pearson Education
- Barnett, R. e Ziegler, M. e Byleen, K. e Sobecki, D. (2011). College Algebra with Trigonometry. New York: McGraw-Hill
- F. Paixão, J. (2020). Sebenta Matemática. IPT: UDMF- IPT
- Ferreira, M. e Amaral, I. (2006). Álgebra Linear 1º Vol. Matrizes e Determinantes. (Vol. 1º Vol.). Portugal: Edições Sílabo
- Larson et al., R. (2006). Cálculo Vol.I. São Paulo: McGraw-Hill
Teaching Method
In-person classes with topic presentations and exercise solutions. Some exercises are specific to the course in question. Calculators and free software are permitted for problem-solving purposes.
Software used in class
e-learning platform; MAFA plotter
